I am conducting a project in three different centers. I have sent questionnaire to 1,000 respondents in each center and got responses of as follows;
1) less than 200 in first two centers, and
2) more than 750 in third center
As response of last center is extremely large as compare to first two.
How I will compare these three centers data. Kindly guide me I want to apply t test and ANOVA.
thank you so much
Crucial question: What is your hypothesis to be tested? What is your research question?
I suppose you want to compare mean responses on each center. If this is your aim, then you can compare this by ANOVA or Welch's ANOVA. Since questionnaire data is not continuous, kruskall wallis test might be better used (of course Kruskal Wallis test has a different null hypothesis which is not about means)
Comparing these will be very difficult. Your response rate in the first two cases was very low. So your surveys represent some small subpopulation of each center. How representative are your responses to the population, and how can you prove this? If you can't, then any differences that you see between centers may be an artifact of the different subpopulations that were sampled. This outcome is uninteresting unless you can clearly identify the subpopulation that was sampled.
I think you need to do ANOVA and to follow it with post hoc to compare between 3 groups. {if you hanlde your data with multiple comparison through ttest, then inflation in alpha will arise}
However, because you have one group obviosly larger in sample size, you need to consider: Weighted Means Analysis, in ANOVA, the attached word file is to help you in how to do weighted means, which was retrived from the following link. Hope this help
https://www.google.jo/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=how+to+do+weighting+scores+between+ANOVA+groups
One of the important issue here is varying non-response rates among the centers. Generally, it is believed that the profiles of non-respondents can be different from those who responded. If the non-response rates would have been comparable between the centers, it would not have mattered. But, 20% versus 75% is quite different.
I am sure that you have some basic information about the respondents say about their occupations, positions are the sectors in which they are working. Now, in each centre, compare the profile of respondents with that of non-respondents. If it is not much different then you may proceed with the further analysis but if their profiles comes out to be different between those who are responding and those who are not responding then you may believe that the responses got are not reresentative and strictly not comparable. If you can do this analysis, then please do this and check it.
all of the above are correct- this is complicated. Also, consider when you can apply weights to responses from each center?
Thanks a lot respected researchers for your valuable feedback. My respondents are undergraduate students from three universities. The first university has responses more than 750 while other two universities have responses less than 200. So, profile of respondents and non respondents is almost same. How I proceed for analysis.
thanks in anticipation.
In RG, such an assumption is fine. In publication you will need data to support the assertion. Can you explain why university 1 had so many more responses? If not, that will greatly limit the journals where this research can be published.
If I were a reviewer the other thing I would do is to say that you have 3 universities. A t-test does not control the experimentwise error rate. So the pairwise p-value is 0.05, and the experimentwise p-value is 1-(1-0.05)^3 = 0.14. I then note that you have 20 variables. Your manuscript error rate is at 1-(1-.14)^20 = 0.95. It is nearly guaranteed with this manuscript that at least one of the claims for statistical significance is significant by chance alone. It is quite likely that at least two significant results are nothing more than an artifact of chance. What should I make of the manuscript now? The solution is to use a combination of univariate test and some multivariate analysis that will give a broad picture and reassure readers that the outcome is more than random chance.
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