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MASTER OF BUSINESS ADMINISTRATION
NAME – KAUSHAL KUMAR
REGISTRATION NO. – 521101945 LEARNING CENTER NAME –
LEARNING CENTER CODE –
COURSE – MBA
SEMESTER – 1
SUBJECT – MB0040 – Statistics For Management
SET NO. –
DATE OF SUBMISSION –
MARKS AWARDED–
Directorate of Distance Learning
Sikkim Manipal University
II Floor, Syndicate Building
Manipal – 576 104
Signature of the Coordinator Signature of the LC Signature of Evaluator
MB0040 – Statistics For ManagementAssignment Set- 1
Question. 1
(a) ‘Statistics is the backbone of decision-making’. Comment. (b) Give plural meaning of the word Statistics?
Answer.1 (a) Due to advanced communication network, rapid changes in
consumer behavior, varied expectations of variety of consumers and new market openings, modern managers have a difficult task of making quick and appropriate decisions. Therefore, there is a need for them to depend more upon quantitative techniques like mathematical models, statistics, operations research and econometricsAs you can see, what the General Manager is doing here is using Statistics to solve a problem and to increase profits. Decision making is a key part of our day-to-day life. Even when we wish to purchase a television, we like to know the price, quality, durability, and maintainability of various brands and models before buying one. As you can see, in this scenario we are collecting data and making an optimum decision. In other words, we are using Statistics. Again, suppose a company wishes to introduce a new product, it has to collect data on market potential, consumer likings, availability of raw materials, feasibility of producing the product. Hence, data collection is the back-bone of any decision making process.
Many organizations find themselves data-rich but poor in drawing information from it. Therefore, it is important to develop the ability to extract meaningful information from raw data to make better decisions. Statistics play an important role in this aspect
(b) Statistics a plural noun :- In its plural sense , Statistics refers to information in terms of numbers or numerical data , such ae population statistics , employment statistics , statistics concerning public expenditure, etc. However, any numerical information is not a statistics. To say, Ram gets Rs.25 per month as per rocket allowance is not statistics .It is the aggregate of data or average that qualifies to be called as statistics, such as; average pocket allowance of the student of class X is Rs. 25 per month, or there are 80 students in class XI compare to just 8 in class XII of your school.
The following table shows a set of data which is statistics, and another set which is not statistics: the figures used are hypothetical.
Data which are not statistics Data which are statistics
1. A cow has 4 legs. 1. Average height of the 26-plus male people in India is 6 feet compared to 5 feet in Nepal.
2. Ram has 100 rupees in pocket. 2. Birth rate in India is 18 per thousand compared to 8 per thousand in U.S.A.
3. A young lady was run over by a speeding truck.
3. Over the past 10 years, India has won 60 test matches in cricket and lost 50.
Question.2-
(a). In a bivariate data on ‘x’ and ‘y’, variance of ‘x’ = 49, variance of ‘y’ = 9 and covariance (x,y) = -17.5. Find coefficient of correlation between ‘x’ and ‘y’.
(b).Enumerate the factors which should be kept in mind for proper planning
Answer.2 – We know that:
r ¿ ∑ xyNσxσy
Given r=∑ xy
N = 17.5
σx=√47=7 σy= √9=3
r ¿ 17 .57 x 3 =0.833
Hence, there is a highly negative correlation .
(b) Planning of a Statistical Survey.
The relevance and accuracy of data obtained in a survey depends upon the care exercised in planning. A properly planned investigation can lead to best results with least cost and time. The planning stage consists of the following sequence of activities.
1. Nature of the problem to be investigated should be clearly defined in an un ambiguous manner.
2. Objectives of investigation should be stated at the outset. Objectives could be to obtain certain estimates or to establish a theory or to verify a existing statement to find relationship between characteristics etc.
3. The scope of investigation has to be made clear. It refers to area to be covered, identification of units to be studied, nature of characteristics to be observed, accuracy of measurements, analytical methods, time, cost and other resources required.
4. Whether to use data collected from primary or secondary source should be determined in advance.
5. The organization of investigation is the final step in the process. In encompasses the determination of number of investigators required, their training, supervision work needed, funds required etc.
Question.3.The percentage sugar content of Tobacco in two samples was represented in table 11.11. Test whether their population variances are same.
