I have survey data with ordinal/categorical data. Most of the time the answers to question are Yes/No. I want to compare the bar charts (normalized) of yes/no from participants who gave a particular answer to a previous question.

  • Eg. Looking at users who answered yes to Q.4, then those that answered no to Q.4, did they answer similarly to Q.6? This will give two distributions/ratios for instance (0.4,0.6) and (0.35,0.65).

Should I use a Chi-squared test? Or use a measure of distribution distance similarity like the Jensen–Shannon divergence?


You can use a Chi-squared test of independence in this case.

I think it will be much easier to apply than the (slightly overkill) Jensen-Shannon divergence.

  • $\begingroup$ what does test of independence mean when using this test? $\endgroup$ – Vass Oct 14 '14 at 12:48
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    $\begingroup$ This refers to the test, developed by Karl Pearson, which is used to asses the independence of two categorical variables. It employs a Chi-squared test statistic, but many other tests do, so it is important to specify that we are using the Chi-squared test of independence. For more information, see en.wikipedia.org/wiki/Pearson's_chi-squared_test or stattrek.com/chi-square-test/independence.aspx . $\endgroup$ – Kees Mulder Oct 14 '14 at 12:57
  • $\begingroup$ great thanks, so the independence refers to them not being essentially the same distribution? $\endgroup$ – Vass Oct 14 '14 at 13:19
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    $\begingroup$ The independence refers to whether or not the two categorical variables depend on each other. If some variable X and Y are independent, the distribution of X is the same for all levels of Y (in your case 2, yes/no), and vice versa. $\endgroup$ – Kees Mulder Oct 14 '14 at 14:28

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