Cross-Cultural Tourism Behaviourconcepts and analysis

Yvette Reisinger, PhD and Lindsay W. Turner, PhD

CONTENTS

Hypothesis testing for cross-cultural comparison

1 Introduction to parametric and non-parametric hypothesis testing

2 The hypothesis test

3 Parametric hypothesis test

3.1 When to use z and t-tests

3.2 One- and two-tailed tests

3.3 One-sample means test example

3.4 Type I and Type II errors

3.5 Two-sample means test

3.6 Unpaired test

3.7 Paired sample test

3.8 Hypothesis interpretation

4 Introduction to non-parametric hypothesis testing

4.1 One-sample non-parametric test

4.2 Paired two-sample non-parametric test

4.3 Unpaired two-sample non-parametric test

4.4 Multiple paired sample test

4.5 Multiple unpaired sample test

5 Cross-cultural behaviour: example analysis

Summary

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Discussion points and questions

References and further reading

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Additional references

Glossary

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Hypothesis testing for cross-cultural comparison

OBJECTIVES: After completing this text the reader should be able to:

1. understand the difference between parametric and non-parametric hypotheses tests

2. conduct one- and two-sample parametric hypotheses tests

3. conduct a range of non-parametric hypotheses tests

4. understand the application of hypothesis testing to cultural tourism analysis

1. Introduction to parametric and non-parametric hypothesis testing

Statistical inference procedures enable researchers to determine, in terms of probability,

whether the observed differences between sample data could easily occur by chance or not.

Whenever random data is collected – usually in tourism this is by some type of survey –

there are likely to be some differences between the survey data and the general population

at large or between different samples. For example, a comparison of the average age (the

sample statistic) between Japanese tourists to Hawaii and the average age of the resident

population of Hawaii is likely to be different. The questions these methods answer is

whether the difference is simply due to chance because a sample of Japanese tourists was

surveyed, or whether it is highly probable that the difference is real. Of course, if the

Japanese tourists were not surveyed because we already knew, perhaps from official

immigration records, the real average age of the population of Japanese tourists (population

parameter), as well as the real average age of the resident population, then the issue of

chance variation from sampling does not arise. In such a case, the comparison is direct and

accurate and the degree of difference is the known non-probable degree of difference. As

such, we no longer need to test for the probability of a difference and we no longer need to

construct an hypothesis test to measure the probability of there being a likely difference.

Since social scientists are commonly dealing with surveyed data, the need for constructing

hypothesis tests to test the difference between means is common. Many statistical texts deal

with this material, along with the concepts of probability and probability distributions (an

understanding of which is needed to use the following material). Here we use this

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opportunity to place the testing of hypotheses into a tourism example framework, describe

the major issues of hypothesis testing facing the tourism cultural researcher, and provide an

example of hypothesis testing in tourism culture research. Further research and a more

complex methodology can be found in our book Cross-Cultural Tourism Behaviour:

concepts and analysis (2003) published by Elsevier Science Ltd.

Before beginning this discussion it is both interesting and important to discuss the

difference between parametric and non-parametric analysis because this leads to a major

decision choice for the researcher – whether to use a parametric or non-parametric

hypothesis test. In the development of modern statistics the first methods developed made a

lot of assumptions about the characteristics of the population from which the samples were

drawn. That is, they made assumptions about the statistical values of the population (called

parameters), which became referred to as parametric tests. The most obvious assumption is

that the scores in the survey were randomly drawn from a normally distributed population.

Another less well-known assumption is that the scores are randomly drawn from

populations having the same variance (standard deviation squared), or spread of scores.

These assumptions make the general overriding assumption that the probability distribution

of the population (from which the sample was drawn) is known in advance. The most

common distribution assumed is the normal distribution.

More recently, distribution free or non-parametric tests have been developed and

subsequently commonly used. These tests have fewer qualifications and in particular do not

have the overriding assumption of a normally distributed population base.

In quantitative terms the difference rests upon the way in which the scores are manipulated.

In parametric tests the scores are added, divided and multiplied and these processes

introduce distortions to the scores so that tests upon the data must use methods assuming a

truly numeric distribution. On the other hand, many non-parametric tests manipulate the

data by ranking and thus avoid the numeric value of the scores themselves. Such tests then

summarize the scores by creating summary statistics (statistics come from samples) that are

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derived physically such as the mode, or the median (where the data is ranked), instead of

the mean (which involves addition and division).

In this text we will look at both types of hypothesis tests (parametric and non-parametric)

and describe their calculation and use. Particular attention will be given to the often under-

used non-parametric tests because data that is culture-based is quite likely to not have a

normal distribution on which to base parametric data manipulations.

2. The hypothesis test

The hypothesis test comprises two mutually exclusive statements, the alternative and the

null hypotheses. The null hypothesis states the negative case, that ‘it is not true or there is

no difference’, and the alternative hypothesis states that ‘it is true or there is a difference’.

The procedure involved is a scientific one that is founded in simple logic for the purpose

of being both open and potentially repetitive (can be replicated by others).

The following steps outline the hypothesis testing procedure.

1. State the null (Ho) and alternative (H1) hypotheses.

2. Choose a statistical test to test Ho. Decide whether parametric or non-

parametric.

3. Specify a significance level (alpha=) or probability level for rejection of Ho.

4. Determine the sample size (N).

5. Assume (or find) the sampling distribution of the statistical test in 2.

6. On the basis of 2, 3, 4 and 5 above, define the region of rejection of Ho.

7. Compute the value of the statistical test using the sample data.

8. If the resultant value of the test is in the rejection area, reject Ho.

9. If the resultant value of the test is outside the rejection area, Ho is not rejected at

the level of α.

Note that not rejecting Ho does not lead unequivocally to the acceptance of H1. This is

because the test did not test H1, but Ho. Note also that the test can be directional, that is,

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one mean is greater than or lesser than the other, and these types of tests are discussed later

under the heading One- and two-tailed tests.

3. Parametric hypothesis test

The most common parametric hypothesis tests are the z-, t- and F-tests. The z- and t-tests

are commonly used for the testing of means and are the focus of the following discussion.

F-tests are most commonly used in multivariate analysis and assume the F probability

distribution. The F-tests are slightly more rigorous in their assumptions than z- and t-tests

(discussed below).

3.1 When to use z- and t-tests

In order to test the null hypothesis it is necessary to determine first whether or not we know

what the standard deviation of the population is. If the population standard deviation (σ) is

known, the hypothesis testing can be done using the z-test. If the population standard

deviation is unknown we should use the t-test. Both tests assume the distribution to be

symmetric but the tails of the distribution are higher for the t than the z-test and there is an

individual difference in the heights of the tails for each sample size (N). This occurs

because the sample standard deviation (s) must be substituted for the population standard

deviation () so that there is more variability resulting from the independence of s and the

sample mean ( ). When is very large, s may be very small and vice versa. This variability

does not occur in the normal distribution as the only random variation occurs with the

population mean (μ) as the other quantities population size (N ) and are non-random.

The following conditions are required for the use of parametric tests.

1. The observations must be independent of each other. The selection of one

person for the survey should not influence the choice of others, and the answer

to one question by a respondent should not bias the answers to other questions.

2. The observations (scores) must be drawn from normally distributed

populations.

3. The populations must have the same variance (be homescedastic).

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4. The variables must be measured in at least an interval scale (known gaps

between each unit of measurement – usually the gap is one: 1,2,3,4,5) so that

meaningful addition, multiplication, subtraction and division can occur.

5. For the F-test the means of these normal and homestadastic populations must be

linear combinations of effects due to columns and/or rows. The effects must be

additive.

If the conditions above are met then the choice of test should be parametric because these

tests are more powerful (more confidence can be placed upon the result) than non-

parametric equivalents. When these conditions are not met and the analysis is still used

there can be no confidence in the results, meaning they are powerless.

3.2 One- and two-tailed tests

The difference between one- and two-tailed tests relates back to point 6 in the steps of

hypothesis testing (see earlier), the region of rejection. The region of rejection in the

probability distribution is in an extreme tail of the distribution of values that are very high

or low relative to the mean (which is toward the middle). These values are so extreme that

when Ho is true the probability is very small (less or equal to alpha) that the sample we

actually observe will yield a mean value among them.

The location of the region of rejection is determined by whether the test is one-tail positive

(one mean is larger than another and the region of rejection is upper values above the

mean) or one-tail negative (one mean is less than another and the region of rejection is

lower values below the mean). If the test is two-tail, there is either a positive or negative

difference (the comparative time taken to register guests in one hotel is faster or slower

than another) and the area of rejection can be in either tail of the distribution.

The size of the region of rejection is expressed as alpha, the level of significance. If

alpha=0.05, then the size of the rejection region is 5 per cent of the entire space under the

curve of the probability distribution. Refer to Figure 1.

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Figure 1. One- and two-tailed tests. (a) Two-tailed test; (b) one-tail positive test’ (c) one-tail negative test.

Notice that the probability distribution is represented in Figure 1 by a symmetrical bell-

shaped curve, with representing the population mean (the most commonly occurring

value at the centre of the curve).

To reject the null hypothesis the calculated value of z- or t from the analysis (t or z

obtained) must be a greater or lesser value than alpha= in the appropriate test (positive or

negative or two-tailed).

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X

X

X

5.0%reject HO

5.0%reject HO

2.5%reject HO

2.5%reject HO

Accept Ho

Accept Ho

Accept HoY

f

Y

f

Y

f

(a)

(b)

(c)

In this comparison it can be seen from Figure 1 that the critical value of is closer to the

mean () in the one-tail test (all other factors being equal). That is the area of rejection in

the one tail test is smaller in each tail than the two-tail test. Hence, the chance of rejection

occurring is higher for a one-tail test than the equivalent two tail test. This is because the

additional knowledge of knowing the direction of rejection allows for a less rigorous test.