Table 1. Percentage sugar content of Tobacco in two samples
Sample A 2.4 2.7 2.6 2.1 2.5
Sample B 2.7 3.0 2.8 3.1 2.2 3.6
Answer.3- The tables 11.11a and 11.11b represent the frequency table required for the calculation of sample means for the data given for two
different methods.
Table 11.11a
x d= x-2.5 d2
2.4 -0.1 0.012.7 0.2 0.042.6 0.1 0.012.1 -0.4 0.162.5 0 0
total -0.2 0.22
Table 11.11b
x d= x-3 d2
2.7 -0.3 0.093.0 0 02.8 -0.2 0.043.1 0.1 0.012.2 -0.8 0.643.6 0.6 0.36
total -0.6 1.14
=14 [ 0.22 - 0.04 / 5 ]
= 0.053
= 156
[1.23-0.053]
= 0.244
not significant
Q4. a. Explain the characteristics of business forecasting.
b. Differentiate between prediction, projection and forecasting.
Answer 4-(a).
Characteristics of business forecasting Based on past and present conditions Business forecasting is based on past and present economic condition of the business. To forecast the future, various data, information and facts concerning to economic condition of business for past and present are analysed. Based on mathematical and statistical methods The process of forecasting includes the use of statistical and mathematical methods. By using these methods, the actual trend which may take place in future can be forecasted. Period The forecasting can be made for long term, short term, medium term or any specific period. Estimation of future The business forecasting is to forecast the future regarding probable economic conditions. Scope The forecasting can be physical as well as financial.
B. A prediction is a statement about the way things will happen in the future, often but not always based on experience or knowledge. While there is much overlap between prediction and forecast, a prediction may be a statement that some outcome is expected, while a forecast may cover a range of possible outcomes. Prediction is closely related to uncertainty. Reference class forecasting was developed to eliminate or reduce uncertainty in prediction
“Forecasting aims to tell of events before they happen. It differs from prediction in that it looks to the future, where as prediction may not (as in a successful reconstruction of some past outcome). Further, forecasting differs from explanation, having the goal of predicting an outcome, rather than the goal of theorising about outcomes. “
A financial projection consists of prospective financial statements that present, given one or more hypothetical assumptions, an entity's expected financial position, results of operations, and cash flows. A financial projection is sometimes prepared to present one or more hypothetical courses of action for evaluation, as in response to a “what if?” scenario.The key difference between a forecast and a projection is the nature of the assumptions. In a forecast, the assumptions represent the company's expectations of actual future events. A projection is used when the assumptions desired are not those believed to be most likely (essentially, the "what if?" scenario).
(b) Prediction, projection and forecasting A great amount of confusion seem to have grown up in the use of words ‘forecast’, ‘prediction’ and ‘projection’.
Forecasts are made by estimating future values of the external factors by means of prediction, projection or forecast and from these values calculating the estimate of the dependent variable.
Question.5-What are the components of time series? Bring out the significance of moving average in analyzing a time series and point out its limitations.
Answer.5 The four components of time series are:
1. Secular trend2. Seasonal variation3. Cyclical variation4. Irregular variation
Secular trend: A time series data may show upward trend or downward trend for a period of years and this may be due to factors like increase in population, change in technological progress, large scale shift in consumer’s demands, etc. For example, population increases over a period of time, price increases over a period of years, production of goods on the capital market of the country increases over a period of years. These are the examples of upward trend. The sales of a commodity may decrease over a period of time because of better products coming to the market. This is an example of declining trend or downward trend. The increase or decrease in the movements of a time series is called Secular trend.
Seasonal variation: Seasonal variation is short-term fluctuation in a time series which occur periodically in a year. This continues to repeat year after year. The major factors that are responsible for the repetitive pattern of seasonal variations are weather conditions and customs of people. More woollen clothes are sold in winter than in the season of summer .Regardless of the trend we can observe that in each year more ice creams are sold in summer and very little in winter season. The sales in the departmental stores are more during festive seasons that in the normal days.
