Doubts analyzing Likert scales

#1
Hi all,

I thought about analyzing results from Likert scale using Kruskal-Wallis, but the more I read about it, the more confused I get. People apparently do not agree about how to use Kruskal-Wallis...

So, I have a questions like this:

- What is influence of factor A, factor B and factor C on factor X?

I am using a 5 points Likert scale (5 - very high influence ... 1 - very low influence). I want to evaluate if there is difference between the influence of factor A, factor B and factor C on factor X.

First of all, if I use Kruskal-Wallis, am I comparing medians or not? I have read people saying the Kruskal-Wallis compares medians and other saying that this is not true :mad: If I am not comparing medians, am I still analyzing if there is difference between the influence of each of the three factors (A, B and C) on factor X?

Second, can I use Kruskal-Wallis? This is a survey result. So, the same group of people that responded about the influence of factor A on factor X, responded about the other relationships (factor B on factor X, and factor C on factor X). Is this breaking the assumption of mutual independence among samples or independence among samples? :confused:

Finally, if the sample sizes are 50 and I only have a 5 point Likert scale, how "rigorous" I need to be regarding the assumption of "populations distribution have the same shape"?

Hope getting some insights soon...

Cheers
 

CB

Super Moderator
#2
- What is influence of factor A, factor B and factor C on factor X?
It might be helpful to describe your variables in a little more detail? It isn't quite clear here which variables are Likert (all of them?), or whether you're talking about individual Likert items or summated Likert scales. A bit more info will no doubt help someone to give you a helpful answer. By the way, "factor" usually describes a categorical/nominal variable (or a latent factor in factor analysis). I'm not sure that's quite what you're describing here.

First of all, if I use Kruskal-Wallis, am I comparing medians or not? I have read people saying the Kruskal-Wallis compares medians and other saying that this is not true :mad:
Kruskal-Wallis is only a test for differences in medians if the distribution of the DV is the same (except for a possible location shift) in all of the groups. Aside from that specific situation, the more general null hypothesis of the Kruskal-Wallis is that: "the samples come from populations such that the probability that a random observation from one group is greater than a random observation from another group is 0.5." (McDonald, 2009 - more info at the linked page).
 
#3
Hello,

It might be helpful to describe your variables in a little more detail? It isn't quite clear here which variables are Likert (all of them?), or whether you're talking about individual Likert items or summated Likert scales. A bit more info will no doubt help someone to give you a helpful answer. By the way, "factor" usually describes a categorical/nominal variable (or a latent factor in factor analysis). I'm not sure that's quite what you're describing here.

To make it clear, I will give an example:

Supposed I have a survey composed of one question:

Question -> What is the influence of the following factors on the factor "Development team teamwork":

a) Team size
b) Members personality
c) Members technical expertise
d) Collective ownership

For each item, the participant would answer with an integer from 1 to 5 (1 - very low influence,..., 5 very high influence).

Suppose that 50 people answered the question (each item). I want to know if there is difference between the influence of the "factors" team size, members personality, members technical expertise and collective ownership on the "factor" development team teamwork.

I thought about comparing the medians of the four samples (items a), b), c) and d)). That is why I thought about using Kruskal-Wallis. The biggest issue I saw about using this technique is that I have the same group of people for the items. I saw that some people say that you need to have different groups of people for each alternative in order to compare the alternatives (samples must be independent) using Kruskal-Wallis. So, my question is: can I consider the samples independent? It is the same group of people, but they are evaluating different things. If I can't consider the samples independent, could I use Friedman ANOVA by Ranks and consider the samples paired?
 

CB

Super Moderator
#4
Supposed I have a survey composed of one question:

Question -> What is the influence of the following factors on the factor "Development team teamwork":

a) Team size
b) Members personality
c) Members technical expertise
d) Collective ownership

For each item, the participant would answer with an integer from 1 to 5 (1 - very low influence,..., 5 very high influence).

Suppose that 50 people answered the question (each item). I want to know if there is difference between the influence of the "factors" team size, members personality, members technical expertise and collective ownership on the "factor" development team teamwork.
Thanks for the added info! :) I want to stress something here though: Your data does not permit you to assess the influence of team size, members personality etc on development team teamwork. It only allows you to investigate your participants beliefs about the influence these variables have. That is a pretty crucial distinction to keep in mind for your write-up. Assessing the actual causal influence of these IV's on your DV would require something closer to an experimental design.

I thought about comparing the medians of the four samples (items a), b), c) and d)). That is why I thought about using Kruskal-Wallis. The biggest issue I saw about using this technique is that I have the same group of people for the items. I saw that some people say that you need to have different groups of people for each alternative in order to compare the alternatives (samples must be independent) using Kruskal-Wallis. So, my question is: can I consider the samples independent? It is the same group of people, but they are evaluating different things. If I can't consider the samples independent, could I use Friedman ANOVA by Ranks and consider the samples paired?
I think you are correct in saying the samples are not independent. A Friedman test sounds sensible. I can't seem to find a source giving a decent definition of the null hypothesis of this test (other than vague statements about the null being of "no differences"), but be careful about this... I suspect the same issue of the test only being a test for differences in medians when distributions are identical over the different "subsamples" applies here as well as for the Kruskal-Wallis test. I believe SPSS has some nonparametric tests more specifically looking for differences in medians.