3.3 One-sample means test example

The one-sample means test compares a single sample mean against a known population

mean. Later on, the cases of using two sample means is analysed separately.

In the study of tourism culture there are not many known population means because culture

is not the focus of most official tourism or census database collections. However, there are

known population demographics such as average age and income obtainable from

government census data. The following example is from preliminary analysis of a collected

sample used to assess the representativeness of the data to the base population.

A survey of 250 Australian host workers on the Gold Coast (Australia) was conducted in

1996. The average age of the workers who were employed in various contact positions with

international tourists was 33 years of age with a standard deviation of 4.85 years of age.

From the 1996 Australian census the average age of the workforce in the area was 38.5

years of age. However, the standard deviation for the population workforce was not

available. It is not uncommon that it is difficult to get variance measures from official

databases and in consequence it is not possible to conduct a z-test. It is reasonable to

assume the population of ages is normally distributed. Nevertheless a test was made for

skew in the survey data and the skew was a small 0.045 measure on a Pearson Skewness

test where zero indicates absolutely no skew and measures above 1.5 are clearly skewed.

Consequently, from the earlier discussion a t test is required.

The null hypothesis in this case is: the average age of the hosts is equal to or greater than

the workforce in general.

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The alternative hypothesis is: the average age of the hosts is lower than the average age of

the workforce in general.

Since the rejection region is determined by the null hypothesis, to reject Ho a one tail

negative test is required.

The value of alpha can be determined for the level of significance =0.05. For a t-test the

sample size is needed to determine alpha and at a very large sample size of 250. However,

the t critical values are approximate to values of the normal distribution beyond about 120°

of freedom (measured as N-1), so for 249° of freedom the critical value becomes 1.96

(two-tail) and 1.645 (one-tail), the same as the normal distribution.

This example draws out the difference between the z- and t-test and how sample size can

be used as another rule for choosing between the z- and t-test procedures. The standard

deviation initially used to determine a z-test could not be done because the standard

deviation of the population was unknown. It has been found in early statistical research that

the normal distribution varies with small sample sizes (the tails get higher). So there is a

different distribution for t from N=1 to 100 or maybe 120 depending on the number of

decimal places. So if the sample size is small the t-test is definitely needed, but if the

sample is 100 or more, the t-test is no longer needed regardless of the known or unknown

values of the standard deviation. This leads to the question of how small does the sample

size need to be before the difference between the values of t and z become so great as to be

worth worrying about. There is no clear answer – some researchers say as low as 30 or 40;

some say as low as 60.

For our example, a sample size of 250 is way beyond 120 and a z-test can be used and the

sample standard deviation can be substituted for the population standard deviation (that

remains unknown).

Therefore, a simple rule can be stated for the choice between z- and t-tests.

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If you don’t know the standard deviation of the population and the sample size is less

than 100 (maybe 60) use the normal distribution z-test. In all other cases use the t

distribution and the t-test.

To conduct the analysis the following information is required:

the sample mean =

the population standard deviation= or sample standard deviation=s

the sample size=N

the alpha significance value=

the population mean=

In our example the information available is:

=33 years of age (sample mean – statistic)

s= 4.85 years (sample standard deviation) population value unknown

N=250 respondents to the survey

=–1.645 (t critical one tail negative at 0.05 significance)

=38.5 years of age (population mean – parameter)

We can now rephrase our scientific model in simple terms to be: is the value of 33 when

drawn from a sample of size N=250, 95 per cent certain to be less than a value of 38.5

given a standard deviation of 4.85?

We know that sample means are approximately normally distributed when the sample size

is 100 or larger. So if the survey were conducted numerous times, with each sample size

larger than 100, we would expect a normal bell shaped curve.

The standard error is calculated as:

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= 4.85

= 0.3067

The standard error can best be understood as the ‘sampling error’. It is a measure of the

inaccuracy of using a sample from a population and weights out the degree of variation in

the data (measured by the standard deviation) by the size of the sample N. The smaller

the degree to which using a sample causes error, the better. So if the variation is high then

a large sample will be needed to reduce error (because the sample size is divided into the

variation). This calculation is a good example of the reason why it is always a good idea

to have a larger rather than smaller sample.

A sampling distribution may have a mean value of 38.5 (represented by zero as the mean of

the normal distribution), occasionally a mean as low as say 30 might occur in any given

sample or markedly higher over 40. The question here is whether the mean found in the

sample is merely lower than 38.5 because it comes from one of many possible sample

variants around a true mean of 38.5, or whether it is so low that it will likely occur five or

fewer times if 100 survey samples were repeatedly taken. If that is the case, the mean of 33

probably comes from another population that has a lower mean than 38.5. So when 33 are

converted to the normal distribution equivalent (where 38.5 is equal to zero) is the value of

33 less than –1.645?

Put in the terminology of hypothesis testing:

If (Z obtained) exceeds –1.645 reject Ho.

Note here the important use of the word ‘exceeds’. In this context the use of ‘exceeds’

means either greater in a positive direction (in our example greater than 1.645) or greater

in the negative direction (in our example a greater negative than –1.645). Therefore, it is

important not to substitute the words ‘greater than’ for the word ‘exceeds’ because while

this would be correct in the positive direction, it would be incorrect in the negative

direction.

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To derive z obtained the formula is:

= = –17.93

Since Z obtained at –17.93 exceeds –1.645 as a greater negative value, the null hypothesis

Ho is rejected and the alternative hypothesis H1 is accepted.

Therefore, it has been decided that the difference between the sample mean and the

population mean is due to something other than random variation. It is 95 per cent certain

that the mean age of the hosts is less than the mean age of the general workforce. In the

example case the Z obtained value is so large at 17.93 that the significance level of 95 per

cent is well and truly exceeded. In fact the significance exceeds 99 per cent (z critical 2.35).

3.4 Type I and Type II errors

Regardless of the results of the computation there is the possibility that an error has been

made. In hypothesis testing the error can take two forms, a Type I error and a Type II error.

A Type I error occurs when the null hypothesis is rejected when in fact it is true.

A Type II error occurs when the null hypothesis is accepted when in fact it is false.

The probability of making a Type I error is determined by the level of significance in the

test. If 95 per cent significance is chosen, then the chance of the null hypothesis being

rejected when in fact it is true must be 5 per cent. Consequently, the higher the level of

significance, the less the chance of a Type I error.

However, what is the probability of committing a Type II error? This probability is less

obvious than the probability of a Type I error and requires separate and less specific

calculation. Before considering this calculation it is best to see the relationship between

each error Type as depicted in Figure 2.

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H1

Critical z

f

0

Type IType II

Accept HO Reject HO

Ho

1

Figure 2. The probabilities of a Type I and Type II error one-tail positive test.

The probability of a Type I error is the area of rejection of the null hypothesis (Ho) to the

right of the critical z-line. The probability of Type II error is the area of the tail of the

alternative hypothesis (H1) that extends into the region of acceptance of Ho to the left of

the vertical line critical z; this has already been defined as the probability that the sample

mean will fall into the acceptance region of Ho, when in fact H1 is correct.

The problem of calculating the area of a Type II error under the normal curve now becomes

apparent in that the calculation requires the knowledge of 1 and an estimate of 1 that is

not known unless the alternative hypothesis structure is a simple equality. In such a case 1

is a known value and 1 can be estimated by and calculation can be straightforward.

However, in most social science situations that is not the case, and the alternative

hypothesis is complex; 1 can take on a range of values above 0 and for a given level of

significance the probability of a Type II error is specified as a function and not a single

value.

As can be seen from Figure 2 if there is a reduction in the Type I error (the critical z-value

line moves to the right) so there is an increase in the Type II error and vice versa.

Consequently, in selecting the level of significance the researcher must determine the

importance of each type of error.

The consequences for the hosts survey on the Gold Coast of a Type II error are not really

high: the average age of the hosts would not be recognized to be less than the general

workforce average age. On the other hand, a Type I error would cause the claim to be made

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that the average age of the host workforce is younger when in fact it was not. Therefore, the

higher the significance level the better.

There are situations where the Type II error can be important and they are common in both

medical and legal research. Consider the case of a corporate lawyer making a decision

concerning whether or not a franchise contract for a travel agent can be broken or not.

According to the results of a survey of lawyers the corporate lawyer may decide that his

client's case differs enough from an adverse precedent to continue with the case, despite

costs. If in fact the precedent covers the case, the lawyer will likely lose. A Type II error

would commit the client to legal costs and subsequent loss of the case and potentially an

adverse continuing financial position for the travel agent. A Type I error would mean the

precedent was judged important when in fact it was not and clients not proceeding with the

case when in fact they would likely win. In such a case the lawyer may use a lower

significance level, to decrease the chance of incurring unnecessary costs (a Type II error).

Fortunately, there is a more reliable way to reduce the probabilities of both error types.

That is by increasing the sample size N. Since the spread in the sampling distribution is

equal to /N (which is estimated by s/N where the population standard deviation is

unknown) a larger value of N will produce a smaller value of the deviation among the

means of the sampling distribution. When sample size increases from N to some larger size

N' the distributions condense around the true means and both error areas in the distribution

curve tails decrease in size. Another reason why using a large sample is important for

parametric analysis.

3.5 Two-sample means test

In the case of a two-sample means tests it is possible to determine the likelihood of two-

sample means coming from the same population. For example, are the average responses to

the question ‘I want to see the historic buildings and architecture’ the same for Chinese and

French tourists? Literature suggests (Guo, 2001) that the Chinese still have a historically

based interest in buildings and architecture that is less common among western tourists.