Cyclical variations: Cyclical variations are recurrent upward or downward movements in a time series but the period of cycle is greater than a year. Also these variations are not regular as seasonal variation. There are different types of cycles of varying in length and size. The ups and downs in business activities are the effects of cyclical variation. A business cycle showing these oscillatory movements has to pass through four phases-prosperity, recession, depression and recovery. In a business, these four phases are completed by passing one to another in this order.
Irregular variation: Irregular variations are fluctuations in time series that are short in duration, erratic in nature and follow no regularity in the occurrence pattern. These variations are also referred to as residual variations since by definition they represent what is left out in a time series after trend, cyclical and seasonal variations. Irregular fluctuations results due to the occurrence of unforeseen events like floods, earthquakes, wars, famines, etc.
Merits and demerits of moving averages method
Merits Demerits
This is a simple method. No functional relationship between the values and the time. Thus, this method is not helpful in forecasting and predicting the values on the basis of time.
This method is objective in the sense that anybody working on a problem with this method will get the same results.
No trend values for some years in the beginning and some in the end. For example, for 5 – yearly moving average, there will be no trend values for the first two years and the last three years.
This method is used for determining seasonal, cyclic and irregular variations besides the trend values.
In case of non–linear trend, the values obtained by this method are biased in one or the other direction.
This method is flexible enough to add more figures to the data because the entire calculations are not changed.
The period selection of moving average is a difficult task. Hence, great care has to be taken in period selection, particularly when there is no business cycle during that time.
If the period of moving averages coincides with the period of cyclic fluctuations in the data, such fluctuations are
automatically eliminated.
Question.6- List down various measures of central tendency and explain the difference between them?
b. What is a confidence interval, and why it is useful? What is a confidence level?
Answer.6 :-( A) Measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. As such, measures of central tendency are sometimes called measures of central location. They are also classed as summary statistics. The mean (often called the average) is most likely the measure of central tendency that you are most familiar with, but there are others, such as, the median and the mode.
The mean, median and mode are all valid measures of central tendency but, under different conditions, some measures of central tendency become more appropriate to use than others. In the following sections we will look at the mean, mode and median and learn how to calculate them and under what conditions they are most appropriate to be used.
Mean (Arithmetic)
The mean (or average) is the most popular and well known measure of central tendency. It can be used with both discrete and continuous data, although its use is most often with continuous data (see our Types of Variable guide for data types). The mean is equal to the sum of all the values in the data set divided by the number of values in the data set. So, if we have n values in a data set and they have values x1, x2, ..., xn, then the sample mean, usually denoted by (pronounced x bar), is:
This formula is usually written in a slightly different manner using the Greek capitol letter, , pronounced "sigma", which means "sum of...":
You may have noticed that the above formula refers to the sample mean. So, why call have we called it a sample mean? This is because, in statistics, samples and populations have very different meanings and these differences are very important, even if, in the case of the mean, they are calculated in the same way. To acknowledge that we are calculating the population mean and not the sample mean, we use the Greek lower case letter "mu", denoted as µ:
The mean is essentially a model of your data set. It is the value that is most common. You will notice, however, that the mean is not often one of the actual values that you have observed in your data set. However, one of its important properties is that it minimises error in the prediction of any one value in your data set. That is, it is the value that produces the lowest amount of error from all other values in the data set.
An important property of the mean is that it includes every value in your data set as part of the calculation. In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero.
When not to use the mean
The mean has one main disadvantage: it is particularly susceptible to the influence of outliers. These are values that are unusual compared to the rest of the data set by being especially small or large in numerical value. For example, consider the wages of staff at a factory below:
Staff 1 2 3 4 5 6 7 8 9 10
Salary 15k 18k 16k 14k 15k 15k 12k 17k 90k 95k
The mean salary for these ten staff is $30.7k. However, inspecting the raw data suggests that this mean value might not be the best way to accurately reflect the typical salary of a worker, as most workers have salaries in the $12k to 18k range. The mean is being skewed by the two large salaries. Therefore, in this situation we would like to have a better measure of central tendency. As we will find out later, taking the median would be a better measure of central tendency in this situation.
Another time when we usually prefer the median over the mean (or mode) is when our data is skewed (i.e. the frequency distribution for our data is skewed). If we consider the normal distribution - as this is the most frequently assessed in statistics - when the data is perfectly normal then the mean, median and mode are identical. Moreover, they all represent the most typical value in the data set. However, as the data becomes skewed the mean loses its ability to provide the best central location for the data as the skewed data is dragging it away from the typical value. However, the median best retains this position and is not as strongly influenced by the skewed values. This is explained in more detail in the skewed distribution section later in this guide.
