SCALES OF MEASUREMENT - ahmadbo.com · •Interjudge reliability can be defined degree of consistency between coders processing the same data (Kassarjian 1977). © 2012 John Wiley

Research Methods for Business

Ahmad Othman @2006 1

Data Analysis (Burns, 2000; Schloss & Smith, 1999)

PARAMETRIC versus NON-PARAMETRIC TESTS

Parametric tests make probability judgment with hypothetical sampling distribution.

Non-parametric tests make probability judgments without hypothetical distribution.

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Advantage & Disadvantage

0902_Characteristic of hypothesis.ppt

01_Main menu_research.ppt

0901_Advantage & Disadvantage.ppt




SCALES OF MEASUREMENT

The data may be

nominal,

ordinal,

interval or

ratio.

[Test]

Main Menu

094_Nominal scale.ppt

095_Ordinal scale.ppt

096_Interval scale.ppt

097_Ratio.ppt

098_Test.ppt

01_Main menu_research.ppt




PARAMETRIC STATISTICS

Parametric statistics make certain assumptions about population parameters.

What are the assumptions?




Assumption #1

The scores in the population are normally distributed about the mean.




Assumption #2

The population variances of the comparison groups in one’s study are approximately equal.




Assumption #3

The scores being analyzed are derived from a measure that has equal intervals.



Statistical Tools (Borg & Gall, 1989)

To analyze research results effectively, four kinds of information about statistical tools are needed.

1. What statistical tools are available?

2. Under what conditions each tools is used?

3. What the statistical results mean?

4. How the statistical calculations are made?

0903_Statistical tool available.ppt




Relationshiphypothesis

Difference or relationship

hypothesis

Differencehypothesis

Between subjects-or matched within-

subjects

Non-parametricSpearman rank order correlation

ParametricPearson product-moment correlation

Between

Start here

Within ormatched

Parametric

Independentt test

Non-Parametric

Mann-Whitney

Parametric

Relatedt test

Non-Parametric

Wilcoxon

091_T test.ppt


9

Chapter 16

Qualitative Data Analysis

© 2012 John Wiley & Sons Ltd. www.wiley.com/college/sekaran


Qualitative Data

• Qualitative data: data in the form of words.

• Examples: interview notes, transcripts of focus groups, answers to open-ended questions, transcription of video recordings, accounts of experiences with a product on the internet, news articles, and the like.



Analysis of Qualitative Data

• The analysis of qualitative data is aimed at making valid inferences from the often overwhelming amount of collected data.

• Steps:

– data reduction

– data display

– drawing and verifying conclusions



Data Reduction

• Coding: the analytic process through which the qualitative data that you have gathered are reduced, rearranged, and integrated to form theory.

• Categorization: is the process of organizing, arranging, and classifying coding units.



Data Display

• Data display: taking your reduced data and displaying them in an organized, condensed manner.

• Examples: charts, matrices, diagrams, graphs, frequently mentioned phrases, and/or drawings.



Drawing Conclusions

• At this point where you answer your research questions by determining what identified themes stand for, by thinking about explanations for observed patterns and relationships, or by making contrasts and comparisons.



Reliability in Qualitative Research

• Category reliability “depends on the analyst’s ability to formulate categories and present to competent judges definitions of the categories so they will agree on which items of a certain population belong in a category and which do not.” (Kassarjian, 1977, p. 14).

• Interjudge reliability can be defined degree of consistency between coders processing the same data (Kassarjian 1977).



Validity in Qualitative Research

• Validity refers to the extent to which the qualitative research results:

– accurately represent the collected data (internal validity)

– can be generalized or transferred to other contexts or settings (external validity).



Getting the Data Ready for Analysis

• Data coding: assigning a number to the participants’ responses so they can be entered into a database.

• Data Entry: after responses have been coded, they can be entered into a database. Raw data can be entered through any software program (e.g., SPSS)



Editing Data

• An example of an illogical response is an outlier response. An outlier is an observation that is substantially different from the other observations.

• Inconsistent responses are responses that are not in harmony with other information.

• Illegal codes are values that are not specified in the coding instructions.



Transforming Data



Getting a Feel for the Data



Frequencies



Descriptive Statistics: Central Tendencies and Dispersions



Reliability Analysis



24

Chapter 15

Quantitative Data Analysis: Hypothesis Testing



Type I Errors, Type II Errors and Statistical Power

• Type I error (): the probability of rejecting the null hypothesis when it is actually true.