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In terms of the statistical analysis three confounding complexities enter into the study of the

difference between two means. One of the complexities has already been encountered in

the previous section; on one-sample tests a difference in statistical manipulations occurs

when the population standard deviation is known and unknown leading to the question of

whether to use a z- or a t-test. The second complexity requires a different calculation when

the samples selected are independent (unpaired) samples as opposed to related (paired)

samples, and the third complexity is that the two-sample test cannot be conducted unless

the populations from which the two samples have been drawn have homogeneous

variances (homoscedasticity). This assumption is often testable in the two-sample case,

unlike the one-sample case.

First of all we shall examine the problems of homogeneous variances and then discuss the

unpaired design analysis (assuming unknown) followed by the paired design analysis

(with unknown).

Although the ultimate interest is the difference between means, any test first assumes

homogeneous variances of the populations. Consequently, a pre-test should be conducted

to test for a difference between the two standard deviations.

The hypotheses for this homoscedastic test are:

The null hypothesis (Ho) states that the observed difference between s2 (1) and s2

(2) (the variance of the first and second samples) is due simply to random

variability, because the population variances are equal.

The alternative hypothesis states that the sample variances are different because the

population variances differ.

The test is two-tail as no direction for the difference is specified.

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The unbiased sample variances are used to calculate a statistic known as the F-ratio, which

is calculated by dividing the larger of the two variances by the smaller (thus always

yielding a positive result):

There is a different F-distribution for different degrees of freedom in the denominator and

numerator of the obtained F-ratio. Critical values of the F-distribution can be read off the

relevant tables, with degrees of freedom at N-1 for both the denominator and numerator,

where N is the sample size.

Values of F smaller than 1 cannot occur in this test, because the larger variance is always

placed over the smaller variance. The conclusion upon the analysis is obtained by the test:

if (F-obtained) positively exceeds F-critical, reject Ho.

In order to continue with the analysis it is necessary that the statistician does not reject the

null hypothesis (Ho), and thus concludes that the samples are likely to be drawn from

populations with equal variances. It is reasonable, and conventional to accept or reject the

null hypothesis at the 95 per cent level of significance. However, acceptance of the null

hypothesis does not mean the statistician is 95 per cent sure that the samples have been

drawn from populations with equal variances, it is merely ‘likely to be so’ because of the

way the hypotheses have been conventionally structured to test the null hypothesis that

there is no difference.

The difference between two sample means can be assumed to create a sampling

distribution, in the same way that the means of samples can also be used to create a

distribution. That is, if numerous means were calculated from numerous samples, or, if

sampling numerous differences between two means from numerous sets of samples were

calculated, they could be used to plot a sampling distribution.

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The parameters would be:

where

= mean of the sampling distribution of the difference between two means. = standard error of the sampling distribution.

The distribution, once plotted, would be normal in shape if large enough sample sizes are

used, and the standard deviations of the populations are known. Unfortunately, the

population standard deviations are rarely known and consequently it is necessary to use

the t distribution rather than the Z distribution.

Now let us consider the analysis of the difference between two sample means, first in the

case of an unpaired analysis and secondly in the case of a paired analysis.

In an unpaired sample design, the individuals making up the samples would be selected

randomly from the relevant population with each member of the population having an

equal chance of being chosen. In a paired sample design the individuals would be chosen

as a matched sample (characteristics of each sample matched as closely as possible to

reduce variability of characteristics other than that being tested) or a related sample (same

individuals used for both samples) and the sample sizes would be the same.

It could be expected that a greater degree of variability between sample observations occurs

with unpaired designs so that extra attempts are made to maintain a control upon random

error.

3.6 Unpaired test

When is unknown, s must be used to estimate ( ) and the sampling distribution is

shaped as a t distribution, with degrees of freedom equal to N1+N2–2.

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Let us use the example discussed previously of the difference between the Chinese and

French in regard to the statement ‘I want to see the historic buildings and architecture’,

measured on a seven-point scale (0=no importance at all to 7=extremely important). Let us

assume the following statistics:

Chinese French= 6.10 N1= 40 = 5.2= 1.2 N2=35 = 0.9

The variances when tested are unlikely to be non-homoscedastic.

The null hypothesis states that the two samples come from the same population, that is,

the means are equal to each other or the Chinese mean is lower than the French mean.

The alternative hypothesis states that the Chinese mean is higher than the French mean.

Consequently, it is a one-tail positive test.

If (t-obtained) exceeds t critical, reject Ho.

To find t-obtained:

t-obtained =

where : ( ) is the calculated statistic. ( ) is the mean of the sampling distribution specified by Ho.

Thus: t-obtained=

In order to find the estimated standard error in the denominator it is necessary to compute

the pooled variance (Sp2). It is feasible to pool the simple variances because homogeneity

of variances has been tested for (refer to the F-test above):

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Thus:

The pooled variance will always fall in between the values of the two individual variances.

The pooled variance is then used to compute the estimated .

Estimated = = = 0.2383.

Now the value of t-obtained can be calculated:

Critical t is derived from the t distribution at N1+N–2 degrees of freedom (40+35–2), or 73

degrees of freedom, to be 1.66 at 95 per cent significance for a one-tail test.

Since 15.85 is greater than 1.66 (critical t) the null hypothesis is rejected and it is concluded

at 95 per cent significance that the Chinese rate buildings and architecture more

importantly as a destination characteristic than the French. The high t-obtained indicates

that rejection is also possible at 99 per cent statistical significance.

3.7 Paired sample test

The use of paired samples eliminates some random variability. Variability is now

concentrated to within sample variability, or variations among the sample individuals. The

between sample variability has been reduced in the paired sample test through the use of

particular sampling methodology such as matched sampling.

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The consequence in statistical terms of reduced variability is a smaller estimated standard

error of the sampling distribution of mean differences (( )) when the correlation

between the samples is positive, which in turn produces a larger t-obtained. The reverse

occurs when the correlation is negative.

Calculation of the paired sample test can be computed via a technique known as the direct-

differences method.

A hypothetical example is used to illustrate the analysis. Management of a particular

airline has agreed that the time taken for some service teams to turn around a large

international aircraft depends upon the length of the incoming flight duration. However,

management has argued with the cleaning union that the time taken to clean the plane is

the same regardless of flight times. In order to test this argument, two eight-person

cleaning teams are compared in the times taken to complete each of their assigned tasks,

team one after a 12-hour flight and team two after a four-hour flight. The teams are

matched in most relevant characteristics including training, job specification and

experience. Table 1 lists the data collected from the test and the analysis procedure. The

data is collected as a percentage efficiency rating for each team member matched by his

or her specific job, and includes both time taken and quality of the finished job measured

as a percentage.

Table 1. Direct difference method for the paired-sample test

Pair Sample 1 Sample 2 Difference (D) (D-D) Difference2

1 70 68 –2  0.5  0.252 65 69  4 –5.5 30.253 56 54 –2  0.5  0.254 73 69 –4  2.5  6.255 62 63  1 –2.5  6.256 60 57 –3  1.5  2.257 78 70 –8  6.5 42.258 65 67  2 –3.5 12.25

Σ =529 =517 Σ = –12 Σ =100.00

= 66.125 Difference – = –1.5 D = = –1.5

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= 64.625

= standard deviation of the D array

= = 3.7796

Standard error of the statistic = = = = 1.3363

t obtained = = = –1.1225

The direct-differences method effectively coverts to a single sample means test where D

equals the mean difference between members of each pair and becomes a single mean.

The similarity can be seen in Table 1 by the calculations of and as both equal

–1.5. Notice that sample two is always deducted from sample one to derive .

The statistic is assumed to come from a sampling distribution that is shaped as a

t-distribution with N-1 degree of freedom. In the example N=8, so d.f.=7. The critical

t-value at 7 d.f. and 95 per cent significance is 2.365 for a two-tail test.

If (t-obtained) exceeds ± 2.365, reject Ho.

Since t-obtained at –1.1225 does not equal or exceed t critical at –2.365, the null hypothesis

is not rejected and the conclusion is that the two samples come from populations with the

same mean, so that there is likely to be no difference between the two teams in terms of

cleaning efficiency. This test could be repeated for numerous team comparisons to see if

the findings (for various different flight times) result in a consistent conclusion.

3.8 Hypothesis interpretation

Finally, in interpreting the results of an analysis, the researcher must be very careful not

to, on the one hand, break any of the statistical rules, and on the other hand make a

post-hoc error.

22

The statistical rules that are most important concern the assumption of data distributions,

most commonly the normal distribution. Both the z-test and the t-test assume data is

distributed normally.

If the data does not come from a population that is normally distributed and the sample is

small in number, (may not be normally distributed) all analysis is circumspect. Second, the

assumption of homogeneous variance is equally important, and failure to test for this is a

major weakness that may render the analysis useless.

Post-hoc errors are often made in social science analysis where the data is less likely to take

the form of an experiment, and this point can best be described by example. If any factor

(independent variable) remains unaccounted for in the analysis it may be a hidden cause of

the effect under study. Random selection of individuals can often be used incorrectly, and

thus not control for extraneous independent variables. For example, it is often stated that

young drivers are more dangerous on the roads because they are less experienced and have

more accidents. While that may be correct, a test that did not allow for the fact that young

drivers choose more dangerous vehicles (faster cars, or older or cheaper cars) may be

committing a post-hoc error.

4. Introduction to non-parametric hypothesis testing

Non-parametric statistical techniques place few limitations upon the level of measurement

for data because they do not require the use of statistical parameters such as the mean and

standard deviation. They make few assumptions that data is distributed in a particular

manner, and no assumption of the normal distribution is necessary except in cases where an

approximation is made because of large sample sizes. They can do this because their

manipulations are based upon nominal or ordinal measurement rather than ratio measures.