Median
The median is the middle score for a set of data that has been arranged in order of magnitude. The median is less affected by outliers and skewed data. In order to calculate the median, suppose we have the data below:
65 55 89 56 35 14 56 55 87 45 92
We first need to rearrange that data into order of magnitude (smallest first):
14 35 45 55 55 56 56 65 87 89 92
Our median mark is the middle mark - in this case 56 (highlighted in bold). It is the middle mark because there are 5 scores before it and 5 scores after it. This works fine when you have an odd number of scores but what happens when you have an
even number of scores? What if you had only 10 scores? Well, you simply have to take the middle two scores and average the result. So, if we look at the example below:
65 55 89 56 35 14 56 55 87 45
We again rearrange that data into order of magnitude (smallest first):
14 35 45 55 55 56 56 65 87 89 92
Only now we have to take the 5th and 6th score in our data set and average them to get a median of 55.5.
Mode
The mode is the most frequent score in our data set. On a histogram it represents the highest bar in a bar chart or histogram. You can, therefore, sometimes consider the mode as being the most popular option. An example of a mode is presented below:
Normally, the mode is used for categorical data where we wish to know which is the most common category as illustrated below:
We can see above that the most common form of transport, in this particular data set, is the bus. However, one of the problems with the mode is that it is not unique, so it leaves us with problems when we have two or more values that share the highest frequency
B. In statistics, a confidence interval (CI) is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval (i.e. it is calculated from the observations), in principle different from sample to sample, that frequently includes the parameter of interest, if the experiment is repeated. How frequently the observed interval contains the parameter is determined by the confidence level or confidence coefficient.
A confidence interval with a particular confidence level is intended to give the assurance that, if the statistical model is correct, then taken over all the data that might have been obtained, the procedure for constructing the interval would deliver a confidence interval that included the true value of the parameter the
proportion of the time set by the confidence level.[ More specifically, the meaning of the term "confidence level" is that, if confidence intervals are constructed across many separate data analyses of repeated (and possibly different) experiments, the proportion of such intervals that contain the true value of the parameter will approximately match the confidence level; this is guaranteed by the reasoning underlying the construction of confidence intervals.
A confidence interval does not predict that the true value of the parameter has a particular probability of being in the confidence interval given the data actually obtained. (An interval intended to have such a property, called a credible interval, can be estimated using Bayesian methods; but such methods bring with them their own distinct strengths and weaknesses).
MB0040 – Statistics For ManagementAssignment Set- 2
Question.1- (a) What are the characteristics of a good measure of central tendency?
(b) What are the uses of averages?
Answer.1-a). the characteristics of a good measure of central tendency are:Present mass data in a concise form
The mass data is condensed to make the data readable and to use it for further analysis.
•Facilitate comparison
It is difficult to compare two different sets of mass data. But we can compare those two after computing the averages of individual data sets.
While comparing, the same measure of average should be used. It leads to incorrect conclusions when the mean salary of employees is compared with the median salary of the employees.
•Establish relationship between data sets
The average can be used to draw inferences about the unknown relationships between the data sets. Computing the averages of the data sets is helpful for estimating the average of population.
•Provide basis for decision-making
In many fields, such as business, finance, insurance and other sectors, managers compute the averages and draw useful inferences or conclusions for taking effective decisions.
The following are the requisites of a measure of central tendency:
•It should be simple to calculate and easy to understand
•It should be based on all values
•It should not be affected by extreme values
•It should not be affected by sampling fluctuation
•It should be rigidly defined
•It should be capable of further algebraic treatment
b) Appropriate Situations for the use of Various Averages
1. Arithmetic mean is used when:
a. In depth study of the variable is needed
b. The variable is continuous and additive in nature
c. The data are in the interval or ratio scale
d. When the distribution is symmetrical
2. Median is used when:
a. The variable is discrete
b. There exists abnormal values
c. The distribution is skewed
d. The extreme values are missing
e. The characteristics studied are qualitative
f. The data are on the ordinal scale
3. Mode is used when:
a. The variable is discrete
b. There exists abnormal values
c. The distribution is skewed
d. The extreme values are missing
e. The characteristics studied are qualitative
4. Geometric mean is used when:
a. The rate of growth, ratios and percentages are to be studied
b. The variable is of multiplicative nature
5. Harmonic mean is used when:
a. The study is related to speed, time
b. Average of rates which produce equal effects has to be found.
