I have a survey data. The format is as follows:
Region 1:
Res Credit Investments
A 1 0
B 5 5
C 2 3
D 1 1
I have survey data on 60 regions and for each region respondents ranging between 1-50 have given a rating between 1-5 for various indicators like credit , investment etc.
Note: Not all 50 respondents have given their response for each region. It varies between 1-50.
My purpose is to test the difference in availability of credit and investment across these 50 regions. I tried working with Kruskal Wallis however if I ma testing it on more than 5 groups, it is creating some self automated groups and as result there is no significant difference among these regions. But if I apply it on just first 5 regions, it is giving a significant difference. Could you suggest some non parametric method to test difference between these 50 regions (at once)?
My ultimate goal is to rank these regions on the basis of these 2 indicators (tied ranks among regions could be accepted).
Hi Anjali
May I ask for some clarification of the research design of your study. You have two variables you are measuring separately: credit, and investment. You assign a value for each of these two variables with a rating scale of 1 to 5, e.g. 3.2 . For each of 60 regions there is a group of respondents (1 to 50) who assign the rating for each of the two variables. You want to know if there is a difference in the mean between regions for each of these two variables of credit, and investment. And you want to use non-parametric tests to determine statistical significance if any. Is this correct?
Raymond A. K. Cox
Thompson Rivers University
Yes sir. But the issue is that out of total respondents, 5 gave rating for credit in region A, while 35 respondents gave their rating for credit in region B. Hence there is a problem of different sample sizes and different standard deviation in responses. So how do I compare? Similar case is for investment rating also across regions.
Hi Anjali
I recommend you forego employing a non-parametric statistical test but instead use a parametric test. One possible method would be to calculate the mean score and standard deviation with sample size for each of the 60 regions. Then you would calculate the mean score and standard deviation with sample size for the other 59 regions. That is, Region 1 would have a Mean 1, Standard Deviation 1, and Sample Size 1. The remaining 59 regions would have a Mean (2-60), Standard Deviation (2-60), and Sample Size (2-60). You would do this computation for the other combinations of 59 regions. Tom compare Region 2 (having the mean, standard deviation, and sample size) you then calculat the comparison subset of Region 1, 3-60 (mean, standard deviation, sample size). Then you can determine the t-statistic for mean differences between each of the 60 regions versus the other 59 regions. An easier approach, but it introduces bias, is to calculate the mean, standard deviation, and sample size for all 60 regions to compare and compare to each individual region. This approach is much more manageable then comparing each pair of regions. The number of pairs here follows the formula (N^2 - N)/2 resulting in 1,770 combinations. That and there are so many comparisons the analysis of results would be too dispersed.
Raymond A. K. Cox
Thompson Rivers University
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