Consequently, where the mean (requiring ratio data) may be used in a parametric analysis,

the median (requiring ordinal data) may be used in a non-parametric calculation.

To facilitate the use of non-parametric techniques, this text discusses several of the most

common tests for use in tourism analysis. These are divided into groups on the basis of the

23

type of sample required. First, one-sample tests are discussed. Second, tests requiring two

related (matched or paired) samples. Third tests requiring two independent (unrelated or

unpaired) samples. Fourth, tests requiring more than two (multiple) related samples and

finally, tests requiring multiple independent samples.

Some non-parametric tests are not covered here, and for wider reference, Brownlee (1965)

is a recommended reading.

4.1 One-sample non-parametric test

The most common non-parametric one-sample test is the Chi-square test and that is what

is covered here. The other reasonably well-known test is the Kolmogorov-Smirnov test.

The one-sample test procedure usually involves the question of goodness-of-fit, where a

single randomly selected sample is compared against the known parameters of a given

distribution. The most common parametric equivalent of this analytic technique is the t-test

used to test the difference between the observed sample mean and an expected population

mean. The Chi-square test can be used when the observed scores fall into two or more

categories (nominal data) and can determine whether there is a significant difference

between the observed frequencies and those expected to occur. The Kolmogorov-Smirnov

test can be used with ordinal data to test for the degree of goodness-of-fit between an

observed set of ranked scores and some theoretical distribution.

The number of categories is undetermined, but there must be at least two. Categorization of

a variable is extremely common and the Chi-square test is often used. Some examples of

variable categorization are:

1. sex, divided into males and females

2. income, divided into low, medium and high

3. opinion when divided into yes, no, undecided.

24

The null hypothesis states what proportion of scores could be expected in each category of

the population. Therefore, it is the null hypothesis that determines the expected frequency

distribution.

The steps for the calculation of the one-sample Chi-square are as follows:

1. Determine the frequency for each category of the observed data. The sum of

frequencies=N.

2. Determine the expected frequency for each category according to the null

hypothesis.

3. Calculate the value Chi-square (2); where:

O=observed frequency.

E=expected frequency.

4. Calculate the number of degrees of freedom; where: d.f.=k-1.

5. Compare the calculated 2 value with the critical values given on the Chi-square

critical value table. If the obtained 2 value is greater than the critical table value,

the null hypothesis is rejected.

Where more than 20 per cent of the expected values are smaller than 5, it is necessary to

combine categories in order to increase the expected count (by decreasing the value of k).

Where only two categories exist (k=2), both expected values must be equal to, or greater

than five.

An example using the one-sample Chi-square test: a car rental company has five airport

rental desks at five major international airports. The marketing manager considers one of

the desks (No. 3) will outsell the other four by twice the number of sales, and has advised

the company to increase staff and car numbers accordingly. The publisher decides to

25

sample the market for the first 200 car rentals at each desk over a period of 3 days. The

following ninety rentals are made:

Desk 1 2 3 4 5 TotalRentals 12 15 28 18 17 90The expected rentals as defined by the marketing manager are:

15 15 30 15 15

The calculation of 2:

The table of critical values of Chi-square for 4 degree of freedom at 95 per cent

significance give a critical Chi-square=9.49. Since the obtained Chi-square value of 1.6 is

less than 9.49 the null hypothesis is not rejected. Therefore, the company may conclude

that the marketing manager correctly assessed the market for the five desks.

Some of the problems associated with Chi-square include, notably, the requirement to have

at least a 5 expected frequency per category 80 per cent of the time, to have an overall

sample exceeding 25 (small samples are not applicable to Chi-square) and no reliance on

order (rank) in the null hypothesis. These problems can often be overcome by using the

Kolmogorov-Smirnov technique provided the data could be ranked.

4.2 Paired two-sample non-parametric test

In the case of two samples, tests are made to determine whether the samples are drawn

from the same, or from different populations. Most commonly one sample has been

exposed to an independent variable (drug, travel, training, changed income, experiment and

so on) and the other sample forms a control group that has not been so exposed.

The two related samples are either matched (paired) or comprise the same objects

(individuals). The parametric technique for analysing two related samples is the paired t-

test discussed above. Apart from being distribution free, the non-parametric test equivalents

26

have an additional advantage in that they do not require that all pairs of observations be

drawn from the same population.

There are three common tests: the Sign test, the Wilcoxon Matched-pairs Signed-ranks test

and the Mc Nemar test for the significance of changes. The Sign test is used to establish

that two conditions are different, making only the one assumption that the independent

variable under study has a continuous distribution. Where the magnitude as well as the

difference between pairs is known, the Wilcoxon Signed-ranks test is a more powerful

technique than the Sign test. The Mc Nemar test for the significance of changes is

particularly useful in the ‘before and after’ research design where the individuals (objects)

in the samples are both the same. For example, the Mc Nemar test may be used to examine

the effect of a training session on a particular type of skill or the influence of an advertizing

promotion upon sales.

The test given here is the Wilcoxon Matched-pairs Signed ranks test because of its

relatively strong power. The Wilcoxon Signed ranks test provides a more powerful analysis

than the Sign Test, considering not only the direction of ranked differences between two

related samples, but also the relative magnitude of the differences. More weight is given to

a pair with a large difference than a pair with a small difference.

This analysis requires slightly more information than the ordinal scale of measurement

because the data must be ranked, and the differences between pairs known. However,

interval scale measurement is not required for each sample because the interval between

observations is not needed. This scale falls in between the ordinal and interval scales and is

termed the ordered metric scale.

The same example given in the paired sample test section above can be used here. The two

teams of aircraft cleaners are a matched paired sample set. The level of measurement is

higher than required for this test but there is no longer an assumption of the normal

distribution, which may well be more accurate. The steps for computation are as shown

below.

27

1. For each related pair calculate the difference between the two scores and note

the sign.

2. Rank the differences calculated in Step 1 regardless of their sign.

3. Disregard those differences equal to zero.

4. If two or more difference values are tied, assign the rank that is the average of

the ranks that would have been assigned if the values had been slightly apart.

That is, assign the average of the tied ranks. For example, –2, –2, +2 are tied

differences. In the ranked array each pair would be assigned say the ranks 3, 4

and 5. Thus 3+4+5/3=4. Ranks 1 and 2 would have been assigned to values

below –2 and the next value would be ranked 6, because ranks 3, 4 and 5 have

already been used and listed as the average 4.

5. Compute T, the Wilcoxon statistic as equal to the smaller sum of like-signed

ranks.

For small samples, where the value of N=(N1+N2) is less than 26, the T value is read off

against the Wilcox T table. The null hypothesis states that the two samples are not different,

that there is no difference in cleaning efficiency between the two flights. If the obtained T

value is equal to or less than the critical T value in the Wilcox T table the null hypothesis

can be rejected at the given level of significance.

For large samples, where the value of N is greater than 25, the distribution under T is

approximately normally distributed with:

mean equal to:

and standard deviation equal to:

The calculation of Z:

28

The normal distribution table can be used to determine the probabilities associated with the

occurrence under Ho of values as extreme as the obtained Z.

For the example data in Table 1, we compare Table 2. The Wilcoxon Table critical value

for N=16 at 0.05 significance two-tail is 30. Since T at 10.5 does not exceed the critical

value of 30 the null hypothesis is not rejected. It is concluded that it is likely there is no

difference in the time taken by the two teams.

Table 2. Number of the significant differences between Australian hosts and Asian language groupsAustralian Australian Australian Australian Australian Australian

Group indicators Max Total Asian Indonesian Japanese Korean Mandarin ThaiCultural values 36 18 14 26 26 12 14Rules of interaction

34 22 24 22 18 18 20

Perceptions of service

29 23 18 23 20 15 24

Forms of interaction

11 7 5 8 7 6 3

Satisfaction 7 3 3 4 3 2 3Total 117 73 64 83 74 53 64

4.3 Unpaired two-sample non-parametric test

As discussed previously, for the case of two paired samples, the most common parametric

technique is the t-test. There are three common methods available, the

Kolmogorov-Smirnov two sample test, the Chi-square two sample test and the

Mann-Whitney U-test. The Kolmogorov-Smirnov technique is used to determine whether

or not the two samples have been drawn from either the same population, or populations

with the same distribution. The Chi-square technique can be used to test when frequencies

recorded into discrete categories are divided between two independent groups with a

significant degree of difference. The Mann-Whitney technique is equivalent to the

Kolmogorov-Smirnov test, but unlike that test is best suited to large rather than small

samples.

The Chi-square test is very commonly used and can be output from SPSS from the

Frequency Tables analysis. The Mann-Whitney U-test is the most powerful of the tests and

is the method discussed here. The Mann-Whitney U-test can be used to test whether two

29

independent groups (measured at least at the ordinal scale) have been drawn from the same

population. Fundamentally, the test examines the combined, ranked array of two samples in

order to measure the degree of randomness in the array. Logically, if the two samples come

from the same population the array will exhibit randomness. Samples drawn from two

different populations would tend to diverge toward different extremes of the columned

ranked array, resulting in little random variability of the array.

The two samples do not have to be of the same size. All values are ranked in order of

increasing size, and each is identified as coming from either N1 or N2. The value of the U

statistic is the sum of the number of times that a score in the sample N2 precedes a score in

the sample N1.

For example, given: N1 N25 83 12 47 6

Step 1, rank values, maintaining sample identity:

Step 2, count the number of times N2 scores precede an N1 score:

1+1+2+3=7

That is, for the first N1 score (ranked 2), one N2 score precedes. For the second N1 score

(3), still only one N2 score precedes. For the third N1 score (5), two N2 scores precede. For

the fourth N1 (7), three N2 scores precede. The total number of N2 scores preceding N1

scores is seven.