Question.2-Calculate the 3 yearly and 5 yearly averages of the data in table below.
Table 1: Production data from 1988 to 1997
Year 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
Production (in Lakh ton)
15 18 16 22 19 24 20 28 22 30
Solution.2:
The table displays the calculated values of 3 yearly and 5 yearly averages.
YearProduction
(Thousand Y Tonnes)
3 –yearly moving totals
3 –yearly moving totals
Ye
Short term fluctuations
(Y – Yc)
1988 151989 18 49 16.33 1.671990 16 56 18.66 -2.661991 22 57 19 31992 19 65 21.66 -2.661993 24 63 21 31994 20 72 24 -41995 28 70 23 51996 22 80 26.66 -4.661997 30
YearProduction
(Thousand Y Tonnes)
5 –yearly moving totals
5 –yearly moving totals
Ye
Short term fluctuations
(Y – Yc)
1988 151989 181990 16 90 18 -21991 22 99 19.8 2.21992 19 101 20.2 -1.21993 24 113 22.6 1.41994 20 113 22.6 -2.61995 28 124 24.8 3.21996 221997 30
Question.3 - (a) What is meant by secular trend? Discuss any two methods of isolating trend values in a time series.
(b)What is seasonal variation of a time series? Describe the various methods you know to evaluate it and examine their relative merits. Answer.3-(a) secular trend : - This refers to the smooth or regular long term growth or decline of the series. This movement can be characterised by a trend curve. If this curve is a straight line, then it is called a trend line. If the variable is increasing over a long period of time, then it is called an upward trend. If the variable is decreasing over a long period of time, then it is called a downward trend. If the variable moves upward or downwards along a straight line then the trend is called a linear trend, otherwise it is called a non-linear trendMethods of Measuring Trend
(i) Free hand or graphic method This is the simplest method of drawing a trend curve. We plot the values of the variable against time on a graph paper and join these points. The trend line is then fitted by inspecting the graph of the time series. Fitting a trend line by this method is arbitrary. The trend line is drawn such that the numbers of fluctuations on either side are approximately the same. The trend line should be a smooth curve. The free hand method has the following disadvantages. i. It depends on individual judgement
ii. It cannot be used for any predictions of trends, as drawing the trend curve is arbitrary
(ii) Semi-average method The methods of fitting a linear trend with the help of semi average method are as follows: i. When the number of years is even:, then the data of the time series is divided into two equal parts. The total of the items in each of the part is done and it is then divided by the number of items to obtain arithmetic means of the two parts. Each average is then centred in the period of time from which it has been computed and plotted on the graph paper. A straight line is drawn passing through these points. This is the required trend line.
ii. When the number of years is odd, then the value of the middle year is omitted to divide the time series into two equal parts. Then the procedure described in ‘i’ is followed.
A trend value of any future year may be predicted by multiplying the periodic increment by the number of years into the future that is desired and adding the result to the best trend value listed in the series.
(b) Seasonal variations Variations in a time series that are periodic in nature and occur regularly over short periods of time during a year are called seasonal variations. By definition, these variations are precise and can be forecasted. The following are examples of seasonal variations in a time series. i. The prices of vegetables drop down after rainy season or in winter months and they go up during summer, every year.
ii. The prices of cooking oils reduce after the harvesting of oil seeds and go up after some time.
