Likert Scale Data

[Gemini]

To all you statistics geniuses,
I have some Likert scale data that I need to analyze. From research, I understand the controversy of using methods for continuous data analysis on the ordinal Likert data. The consensus seems to be to use the Chi-Squared, Wilcox, or Kruskal-Wallis methods depending on the situation. None of these am I very familiar with, so if anyone can help me, here's the problem: I have 6 rows of data over 8 columns representing 6 participants' aswers to the same 8 questions. The 6 participants are categorically divided into 2 groups of 3. The answers were all on a scale of 6 levels and all questions referred to the same major topic. I want to gage the participants' overall attitude toward the subject and be able to state whether or not there is a significant difference between the two groups. It's not much data, but maybe I can do something with it.

[lumhearts]

Gemini,
Here is one way. Create a new variable that is the mean of the 8 items. You can do this because you said the items all measure same topic. Make sure this makes logical sense. Check to see if all items are coded in the same direction (i.e., 1 = bad, 6 = awesome). Then make a comparison of the two groups using your new variable. Your not going to get too far with six subjects no matter what you do - so - use both t test and Wilcoxon and compare results.

[Jackalope]

Gemini:

I am not sure that Kruskal-Wallis is an appropriate for your particular situation given its limited sample size as Kruskal-Wallis is based on the non-parametric method. My 2 cents.

Jackalope

[Gemini]

Lumhearts,

Thanks for your reply. Comparing the Wilcox to the t is a good idea, but I still need some help on the Wilcox. So, I'm using the row averages to do the U test:
Sample A: 5, 5.25, 5.625 >> Ranks 3, 4, 6
Sample B: 2.75, 4.625, 5.5 >> Ranks 1, 2, 5
T= 13, n1=3, n2=3 >> U=2
Now, I can't find a U-Distribution table with my sample sizes; am I just out of luck? How would I use it anyway? If my u value is greater than the critical value, then there is a significant difference? What about confidence and power with the Wilcox method? Any help is appreciated.

[lumhearts]

Hey Gemini,
I checked and your statistic is right. Your logic is right also about the critical value. Usually, computers will compute either an exact p-value or an approximated p-value. In this case since your sample is so small you would use the exact p-value - which is 0.200 for a one-sided test.

I'm not sure why you're doing this analysis - but you really can't do much (inferentially) with such a small sample. If you really need to make something work - maybe use descriptive stats and state that the mean and median are both larger for group A.

[August 15]

Hey Gemini,

I just finished writing up a research question that used Wilcoxon sign-rank test as the data was ordinal. My data was on a 7pt Likert scale with 4 being ambivalent. I wanted to know if the participant responses were significantly different from ambivalent, and I used an old SPSS (v13). Do you have SPSS? If so, go to Analyze-->Nonparametric Tests-->2 related samples. It will calculate the critical value (although it looks like Lumhearts did it for you anyways) and tell you whether or not the result is significant.

To answer your question, for Wilcoxon, your W must be or be below the cv to be significant. Here's site that might be helpful to you, it provides cvs: http://www.sussex.ac.uk/Users/grahamh/RM1web/WilcoxonTable2005.pdf

Also, for quite some time, I didn't realize SPSS could actually do the test for me, so I had completed a lot by hand by the time things clicked for me. I used this site to walk me through the process: http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test look at the example.

I sure hope you find this helpful. This is the first time I feel like I actually had some knowledge to help someone else instead of always asking! Let me know how this works for you. Best of luck.

[Gemini]

lumhearts,

What I'm trying to do with this data is to show colleagues that we can get more understanding from survey data than we have been. I guess I need a better sample to work with, but your help has been appreciated. How did you get that p-value for this test?