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I have some linguistics categorical data to analyse. There are 5 speakers (M1-M5), and they read out certain words. The words are 200 in number, but speakers only read out the words if they understand its meaning. They are shown in random order with other filler words. The speakers produce sounds which are categorized in 4 categories - A,B,C,D. The data looks like this: 

   M1   M2  M3  M4  M5
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A   4   1   2   88   0
B   4   31  0   0   15
C   17  3   37  7   43
D   11  79  84  7   65

This means speaker M1 says 4 words which are in category A, 4 words in category B, 17 words in category C and 11 words in category D. This also means each speaker has a certain preference. I want to be able to conclude that they have specific preferences like M1 prefers C, M2 prefers D and so on.

I have been asked to use the Chi-sq test for this, but I am not sure if that is the right test. Any pointers?

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  • $\begingroup$ A simple short answer would be: yes you can use the chi-square test on this kind of data. Simply put a chi-square test would tell you whether there is any difference in the distribution of categories A-D between the speakers. Amongst others, it will not tell you which speaker differs from which other speaker. Therefore, whether the Chi-sq test is the right test is something which depends on the (research) question. To answer that, you'll need to elaborate. $\endgroup$
    – IWS
    Commented May 23, 2017 at 11:10
  • $\begingroup$ Thank you @IWS. By "difference in distribution of categories A-D between speakers" do you mean I will be able to just say that speakers do different things? My goal or research question is: Can we say with any confidence (statistically) which category each speaker prefers? I do not mind running separate tests for each speaker. While I may not be able to conclude that all speakers prefer one particular category (they clearly don't), but definitely M2,M3 and M5 seem to prefer category D. $\endgroup$
    – Ruks
    Commented May 24, 2017 at 1:54

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As far as I can tell from your description, your data violates one of the assumptions of a Chi-square test, namely that observations are independent (only one observation per subject).

Unfortunately I'm not sure what analysis your should use, but this post on The Analysis Factor may guide you: http://www.theanalysisfactor.com/models-repeated-measures-continuous-categorical-count-data/

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  • $\begingroup$ ..I am not sure I understand how the data violates the independence assumption. Is it because the same words were shown to each of the 5 speakers? The observations are not connected in any way. Unfortunately I had no control in the design of experiment and collection of data, I came in only after the data was collected. Thank you for the link. I need to think whether I need to use GLMM $\endgroup$
    – Ruks
    Commented May 24, 2017 at 2:01
  • $\begingroup$ Basically means that each participant can only be counted once in a table. Here for example, subject M1 is contributing 36 'counts' to the table. To my mind, M1 through M5 is your sample size, not a categorical variable. $\endgroup$
    – Peter K
    Commented May 24, 2017 at 3:37

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