Measurement of Seasonal Variation In order to isolate and identify seasonal variations, we first eliminate as far as possible the effect of trend, cyclical variations and irregular fluctuations on the time series. The main methods of measuring seasonal variations are:
Seasonal variation index or seasonal average method
Seasonal variation through moving averages
Chain or link relative method
Ratio to trend method
Now we will discuss separately each of the methods of measuring seasonal variation. 1. Seasonal average method In the seasonal average method, the steps followed are described below. i) The time series is arranged by years and months or quarters.
ii) Totals of each month or quarter over all the years are obtained.
iii) The average for each month or quarter is obtained. The average may be mean or median. In general, we take mean if not specified otherwise.
iv) Taking the average of monthly or quarterly average equal to 100, seasonal index for each month or quarter is calculated by the following formula:
v) Seasonal Index for a month (or quarter) =
Month (or quarterly) Average for the Monthly (or quarter)
X 100 Average or monthly (or quarterly) averages
Symbolically, seasonal index for first term is given by:- I1=S1/S x 100
Where, S1 = Average of first term S = Average of all terms Sj / k j = 1, 2, 3, 4……..k k = 12 for monthly data
k = 4 for quarterly data
The merits of seasonal average method1. This method is the simplest one. 2. This method is useful where no definite trend exists in the time series.
2.Seasonal variation through moving averages “Seasonal variation through moving averages method is also known as percentage of moving average method.” The steps involved in the computation of seasonal indices by this method are described below. i) The moving averages of the data are computed. If the data are monthly then 12-monthly moving averages, if they are quarterly, then 4-quarterly moving averages will be computed. In both the cases, time periods of moving averages are even. Hence, these moving averages are to be centred. ii) Under additive model, from each original value, the corresponding moving average is deducted to find out short time fluctuations, which is given as: Y – T = S + C + I
iii) By preparing a separate table, monthly (or quarterly) short time fluctuations are
added for each month (or quarter) over all the years and their average is obtained.
These averages are known as seasonal variations for each month or quarter.
iv) If we want to isolate / measure irregular variations, the mean of the respective
month or quarter is deducted from the short time fluctuations.
3.Chain or link relative method
The steps involved in the chain or link relative method are described below.
i) Each quarterly or monthly value is divided by the preceding quarterly or
monthly value and the result is multiplied by 100. These percentages are known as
Link Relatives of the seasonal values. Thus:
Link Relative = current season value X 100
Previous season value
There shall be no Link Relative corresponding to the first.
ii) The mean of the link relatives for each season is computed over all the years.
Median can also be taken instead of mean of the Link Relatives.
iii) These average link relatives are converted into chain relatives. The chain
relative of first is taken as 100.
The Chain Re lative of current Year
= (Average link Relative of Current year X Chain Relative Previous year )
100
iv) The second chain relative of first is computed on the basis of the chain relative
for the last:
The Chain relative of first quarter
= (Average link Relative of the first quarter X Chain Relative of the last )
100
This chain relative may or may not be 100. It is not equal to 100 due to secular trend. If it is 100, go to ‘step vi’, if it is not 100, go to ‘step v’ and then go to ‘step vi’.
v) Compute the difference ‘d’ between the new chain relatives first obtained in ‘step iv’ and chain relative assumed as 100. ‘d’ is divided by the number of seasons and the resulting figure is multiplied by 1, 2, 3 and the product is deducted respectively from the chain relatives of 2nd, 3rd, and 4th quarters. These are called corrected relatives.
vi) The seasonal indices are obtained when the corrected chain relatives are expresses as percentage of their relative averages
4.Ratio to trend method The steps to determine seasonal indices by this method are as described below. i) Determine the trend values by the method of least squares.
ii) To find ratio to trend, divide the original data by the corresponding trend values and multiply these ratios by 100, that is, Ratio to trend = ( Original data / Trend value) X 100
iii) Calculate the Arithmetic Mean of the Trend Ratios obtained in ‘step ii’. iv) Finally all the trend ratios will be converted into seasonal indices. For this, add all averages obtained in ‘step iii’ and find their general average. Seasonal indices are calculated by using the following formula:
Seasonal Indices = ( Quarterly Averages / General Average) X 100
Question.4-The probability that a contractor will get an electrical job is 0.8, he will get a plumbing job is 0.6 and he will get both 0.48. What is the probability that he get at least one? Is the probabilities of getting electrical and plumbing job are independent?
Answer.4
Question. 5-(a) Discuss the errors that arise in statistical survey.
(b) What is quota sampling and when do we use it?