Where ties occur, the generally accepted procedure is to use the average rank for all the

tied values. Since the sample distribution for U is known, the probability of obtaining a

value as extreme as 7 can be determined.

30

For samples smaller than 21 there are U tables. In our sample above N1=4, N2=4 and U=7.

From the U table for sample sizes less than 9 with the probability at 0.05 (two tail) the

nearest p value is 0.057 with U=2. Since U=7 is greater than U critical at 2 we cannot reject

the null hypothesis. The value searched for in the U table (in the above case from the

column represented by N1=4 and N2=4) is determined by the level of significance and

whether the test is one- or two-tail. Thus, by example:

One-tail 95%, =0.05 one-tail 90%, =0.10

Two-tail 95%, =0.025 two-tail 90%, =0.05.

On finding the closest value the U critical value can be read off. Note here that if U-

obtained is less than U-critical the null hypothesis is rejected.

For samples larger than 20 the normal distribution can be used where:

and:

If ties occur the standard deviation becomes:

where: summing the T’s overall groups of tied observations. N' = N1+N2

31

and:

where: R1=sum of ranks assigned to group N1.

and where: T=a correction factor for the number of ties:

where: t=number of observations tied for a given rank.

4.4 Multiple paired sample test

In the previous sections statistical techniques for analysis of differences between a single

sample and a specified population, and of differences between two samples have been

discussed. This section examines techniques for testing for a significant difference between

three or more samples, drawn from the same population, or from populations with the same

parameters.

There are two common tests for related samples: the Cochran Q test and the Friedman

two-way analysis of variance. The Cochran test is particularly useful for nominally

measured data, while the Friedman analysis is best suited to ordinal scale measurement and

is the more powerful test.

Data is cast into a table of K columns and N rows where the K columns represent the

number of samples (three or more). Since the samples are matched, the number of cases

(N) is the same for each.

The matching may be achieved by studying one group of individuals under several

conditions (where the conditions are the samples), or by obtaining several sets each with K

matched subjects. In this example, suppose the design comprises three sets under four

conditions, where K=4 and N=3. Each group of subjects (three of) contain four matched

subjects and one is assigned to each of the four conditions:

Conditions (samples), K=4

32

1 2 3 4Set 1 7 3 8 1

N=3 Set 2 6 8 2 4Set 3 9 1 4 2

The conditions could be four different brands of the same package tour to the same

destination and the test could be to determine whether there is any perceived difference in

quality. Each set from 1 to N contains 1 to K individuals who have been matched on basic

variables such as age, sex and socio-economic status. Each individual in a set is randomly

assigned to rate the quality of the brand using a specified ordinal scale. The null hypothesis

is that all the samples (columns) come from the same population because there is no

difference in the perceived quality of the given four brands.

In the Friedman test the first step is to rank the scores in each row. The lowest score is

ranked one, the highest is K. Thus, for the example data:

Package brands, K=4

1 3 4 5Set 1 3 2 4 1

N=3 Set 2 3 4 1 2Set 3 4 1 3 2Rj 10 7 8 5

If the null hypothesis were to be accepted, we would expect the ranks 1 to K (1 to 4 above)

to be represented equally in each column. Consequently, the totals (Rj) for each column

would be approximately equal.

The Friedman test analyses the rank totals (Rj) to estimate whether they differ significantly.

The value calculated is symbolized as Chi-r-square and is distributed approximately as

Chi-square with degrees of freedom = K–1. The formula is:

where: N=number of rows. K number of columns.

33

Rj=total of ranks in jth column. Thus:

The significance of Chi-r-square is determined by examining the Friedman probability

table. For K=4 and N=3 a value of Chi-r-square=2.6 has a probability of 0.524. Should

the null hypothesis be rejected at a 0.524 level of significance? This is not high and does

not justify the rejection of the null hypothesis. It is likely the four brands of tours are not

perceived to have different quality.

If N and/or K is larger than those shown in the Friedman table the Chi-r-square table of

critical values is used, with degrees of freedom at K –1.

4.5 Multiple unpaired sample test

This section examines the case of non-parametric tests for the significance of the

difference between three or more independent samples. There are two common tests: the

Chi-square multiple independent sample test and the Kruskal-Wallis one-way Analysis of

Variance test.

The Chi-square test is suitable when the data falls into discrete categories measured at

either the nominal or ordinal scale. There is no difference in the computation of the Chi-

square multiple sample test and the two-sample test. The Kruskal-Wallis technique tests the

null hypothesis that the K (multiple) samples come from the same population or from

populations with the same parameters. The test requires data at the ordinal scale of

measurement and assumes that the variable measured has an underlying continuous

distribution. The Kruskal-Wallis test is done here because although it is less commonly

seen than the Chi-square test, it is more powerful.

Since the samples are unpaired there is no need to have the same number of observations in

each sample.

34

The first step of computation is to rank the observations for each sample in an increasing

series with the smallest ranked as one, and the largest ranked N. Ranking is carried out

across all the samples to form one series.

For example, suppose a large company wishes to test the efficiency of its management

teams in three different countries. Each team has been created independently by three

different subsidiaries of the corporation. The staff of each management team is set a

simple efficiency test and a percentage score results:

Team 1 Team 2 Team 3Test Rank Test Rank Test Rank80 10 82 12.5 65 3.092 18 83 14.0 82 12.595 19 71 7.0 91 16.091 16 75 9.0 70 5.597 20 73 8.0 60 1.099 21 81 11.0 65 3.091 16 70 5.5

65 3.0Rj=120 Rj=70 Rj=41

=14400 =4900 =1681Nj=7 nj=8 nj=6

Each score above is ranked in increasing order and where ties occur, each score (tied) is

given the mean of the rank for which it is tied.

The null hypothesis states that the samples come from the same population or identical

populations with regard to means. Therefore, the null hypothesis is that there is no

difference in the average efficiency rating of the three different management teams.

The Kruskal-Wallis statistic is termed H and is calculated by the formula:

where: K=number of samples.

35

nj=number of cases in the jth sample. N=the total number of cases (nj). Rj=sum of the ranks in the jth sample.

The H statistic is distributed approximately as Chi-square with degrees of freedom=k–1.

Consequently:

The sign of H is ignored.

There are several tied ranks in the previously presented data. Since the value of the H

statistic can be slightly affected by ties it is necessary to correct for this factor via the

formula:

where: T=t3–t (where t is the number of tied observations in a tied group of scores).

N=is the total number of cases for all samples.

T=to sum T for all groups of ties.

The value of H is divided as:

The effect of the division is to increase the size of H slightly and this in turn makes H more

statistically significant than it would otherwise have been.

36

Correcting for ties in the example, it is first necessary to recognize the tied groups:

65 thrice at rank  3=T=27-3= 2470 twice at rank  3=T= 8-2=  682 twice at rank  9=T= 8-2=  691 thrice at rank 11=T=27-3= 24

60

Therefore, the correction factor for ties:

The H now becomes:

When the number of cases for the three or more samples is greater than five or there are

more than three samples, the Chi-square table of critical values is used to determine the

statistical significance of H at K–1 degrees of freedom. At 0.5 significance critical Chi-

square at 2 degrees of freedom is 5.99.

If (H-obtained) exceeds critical Chi-square, reject Ho.

Because 10.69 is greater than 5.99 the null hypothesis is rejected in favour of the

alternative hypothesis. The conclusion is that the management teams do differ from country

to country in terms of efficiency at 95 per cent statistical significance. For a higher level of

significance at 99 per cent, critical Chi-square is 9.12 (at 2 degrees of freedom), and with

H-obtained at 10.69, the null hypothesis can still be rejected.

37

If the number of cases in each of only three samples is five or less, the Chi-square

approximation to the sampling distribution of H becomes less reliable and the critical value

should be derived from the Kruskal-Wallis table. This table gives the possible sample sizes

in the first columns, followed by values of H and p (probability under Ho) in the columns

to the right.

5. Cross-cultural behaviour: example analysis

The following example analysis is part of a paper titled Cultural Differences between Asian

Tourist Markets and Australian Hosts: Part 1, by Y. Reisinger and L. Turner reprinted from

the Journal of Travel Research Vol. 40, number 3, 2002, pp. 295–315 with permission

from Sage Publications. This study provides a good example of the use of the Mann-

Whitney U-Test on large samples.

The main research objectives of this study are to:

1) identify the key cultural differences between the Asian tourist markets and the

Australian host population, as a representative of western culture,

2) determine the key dimensions of these differences, and their indicators, and

3) identify major cultural themes that should be included in every promotional strategy

aiming at the Asian tourist market.

Only objective one is analysed here. The remaining objectives involve the use of

principal components analysis, a technique discussed in Chapter 7 of our book Cross-

cultural tourism behaviour: Concepts and analysis (2003).

Culture, in this paper, refers to a stable and dominant cultural character of a society

shared by most of its individuals, and remaining constant over long periods of time.

Culture does not refer to the subcultures of many ethnic groups living in a society that

may be distinguished by religion, age, geographical location or some other factor, nor the

individual’s character that can be influenced by environmental forces and easily changed

over time.

38

The two distinct groups, tourists and hosts, were chosen for the study because these groups are the major tourism players. Hosts in this study are nationals of the visited country who are employed in the tourism industry and provide a service to tourists (e.g., front office employees, bus drivers, shop assistants, waitresses, custom officials). Knight (1996) referred to hosts as those who provide tourism services (e.g. shelter, accommodation and food) are in direct contact with tourists and derive direct benefits from the tourists. Nettekoven (1979) referred to them as ‘professional hosts’ who are employed in the places of most frequent tourist visitation. These places offer maximum opportunities for a direct tourist-host contact. As a result, hosts represent the first contact points with tourists. Consequently, cross-cultural differences in the interpersonal interaction in the tourism context are most likely to be apparent in these two groups, tourists and hosts.

