Chi Square or T Tests for Likert Scale Type Survey

#1
So I have a 4 point likert-type scale with approximately 20 questions. I have categorized each item to be either agree or disagree. I mainly did this because the previous person who used this scale did this. However, that person only displayed frequency data for it and did not run any tests for significance or association.

Is it OK to run a chi square on the frequency counts of agree and disagree responses based on gender for the entire scale or does it somehow violate the independence assumption?



I ask this because compared to a vote where people say yes or no one time, people actually are saying agree or disagree several times by way of multiple questions.

To clarify, I do not want to test just a single question out of the scale. I want to do frequency counts for the whole scale and then do a chi square.

If it isn't possible, would just leaving it as a 4 point scale and then using a t-test work?

By the way, there were only 10 males and 10 females who participated in the survey.

The hypothesis is, basically, that males responses will differ significantly from females.
I don't want to get any more complicated than that. I know the chi square is association. I can stick with that hypothesis too.

I'm on a very limited time constraint and am not looking for the best way to do it, just an acceptable easy way to do it.

Please, any help would be much appreciated. Thanks!
 

hlsmith

Omega Contributor
#2
I did not follow the part about using multiple questions, but if it is just treating the response scales as 4 points or binary - I follow that.


The ttest approach may be suspect since you are using integers and have a small sample. You lose information when collapsing scales, but it is regularly done. Per your description, I would say to run Fisher's exact test on either binary or categorical outcome. The chi-sq is approximately same as Fisher's exact as sample size increases, but you will have sparse counts given the sample size, so should use Fisher's exact test.