Answer.5(a) Errors that arise in statistical survey Legibility The data must be legible. If a response is not presented clearly, the investigator has to rewrite it. Completeness An unanswered response on a questionnaire implies either the respondent did not answer the entry or the investigator did not record the data. If the fault is the investigators, then the investigator has to fill the missing entry. If an entry is missing as a result of omission of that entry by the respondent, then the investigator has to conduct the survey again to gather the missing entry. Consistency
The investigator has to examine each questionnaire to check inconsistency or inaccuracy in any statement. For example, the numerical figures of attributes such as income, height, weight may be inconsistent. In such cases, it is the duty of the concerned investigators to make the necessary corrections. The investigators have to make sure that the collected data must be free from redundant responses or duplicate entries.
(b) Quota sampling is a method for selecting survey participants. In quota sampling, a population is first segmented into mutually exclusivesub-groups, just as in stratified sampling. Then judgment is used to select the subjects or units from each segment based on a specified proportion. For example, an interviewer may be told to sample 200 females and 300 males between the age of 45 and 60. This means that individuals can put a demand on who they want to sample (targeting)
This second step makes the technique non-probability sampling. In quota sampling, the selection of the sample is non-random sample and can be unreliable. For example, interviewers might be tempted to interview those people in the street who look most helpful, or may choose to use accidental sampling to question those closest to them, for time-keeping sake. The problem is that these samples may be biased because not everyone gets a
chance of selection. This non-random element is a source of uncertainty about the nature of the actual sample and quota versus probability has been a matter of controversy for many years.
Quota sampling is useful when time is limited, a sampling frame is not available, the research budget is very tight or when detailed accuracy is not important. Subsets are chosen and then either convenience or judgment sampling is used to choose people from each subset. The researcher decides how many of each category is selected.
Quota sampling is the non probability version of stratified sampling. In stratified sampling, subsets of the population are created so that each subset has a common characteristic, such as gender. Random sampling chooses a number of subjects from each subset with, unlike a quota sample, each potential subject having a known probability of being selected.
Question.6-(a) Why do we use a chi-square test? (b) Why do we use analysis of variance?
Answer 6 (a) chi-square test :- Chi-Square test is a non-parametric test. It is used to test the independence of attributes, goodness of fit and specified variance. The Chi-Square test does not require any assumptions regarding the shape of the population distribution from which the sample was drawn. Chi-Square test assumes that samples are drawn at random and external forces, if any, act on them in equal magnitude. Chi-Square distribution is a family of distributions. For every degree of freedom, there will be one chi-square distribution. An important criterion for applying the Chi-Square test is that the sample size should be very large. None of the theoretical expected values calculated should be less than five.
The important applications of Chi-Square test are the tests for independence of attributes, the test of goodness of fit and the test for specified variance.
(b) Analysis of Variance :- Analysis of variance is useful in such situations as comparing the mileage achieved by five different brands of gasoline, testing which of four different training methods produce the fastest learning record, or comparing the first-year earnings of the graduates of half a dozen different business schools. In each of these cases, we would compare the means of more than two samples. Hence, in most of the fields, such as agriculture, medical, finance, banking, insurance, education, the concept of Analysis Of Variance (ANOVA) is used. In statistical terms, the difference between two statistical data is known as variance. When two data are compared for any practical purpose, their difference is studied through the techniques of ANOVA. With the analysis of variance technique, we can test the null hypothesis and the alternative hypothesis. Null hypothesis, ‘H0’: All sample means are equal. Alternate Hypothesis, ‘HA’: all sample means are not equal or at least one of sample means differ. Initially the technique was applied in the field of Zoology and Agriculture, but in a later stage, it was applied to other fields also. In analysis of variance, the degree of variance between two or more data as well as the factors contributing towards the variance is studied. In fact, Analysis of Variance is the classification and cross-classification of statistical data with the view of testing whether the means of specific classification differ significantly or whether they are homogeneous. The Analysis of Variance is a method of splitting the total variation of data into constituent parts which measure different sources of variations. The total variation is split up into the following two-components.
Variance within the subgroups of samples
Variation between the subgroups of the samples
Hence, the total variance is the sum of variance between the samples and the variance within the samples. After obtaining the above two variations, these are tested for their significance by F-test which is also known as variance ratio test.
The ‘F’ statistic is defined as F = S12 / S22 where S1 > S2. It is used to test differences between variance, that is, whether two populations can be considered to have same variance or not.