A sample of 618 Asian tourists visiting the Gold Coast region, Australia’s major tourist

destination, were personally interviewed in their own language, alongside 250 Australian

service providers. Asian tourists were surveyed in a variety of locations on the Gold

Coast, where there is a large concentration of Asian tourists. The total population of

Asian tourists was divided into five mutually exclusive and exhaustive strata (Asian

language groups), which represented distinct Asian tourist markets: Indonesian, Japanese,

Korean, Mandarin and Thai. The selection of cultural language groups was based on the

statistical data showing the arrivals of international tourists to Australia from major

countries of origin. A representative sample of respondents was chosen from each

stratum. The sample elements were not selected in proportions that reflected the size of

each major Asian tourist market on the Gold Coast, rather the emphasis was on getting a

maximum number of respondents from different language groups. An attempt was,

however, made to choose respondents from a wide variety of socio-demographic

backgrounds. This was done to ensure the samples were representative of the central

tendency of their culture. The respondents were equivalent in their characteristics in

39

terms of the purpose of travel and length of stay on the Gold Coast. Australian hosts were

randomly selected from a variety of sectors of the tourism and hospitality industry on the

Gold Coast such as accommodation, transportation or entertainment in the same time

period. Again, disproportionate samples were taken from each stratum because

proportionate samples would have resulted in small samples. The study was conducted

over the period 1994 to 1995.

Five measurement groups of cultural values, rules of social behaviour, perceptions of

service, forms of interaction and satisfaction with interaction were measured by a

structured questionnaire. Personal values were measured using the Rokeach Values

Survey (RVS) (Rokeach, 1973). The RVS was assessed as the best available instrument

for measuring values, because it is ‘based on a well-articulated conceptualization of value’

and is successful in ‘finding specific values that differentiate various political, religious,

economic, generation and cultural groups’ (Braithwaite and Law, 1985, p. 250). The RVS

has been used in numerous studies to measure human values (e.g., Feather, 1980a,b,c;

1986a,b; Ng et al., 1982) and it has identified cultural differences between countries,

including differences between western and Asian countries. The 36-item RVS scale

produced a Cronbach Alpha value of 0.9497 that indicated that the RVS was a very

reliable instrument. In respect of validity, all items were adapted from the RVS (Rokeach,

1973), which measured human values. Rokeach (1973) selected only those values, which

were considered to be important across culture, status and sex (Rokeach, 1971). The

respondents were asked to indicate the importance of specific values by rating them on a

6-point scale, ranging from 1 (not important) to 6 (extremely important).

Rules of social interaction were measured using Argyle et al.’s (1986) list of thirty-four

rules of social behaviour, which has also been widely used and assessed as a reliable and

valid measure of the rules of social relationships. Only the rules that were applicable to

tourist-host interaction were included and the rules that governed family invitations, social

visitation or sexual activity were excluded. The rules specific to Asian cultures such as the

clear indication of intentions, conforming to rules of etiquette and the status of the other

person, having a sense of shame and avoiding embarrassment were included. These rules

40

were chosen from the literature on interpersonal relations in Asian cultures, and focus group

discussions with Asian students. The Alpha Cronbach was 0.9048 indicating that the

instrument was highly reliable. The respondents were asked to indicate the importance of

specific rules on a 6-point scale, ranging from 1 (not important) to 6 (extremely important).

Perceptions of service were measured using a 22-item SERVQUAL instrument

(Parasuraman’s et al., 1985, 1988), which has also been widely applied in empirical

studies in various disciplines, including the hospitality and tourism industry, and assessed

as reliable and highly valuable (Fick and Ritchie, 1991; Luk et al., 1993; LeBlanc, 1992;

Saleh and Ryan, 1991). However, the SERVQUAL scale was modified by eliminating all

the positive and negative statements that made a comparison of responses difficult,

including the word ‘should’. Only the words describing service (adjectives) were used.

Also, the scale was supplemented by additional items to reflect the distinctive features of

a high quality service as perceived by Asian visitors (e.g., the ability of hosts to speak an

Asian language, treat tourists as guests, know Asian culture and customs). These

distinctive items of service were identified on the basis of the literature review about

service quality. The responses were measured on a 6-point scale, ranging from 1 (least

important) to 6 (extremely important).

Tourist-host interaction was measured using a list of various forms of interaction such as

playing sport together, having a close relationship or sharing a meal. These items were

adapted from several studies’ direct and indirect measures of social contact (Black and

Mendenhall, 1989; Kamal and Maruyama, 1990; McAllister and Moore, 1991). Again,

the responses were measured on a 6-point scale ranging from 1 (least preferred) to 6

(most preferred).

Satisfaction with interaction was measured using a list of various components of

satisfaction with social interaction such as satisfaction with language spoken,

conversation or time spent together. The items were measured on a 6-point scale ranging

from 1 (dissatisfied) to 6 (extremely satisfied).

41

The instrument was translated into Asian languages and back translated to the English

language by a professional translating agency. The instrument was pre-tested twice in

two pilot studies to ensure it was clear and understandable: once on a sample of twenty

Australian tourists and twenty providers, and the second time on a sample of fifty Asian

tourists. Professional native Asian language speaking interviewers were hired to collect

data. In total the data collection process resulted in surveying 870 respondents: 250

Australian hosts and 618 Asian tourists from five language groups (106 Indonesian, 108

Japanese, 172 Korean, 130 Mandarin speaking, and 102 Thai).

The Mann-Whitney U-Test is used instead of a z-test of the means of the variables,

because not all variables were (or could be transformed to be) normally distributed.

Analysis is done on the SPSS system. The results of the Mann-Whitney U-Test

identified significant differences in all five measurement groups (cultural values, rules

of behaviour, perceptions of service, forms of interaction, satisfaction with interaction)

between the total Asian and Australian populations with seventy-three out of 117 (62.4

per cent) areas of measurement showing significant cultural differences between the

Australian and the total Asian samples (refer to Table 3).

Table 3. The Mann-Whitney U-test of the differences in cultural values, rules of social interaction, perceptions of service, forms of interaction and satisfaction with interaction between Australian hosts (n=250) and total Asian tourists (n=618)

Measurement Group z-Test z-Test z-Test

Cultural valuesa comfortable life -1.4703 Pleasure -2.0275* forgiving -0.1657an exciting life -1.1237 Salvation -5.5966*** helpful -0.0107a sense of accomplishment -1.8044 Self-respect -6.7442*** honest -3.1904**a world of peace -1.4887 social recognition -1.6728 imaginative -1.0280a world of beau -0.5049 true friendship -2.4880* independent -3.7725***Equality -2.8793** Wisdom -0.0306 intellectual -2.1053*family security -2.8891** Ambitious -2.2367* logical -0.7708Freedom -6.5026*** Broad-minded -0.4982 loving -2.6717**Happiness -3.2357** Capable -1.1952 obedient -1.0057inner harmony -2.1927* cheerful -1.7364 polite -3.3062***mature love -3.4440*** clean -2.7369** responsible -0.0102national security -1.3962 courageous -1.1777 self-controlled -2.4574*

Rules of social interactionshould address by first name -5.6758*** should take others’

time-3.2099** should have a

sense of shame-5.6699***

should shake hands -6.8501*** should develop relationship

-5.6425*** should ask for financial help

-0.6472

42

should look in the eye -9.5694*** should touch the other person

-1.2410 should ask for advice

-1.4431

should think about own needs -0.4808 should acknowledge birthday

-2.5842** should ask personal questions

-5.2496***

should express opinion -0.5112 should be neatly dressed

-1.2572 should respect others’ privacy

-6.3187***

should show intentions clearly -5.8349*** should conform to etiquette

-3.9182*** should show interest in other

-7.1359***

Should obey instructions -6.3291*** should conform to status

-2.0481* should show respect to other

-8.1729***

Should criticize in public -7.0109*** should swear in public

-5.4757*** should show affection

-1.2262

Should compliment other -7.9697*** should not make fun of other

-0.3453 should show emotions

-3.9084***

should apologize if not at fault -0.4428 should avoid arguments

-6.6947*** should talk about sensitive issues

-0.8220

should compensate if at fault -3.0403** should avoid complaining

-2.9989**

Should repay favours -0.6371 should avoid embarrassment

-0.6598

Perceptionsneatly dressed -5.2277*** polite -3.0413** keep tourists

informed-4.8190***

perform service required -6.2694*** respectful -5.0529*** listen to tourists -5.7517***responsive to tourists’ needs -6.6850*** considerate -3.2617** need adequate

explanations-3.2087**

Require help -1.2015 treat as guests -4.8425*** understand tourists’ needs

-5.6261***

prompt service -7.5167*** trustworthy -3.7197*** anticipate tourists’ needs

-5.0024***

Service on time -7.5816*** confident -0.4764 need individualized attention

-4.2763***

find solutions to problems -5.0824*** concerned about welfare

-5.4387*** know Asian culture/customs

-0.4982

answer questions -4.5351*** approachable -3.5354*** speak Asian languages

-0.3821

provide accurate information -6.4345*** easy to find -7.7714*** know Australian history/culture

-0.7542

Friendly -0.9894 easy to talk to -2.9905**

Forms of interactioninvite home -9.8994*** have close

relationship-7.8447*** exchange gifts -2.4978*

play sport together -3.6514*** share a meal -5.6582*** have business contact only

-2.6874**

share recreation facilities -0.5862 chat on a street -0.0996 have no contact at all

-0.6818

take part in family parties -7.9068*** talk in shops -0.5012

Satisfaction with tourists/hosts -4.9786*** with time spent

together-3.4804*** with service

provided-0.7144

with conversation -0.2667 with language skills

-1.9804*

with friendship -0.8191 with knowledge of others culture

-0.3272

43

* p<0.05; **p<0.01; ***p<0.001.