• Type II error (): the probability of failing to reject the null hypothesis given that the alternative hypothesis is actually true.

• Statistical power (1 - ): the probability of correctly rejecting the null hypothesis.



Choosing the Appropriate Statistical Technique



Testing Hypotheses on a Single Mean

• One sample t-test: statistical technique that is used to test the hypothesis that the mean of the population from which a sample is drawn is equal to a comparison standard.



Testing Hypotheses about Two Related Means

• Paired samples t-test: examines differences in same group before and after a treatment.

• The Wilcoxon signed-rank test: a non-parametric test for examining significant differences between two related samples or repeated measurements on a single sample. Used as an alternative for a paired samples t-test when the population cannot be assumed to be normally distributed.



Testing Hypotheses about Two Related Means - 2

• McNemar's test: non-parametric method used on nominal data. It assesses the significance of the difference between two dependent samples when the variable of interest is dichotomous. It is used primarily in before-after studies to test for an experimental effect.



Testing Hypotheses about Two Unrelated Means

• Independent samples t-test: is done to see if there are any significant differences in the means for two groups in the variable of interest.



Testing Hypotheses about Several Means

• ANalysis Of VAriance (ANOVA) helps to examine the significant mean differences among more than two groups on an interval or ratio-scaled dependent variable.



Regression Analysis

• Simple regression analysis is used in a situation where one metric independent variable is hypothesized to affect one metric dependent variable.



Scatter plot

30 40 50 60 70 80 90

PHYS_ATTR

20

40

60

80

100

LK

LH

D_

DA

TE



Simple Linear Regression

Y

X

0̂0̂0̂ 0̂ 0̂ 0̂ `0?

0̂

iii XY 10

1̂

1



Ordinary Least Squares Estimation

Yi

Xi

Yiei

n

1i

2i Minimize e

ˆ



SPSS

Analyze Regression Linear

Model Summary

.841 .707 .704 5.919

Model

1

R R Square

Adjusted

R Square

Std. Error of

the Estimate

ANOVA

8195.319 1 8195.319 233.901 .000

3398.640 97 35.038

11593.960 98

Regression

Residual

Total

Model

1

Sum of

Squares df Mean Square F Sig.



SPSS cont’d

Coefficients

34.738 2.065 16.822 .000

.520 .034 .841 15.294 .000

(Constant)

PHYS_ATTR

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.



Model validation

1. Face validity: signs and magnitudes make sense

2. Statistical validity:

– Model fit: R2

– Model significance: F-test

– Parameter significance: t-test

– Strength of effects: beta-coefficients

– Discussion of multicollinearity: correlation matrix

3. Predictive validity: how well the model predicts

– Out-of-sample forecast errors



SPSS

Model Summary

.841 .707 .704 5.919

Model

1

R R Square

Adjusted

R Square

Std. Error of

the Estimate



Measure of Overall Fit: R2

• R2 measures the proportion of the variation in y that is explained by the variation in x.

• R2 = total variation – unexplained variation

total variation

• R2 takes on any value between zero and one:– R2 = 1: Perfect match between the line and the data points.

– R2 = 0: There is no linear relationship between x and y.



SPSS

Model Summary

.841 .707 .704 5.919

Model

1

R R Square

Adjusted

R Square

Std. Error of

the Estimate

= r(Likelihood to Date, Physical Attractiveness)



Model Significance

• H0: 0 = 1 = ... = m = 0 (all parameters are zero)

H1: Not H0



Model Significance

• H0: 0 = 1 = ... = m = 0 (all parameters are zero)

H1: Not H0

• Test statistic (k = # of variables excl. intercept)

F = (SSReg/k) ~ Fk, n-1-k

(SSe/(n – 1 – k)

SSReg = explained variation by regression

SSe = unexplained variation by regression



SPSS

ANOVA

8195.319 1 8195.319 233.901 .000

3398.640 97 35.038

11593.960 98

Regression

Residual

Total

Model

1

Sum of




Parameter significance

• Testing that a specific parameter is significant (i.e., j 0)

• H0: j = 0

H1: j 0

• Test-statistic: t = bj/SEj ~ tn-k-1

with bj = the estimated coefficient for j

SEj = the standard error of bj



SPSS cont’d

Coefficients

34.738 2.065 16.822 .000

.520 .034 .841 15.294 .000

(Constant)

PHYS_ATTR

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.



Conceptual Model

Physical Attractiveness

Likelihood to Date

+


Multiple Regression Analysis

• We use more than one (metric or non-metric) independent variable to explain variance in a (metric) dependent variable.


