## Comparing different percentages of a sample?

Discuss statistics related things
Tobes
Posts: 7
Joined: Thu Feb 15, 2024 6:02 pm

### Comparing different percentages of a sample?

Hi all!

I have a question regarding the most suitable statistical tests to use in Jamovi for the following.

500 participants answered different questions on a 5-point Likert scale. The data available to me is percentages of the participants that have indicated either 1-2, 3 or 4-5 on the Likert scale. I don't have any additional information regarding the sample apart from the size, e.g., mean or standard deviation.

Say, for example, that I would like to compare if the proportion of participants that answered 4-5 on a question (40%) is significantly larger than the proportion that answered 1-2 (30%).

1. Which test would be most suitable here to compare two proportions as above (i.e., 30% and 40%)?

2. Which test would be most suitable here to compare three or more proportions (for example 5%, 20% and 40%)?

Thanks!
reason180
Posts: 294
Joined: Mon Jul 24, 2017 4:56 pm

### Re: Comparing different percentages of a sample?

Hi. I believe these are the kinds of analyses you want to conduct:
Untitled3.gif (918.54 KiB) Viewed 970 times
Tobes
Posts: 7
Joined: Thu Feb 15, 2024 6:02 pm

### Re: Comparing different percentages of a sample?

Thank you very much!
Tobes
Posts: 7
Joined: Thu Feb 15, 2024 6:02 pm

### Re: Comparing different percentages of a sample?

Come to think about, when using chi square like this, one seems to only get one set of results (one X2 and one p-value) from the significance testing when comparing three proportions, say 30%, 33% and 37%. But how does one know the significance (if it exists) of each comparison, that is 37% over 33%, 37% over 30%, and 33% over 30%, respectively?
reason180
Posts: 294
Joined: Mon Jul 24, 2017 4:56 pm

### Re: Comparing different percentages of a sample?

You have to do a separate Chi Square test (or alternatively, a separate binomial test) on a subset of the data that contains only the two frequencies of interest. This is illustrated in the lower half of the image, above.
Tobes
Posts: 7
Joined: Thu Feb 15, 2024 6:02 pm

### Re: Comparing different percentages of a sample?

Oh, I understand.