The Mann-Whitney U-Test also identified significant differences in all five measurement

groups between the individual Asian language groups and the Australian sample. The

Japanese were the most distinct from the Australian hosts. Out of 117 areas of

measurement, eighty-three significant differences were found between Australian hosts and

Japanese tourists, seventy-four between the Korean sample, sixty-four between the

Indonesian and Thai samples and fifty-three between the Mandarin sample (refer to Table

3).

Summary

Hypothesis testing is useful for comparing sample means from tourism surveys.

Difference between parametric and non-parametric analysis were described. The text

explained how to conduct hypothesis testing and when to use the z- and t-tests. One- and

two-tailed tests relate to the direction of the comparison between means. Single sample

means test compares a single sample mean with a population mean. Two- sample means

test compares two sample means against each other. Two samples can be paired (matched

or same individual cases) or unpaired (independent cases). Non-parametric tests can be

useful where a normal distribution cannot be assumed. One-sample non-parametric Chi-

square test is useful. A paired two-sample test example is the Wilcoxon-Signed Ranks

test. The unpaired two-sample non-parametric test is the Mann-Whitney U-test. The

multiple paired sample test is the Friedman two-way analysis of variance test and the

multiple unpaired test the Kruskal-Wallis test. Example application to tourism culture

analysis using the Mann-Whitney U-test was presented.

Discussion points and questions

1. Explain the difference between parametric and non-parametric statistical tests.

2. Why is a quantitative procedure useful in testing the relationship between

samples?

3. State three assumptions of parametric statistical tests.

4. What is the difference between unpaired and paired samples?

5. If the null hypothesis is accepted, why is the significance level not used?

44

6. What is post hoc error in hypothesis testing?

7. Create an example of a problem that would need to be analysed by the

Friedman Two-way Analysis of Variance Test.

8. Define Type II Error.

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Glossary

Achievement refers to the orientation by which people and objects are judged on the basis of

their performance.

Ascription refers to the orientation by which people assess others on the basis of inherent

qualities (gender, family heritage) and the qualities ascribed to them.

Affective neutrality is an orientation by which people express emotional self-restraint, and

their behaviour is guided by cognitive information and facts.

Affectivity is an orientation in which people look for immediate gratification and their

behaviour is guided by emotions.

93

Attitudes are a number of beliefs, and the general evaluation of people, objects or issues;

enduring dispositions to consistently respond in a given manner to various aspects of the

world; composed of affective, cognitive, and behavioural components; influenced by values;

formed on the basis of perception.

Attribution is the process by which an individual ascribes qualities and meanings to others

and objects, based on the individual’s own experiences, values, and beliefs.

Alternative hypothesis is a statement expressing the positive relationship between the two

parameters of a hypothesis test.

Beliefs are an individual’s representations of the outside world directed toward specific

objects/persons; are not accepted by all members of a social group.

Causal research is research that is conducted to identify cause–effect relationships between

variables.

Chi-square test is a hypothesis test that compares the expected and observed data

distributions.

Collateral relationships are relationships between an individual and a group.

Collective orientation is an orientation by which people are concerned about the interests

and well-being of others.

Communality in factor analysis is a measure of the percentage of a variable’s variation that

is explained by a factor.

Communication is a process through which participants create and share information as

they move toward reaching a mutual understanding, shared meaning and consensus.

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Component score is a measure of the relationships of each original data case to each of the

linear principal components in factor analysis.

Confidence level is a percentage or decimal value that states how confident a researcher can

be about being correct; shows the range of values between which the true parameter will lie

at a given probability.

Correlation coefficient is a statistical measure of the linear relationship between two or

more variables.

Cross-cultural tourist–host contact is a personal encounter between international tourists

and hosts who are members of two or more different cultural groups.

Cross-validation is a procedure that divides the sample into two parts to conduct a

validation test; it is used to compare competing models and the difference between samples

belonging to different populations, and to assess the impact of moderating variables.

Contact in this book reference is made to social contact, which is an interpersonal

interaction or association between people. For the purpose of this book ‘contact’ and

‘interaction’ are used interchangeably.

Contact hypothesis refers to social contact between individuals from different cultural

groups; it suggests that such contact may result in either positive or negative outcomes.

Cultural differences are the differences between members of different societies that are

reflected in their cultural orientations, communication patterns, social categories and

behaviour.

Cultural values are strong beliefs (opinions, mental images) of what is important,

appropriate and socially accepted in life in a wide range of situations in particular cultural

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groups; they represent cultural predispositions to social behaviour, determine perceptions,

motivation, and represent criteria and standards for evaluation.

Culture is the total way of life of a people, composed of the learned, shared and

commonly accepted cultural values, behaviour patterns, knowledge, norms, laws, beliefs,

art, morals, and material objects of a particular group of people; it distinguishes the

members of one group from another.

Culture shock is the stressful psychological and physical experience that an individual may

encounter when entering an unfamiliar environment or different culture.

Data matrix is the arrangement of numeric values into a table of rows and columns.

Degrees of freedom refer to the extent to which any data set is free to vary. Normally N-1

or the total number of values less 1.

Dependent variable is a variable that is to be predicted or explained.

Diffuseness is an orientation in which people categorize others and objects in a holistic

manner by integrating the details of patterns, structures and theories.

Dimension is a concept normally measured by a set of variables.

Endogenous constructs are constructs that are determined by other constructs and

relationships contained in a model.

Ethnocentrism is a belief in one’s own cultural superiority; judgement of others according

to the categories of one’s own culture.

Exogenous constructs are independent variables that are not determined by any other

variable.

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Exploratory research is initial research conducted to clarify and define the nature of a

problem.

Expressive orientation is an orientation in which social interactions are valued for their own

sake, for example, people value friendships.

Factor analysis is a statistical method designed to identify the underlying dimensions in

a data matrix; it reduces the number of analysed variables to another minimum number of

underlying common dimensions (factors) to explain the variety in a set of observed

variables.

Factor loading in factor analysis, is a measure of the importance of each variable in

measuring each factor.

Factor rotation is a method used to rotate the factor around the origin so as to increase the

‘fit’ of the factors to the variables.

Factor scores are the scores equivalent to principal component scores, calculated in Factor

analysis.

Feminine culture is one in which social roles of gender are equal; is concerned with social

welfare and social justice.

Fit measures are the measures that assess the overall fit of a model to data.

Frequency distribution is an organized set of data counting the number of times a particular

value of a variable occurs.

F-statistic is a test statistic that measures the proportion of one sample variance to another

sample variance, as well as the variance between groups to the variance within groups.

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F-test (analysis of variance) is a test that determines whether there is more variability in the

scores of one sample than in the scores of another sample.

High-context culture is one in which the meanings of a communication message are

stated in indirect ways, mostly conveyed in non-verbal codes, and depend on the context

of the communication and situation.

Host is a resident of the visited country, working in the tourism industry, associating, taking

care of, and providing service to tourists such as hoteliers, front office employees, waiters,

shop assistants, custom officials, tour guides, taxi and bus drivers.

Hypothesis is an unproven proposition stated as a premise – a proposition that is empirically

testable.

Hypothesis testing is a statistical procedure that determines, in terms of probability, whether

the observed differences between sample data could easily occur by chance or not;

comprises two mutually exclusive statements (premises), the alternative and null

hypotheses. The objective of the statistical procedure is to determine by probability which

hypothesis (null or alternative) is true.

Image is a mental picture, idea, impression or representation of others or objects in the

individual’s mind.

Independent variable is a variable that predicts or explains the dependent variable, and is

independent of each other independent variable.

Individualist relationships are the relationships that emphasize individualism in

interpersonal relations.

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Individualistic culture is one in which the individual’s goals are valued more than those

of the community or group.

Instrumental orientation is an orientation in which social interactions help to achieve

certain goals; for example, social contacts can be used to find jobs.

Intercept is a point at which a regression line intersects the Y-axis on an X and Y graph.

Intercultural communication is communication between at least two individuals who are

culturally different from each other in their value orientation, preferred communication

codes, role expectations, and perceived rules of social interaction; depends on cultural

exclusivity, personal individuality and uniqueness; must acknowledge differences between

people.

Interculturalness is the extent of cultural similarity or difference between contact

participants.

Intercultural contact involves direct face-to-face encounters between individuals with

differing cultural backgrounds.

Intercultural tourist–host contact is a personal encounter between international tourists and

hosts who are members of two different cultural groups.

International tourist is a temporary overseas visitor (culturally different) arriving in a

different country for a minimum 24 hours and maximum 12 months, for the purpose of

leisure, recreation, holiday, health, study, religion, sport, business, family or meeting.

Interval scale is a scale that places and distinguishes objects according to their importance

in units of equal interval, away from an unknown zero location.

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Kaiser’s Varimax rotation is the most commonly used method of orthogonal rotation in

factor analysis, which maximizes the variance between the dimensions.

Latent variables are variables that are not directly observed and measured.

Lineal relationships are relationships that are characterized by hierarchy in society,

obedience and loyalty to authority, feelings of duty, submission to the group and elders.

LISREL stands for LInear Structural RELationships; it is a statistical package designed to

estimate models involving linear structural relationships among observed and unobserved

variables; it represents an attempt to establish a chain of cause and effect between

variables.

Long-term orientation stands for the fostering of virtues oriented towards future rewards, in

particular perseverance, thrift, patience and savings; it is the opposite of short-term

orientation; together they form a dimension of national cultures labelled ‘Confucian

dynamism’.

Low-context culture is one in which the messages of communication and their meanings

are stated clearly and explicitly and don’t depend on the context of the communication

situation.