Conceptual Model

Perceived Intelligence


+

+Likelihood

to Date


Model Summary

.844 .712 .706 5.895

Model

1

R R Square

Adjusted

R Square

Std. Error of

the Estimate

ANOVA

8257.731 2 4128.866 118.808 .000

3336.228 96 34.752

11593.960 98

Regression

Residual

Total

Model

1

Sum of


Coefficients

31.575 3.130 10.088 .000

.050 .037 .074 1.340 .183

.523 .034 .846 15.413 .000

(Constant)

PERC_INTGCE

PHYS_ATTR

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.


Conceptual Model



Likelihood to Date

Gender

+ +

+


Moderators• Moderator is qualitative (e.g., gender, race, class) or quantitative

(e.g., level of reward) that affects the direction and/or strength of the relation between dependent and independent variable

• Analytical representation

Y = ß0 + ß1X1 + ß2X2 + ß3X1X2

with Y = DVX1 = IVX2 = Moderator


Model Summary

.910 .828 .821 4.601

Model

1

R R Square

Adjusted

R Square

Std. Error of

the Estimate

ANOVA

9603.938 4 2400.984 113.412 .000

1990.022 94 21.170

11593.960 98

Regression

Residual

Total

Model

1

Sum of



Coefficients

32.603 3.163 10.306 .000

.000 .043 .000 .004 .997

.496 .027 .802 18.540 .000

-.420 3.624 -.019 -.116 .908

.127 .058 .369 2.177 .032

(Constant)

PERC_INTGCE

PHYS_ATTR

GENDER

PI_GENDER

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.

interaction significant effect on dep. var.


Conceptual Model



Communality of Interests

Likelihood to Date

Gender

Perceived Fit

+ +

+

+

+


Mediating/intervening variable• Accounts for the relation between the independent and

dependent variable

• Analytical representation

1. Y = ß0 + ß1X=> ß1 is significant

2. M = ß2 + ß3X=> ß3 is significant

3. Y = ß4 + ß5X + ß6M=> ß5 is not significant=> ß6 is significant

With Y = DV

X = IV

M = mediator


Step 1

Model Summary

.963 .927 .923 3.020

Model

1

R R Square

Adjusted

R Square

Std. Error of

the Estimate

ANOVA

10745.603 5 2149.121 235.595 .000

848.357 93 9.122

11593.960 98

Regression

Residual

Total

Model

1

Sum of



Step 1 cont’d

Coefficients

17.094 2.497 6.846 .000

.030 .029 .044 1.039 .301

.517 .018 .836 29.269 .000

-.783 2.379 -.036 -.329 .743

.122 .038 .356 3.201 .002

.212 .019 .319 11.187 .000

(Constant)

PERC_INTGCE

PHYS_ATTR

GENDER

PI_GENDER

COMM_INTER

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.

significant effect on dep. var.


Step 2

Model Summary

.977 .955 .955 2.927

Model

1

R R Square

Adjusted

R Square

Std. Error of

the Estimate

ANOVA

17720.881 1 17720.881 2068.307 .000

831.079 97 8.568

18551.960 98

Regression

Residual

Total

Model

1

Sum of



Step 2 cont’d

Coefficients

8.474 1.132 7.484 .000

.820 .018 .977 45.479 .000

(Constant)

COMM_INTER

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.

significant effect on mediator


Step 3

Model Summary

.966 .934 .930 2.885

Model

1

R R Square

Adjusted

R Square

Std. Error of

the Estimate

ANOVA

10828.336 6 1804.723 216.862 .000

765.624 92 8.322

11593.960 98

Regression

Residual

Total

Model

1

Sum of



Step 3 cont’d

Coefficients

14.969 2.478 6.041 .000

.019 .028 .028 .688 .493

.518 .017 .839 30.733 .000

-2.040 2.307 -.094 -.884 .379

.142 .037 .412 3.825 .000

-.051 .085 -.077 -.596 .553

.320 .102 .405 3.153 .002

(Constant)

PERC_INTGCE

PHYS_ATTR

GENDER

PI_GENDER

COMM_INTER

PERC_FIT

Model

1

B Std. Error

Unstandardized

Coefficients

Beta

Standardized

Coefficients

t Sig.

significant effect of mediator on dep. var.

insignificant effect of indep. var on dep. Var.

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SCALES OF MEASUREMENT - ahmadbo.com · •Interjudge reliability can be defined degree of consistency between coders processing the same data (Kassarjian 1977). © 2012 John Wiley