Masculine culture is one in which social gender roles are clearly distinct: men are supposed

to be assertive, tough and focus on achievement and material success; women are supposed

to be more modest, gentle and concerned with the quality of life.

Measurement model is the formal specification of the model that describes which variables

measure which constructs; it translates the path diagram in structural equation modelling

into a series of linear equations which link constructs together.

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Measures of association is a term that refers to statistical techniques that measure the

strength of a relationship between variables.

Model identification is the extent to which the information provided by data is sufficient to

enable parameter estimation.

Modification indices are the indices that are used to decide which parameters should be

added or deleted from a structural equation model.

Motivation is a psychological force, which induces and drives an individual to choose one

action over another.

Multiculturalism is the recognition and acceptance that several different cultures can

exist in the same environment and benefit each other.

Multiple-paired sample test determines whether there are any significant differences

between three or more samples, to establish whether or not they are drawn from the same

population.

National culture refers to the collective programming of the mind by people of a particular

country.

Needs are necessities and wants arising from the circumstances of a case, situation or time;

conditioned by the lack of something requisite; are determined by cultural values.

Nominal scale is a scale in which the numbers or letters are assigned to an object for its

identification or classification. Normally measured numbers cannot be arithmetically manipulated.

Non-parametric hypothesis testing refers to non-parametric statistical techniques that do

not require the use of statistical parameters such as the mean and standard deviation.

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Normal distribution is a symmetrical bell-shaped distribution showing that the expected

probability distribution of a variable varies uniformly away from the mean.

Norms are special rules and refer to established behaviour patterns for the members of a

social system; contain a statement of ideal behaviour; their acceptance or rejection depends

on values; are not standards and do not have ‘ought’ character.

Null hypothesis is a statement expressing the ‘no’ or negative relationship between the

two parameters of the hypothesis test.

Oblique rotation is the rotation by which the angle between the factors (dimensions) in a

factor analysis can be found to be other than at 90°.

Offending estimates are coefficients that exceed pre-specified limits.

One-sample means test is a statistical test that compares a single sample mean against a

known population mean.

One-sample non-parametric test is a statistical test that determines whether there is a

significant difference between the observed frequencies of nominal data and those

expected to occur in a uniform or known distribution.

One-tailed hypothesis test is a statistical test wherein the direction of the comparison of

the sample statistic against the population parameter is known in advance.

Orthogonal rotation is a rotation in which the factors (dimensions) are always kept at a

maximum degree (90°) during rotation in a factor analysis procedure.

Paired-sample parametric test is a statistical test that compares whether two statistics

from matched samples come from the same population.

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Parameter is a variable or measured characteristic of a population.

Parametric hypothesis testing refers to parametric statistical techniques that test hypotheses

involving parameters such as the mean and standard deviation.

Particularism refers to the manner by which people use particular rules to describe others,

objects and the universe in specific categories that are unique to the situation; opposite of

universalism.

Path diagram is a graphically presented diagram that shows all relationships between

constructs and their indicators described by geometric symbols; represents a visual

representation of the hypothesis and the measurement scheme in a structural equation

analysis.

Perceptions are feelings, impressions, thoughts, beliefs; the ways in which people see the

world and assign meanings to objects or situations; depend on external factors such as the

cultural environment, and internal factors such as the characteristics of the perceivers;

predispositions to act in a predictable manner; influence evaluation and satisfaction; allow

for interpretation of others interaction; can be changed over time.

Population is any complete group of entities (people, objects) that share some common

characteristics.

Population distribution refers to a frequency distribution of the elements of a population.

Population element is an individual member of a population.

Population parameters are the variables in a population or measured characteristics of the

population.

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Power distance culture is one in which the more powerful members of a society control

resources and demand obedience of those who do not have power; the power is distributed

unequally.

Rokeach Value Survey is an instrument for measuring human values developed by

Rokeach.

Principal Components Analysis finds the dimensions of a large data set on the basis of

dividing total variance into as many distinguishable groups as possible.

Probability is the long-term relative frequency with which an event occurs, and hence the

percentage chance of an event occurring.

Probability distribution is a distribution of all possible outcomes and their probabilities.

Q-plot is the picture of fit obtained by plotting the standardized residuals (horizontal axis)

against the quartiles of the normal distribution (vertical axis).

Quantitative methods are the scientific techniques that provide a wide and sophisticated set

of inter-related statistical analysis tools that are applied to research using data measured at

the nominal to ratio scale.

Random error is an error that occurs by chance due to unexplained variation.

Ranking is a measurement procedure that requires respondents to rank in order a set of

objects or people in overall preference or on the basis of some characteristic.

Rating is a measurement procedure that requires respondents to rate a set of objects or

people in overall preference or on the basis of some characteristic.

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Ratio scale is a uniform scale that has absolute rather than relative quantities measured in

known intervals from zero.

Reliability is the degree to which measures are free from random error and thus yield

consistent results.

Research objective is the researcher’s interpretation of the problem at hand; it explains the purpose

of the research in measurable terms, identifies variables and defines goals which research should

accomplish.

Residual is the difference between the actual value of the dependent variable and the

estimated value of the dependent variable in a regression equation.

Rotation in factor analysis, a new solution that is obtained by rotating the axes representing

factors (dimensions); produces clearer divisions between factors (dimensions).

Rules of social interaction are principles by which interpersonal interaction should

conform, standards of behaviour, customs; provide directives and regulate social contact,

indicate what is permitted and not permitted in personal interaction; and represent a base for

expectations from interaction.

Sample bias is a tendency for the results of a sample to deviate in one direction from the

true value.

Sample size is the number of sampling units in a study.

Sampling is the process by which a chosen number of items or parts of a large population

are used to make inferences about the whole population.

Sampling frame is a list of elements from which a sample may be drawn.

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Satisfaction are positive feelings, reactions, contentment obtained from fulfilling needs and

wants considered important; psychological outcome deriving from an experience; it is a

function of expectations and perceptions.

Self-orientation is an orientation in which people emphasize own goals and needs, look

after themselves and take on individual initiatives.

Semantic differential is a measure of attitudes that consist of a series of 7-point rating scales

that use bipolar adjectives at the beginning and end of each scale.

Service quality is concerned with the attributes of the service itself; way of thinking about

how to satisfy customers so that they hold positive perceptions of the service.

Short-term orientation stands for the fostering of virtues related to the past and present, in

particular respect for tradition, preservation of ‘face’, and fulfilling social obligation; is the

opposite of long-term orientation and together they form a dimension of national cultures

labelled ‘Confucian dynamism’.

Significance level is the critical probability in choosing between the null and alternative

hypotheses; the probability level that is too low to support a null hypothesis.

Slope is the inclination of a regression line as compared to a base line.

Specificity is an orientation in which people categorize others and objects according to

specific details such a facts, tasks, and numbers.

Split-half method is a method that assesses reliability by measuring the degree of internal

consistency; it tests the results of one-half of a set of scaled items against the results from

the other half.

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Standardized normal distribution is a purely theoretical probability distribution that shows

a specific normal curve for the standardized value z; a normal curve has a mean of 0 and a

standard deviation of 1.

Statistically significant is a term indicating that the relationship between two measures is

sufficiently strong to eliminate the possibility that it is due to pure chance. The

‘significance level’, usually 0.05 or 0.001, is the risk that the relationship could be

accidental.

Stereotyping refers to the attribution of certain traits, labelling and perceptions of people and

objects on the basis of common characteristics; judging others on the basis of their ethnic

group membership, occupation, age or sex; a generalization about some group of people that

oversimplifies their culture.

Structural equation modelling is a multivariate statistical technique that determines the

pattern of a series of inter-related dependence relationships simultaneously between latent

constructs, each measured by observed variables; it combines multiple regression and factor

analysis.

Structural model is a model that shows the defined relationships between latent constructs

and their measurable variables, reflecting proposed hypotheses.

Subculture refers to similarity among people based on race, ethnicity, a geographic region,

economic or social class that is normally found in a small group within another larger

cultural cluster.

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T-distribution is a symmetrical, bell-shaped distribution that is dependent upon sample

size; it has a mean of 0 and a standard deviation equal to1.

Test–retest method is a method that measures reliability by administering the same scale or measure to the same respondents at two separate occasions in time to test for stability.

Total variance is the sum of within-group variance and between-group variance.

T-test is a uni-variate hypothesis test that uses the t-distribution rather than the z-distribution; it is used when the population standard deviation is unknown and the sample size is small.

T-test for difference of means is a procedure that tests the hypothesis to see whether the

mean scores on some interval- or ratio-scaled variable will be significantly different for

two independent samples or groups.

Two-tailed hypothesis test is a statistical test wherein the direction of the comparison of

the sample statistic against the population parameter is not known in advance.

Two-sample means test determines whether two sample means come from the same

population.

Type I error occurs when the null hypothesis is rejected when in fact it is true.

Type II error occurs when the null hypothesis is accepted when in fact it is false.

Uncertainty avoidance culture is one in which the members of a culture feel threatened by

uncertain situations and behaviour.

Universalism refers to the manner by which people describe themselves and objects

according to universal and general rules by following a standardized pattern.

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Unpaired parametric test is a statistical test that uses data measured at least at the

interval scale to determine whether unrelated samples come from the same population or

not.

Validity is the ability of the scale to measure what was intended to be measured.

Variable is anything that may be assigned different numerical values.

Variance is a measure of dispersion – the degree to which items in a sample or population

differ in numeric size.

Values are what people who share the same culture regard strongly as good or bad.

Z-test is a hypothesis test that uses the standardized normal distribution to establish expected

probability.

Z-test for difference of proportions is used to test the hypothesis that two proportions will

be significantly different for two independent samples or groups.

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