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I have a table of frequencies of symptoms between 4 different age categories, and I want to see if the observed frequencies are significantly different between the groups. It is about a scoring instrument which consists of 21 items. We want to see if the frequency of each item differs between the 4 different age groups.

What are my possibilities?

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  • $\begingroup$ It depends on how those frequencies might be interrelated: you haven't given enough details for us to assume that they represent statistically independent observations, for instance. Do you think you could flesh out your post a little to provide some of this important information? $\endgroup$ – whuber Aug 14 '16 at 22:54
  • $\begingroup$ Thank you for your response. It is about a scoring instrument. Which consists of 21 items, we want to see of the frequency of each item differ between the 4 different age groups. Do u think u have enough information now? $\endgroup$ – Tirsha Aug 14 '16 at 22:59
  • $\begingroup$ It's important that the post itself include such information, Tirsha. (These comments could disappear at any time.) $\endgroup$ – whuber Aug 14 '16 at 23:04
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Summarising from McHugh (2013), the $\chi^2$ test has six conditions specific to the test. Two relevent assumptions here are:

  • "Each subject may contribute data to one and only one cell in the test"
  • "The value of the cell expecteds should be 5 or more in at least 80% of the cells, and no cell should have an expected of less than one"

The first assumption is usually used to caution about applying to panel data, but would also apply here, depending on how you tabulated your 21 items (assuming each subject could have multiple 'items'). The second assumption is self explanatory, and a practical example is given here.

A reproducible example / clearer description would help with suggestions for alternatives. However, common options are Fisher's exact test, and (according to McHugh) the Maximum likelihood ratio $\chi^2$ test. If you have matched pairs, then McNemar's test.

NB. Fisher's exact test assumes fixed totals. Read more here.

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Your experiment looks like a 4x4 contingency table, where the rows and columns represent expected and observed cell counts.

Since your input size is small, you should consider the Fischer's Exact test. The chi-square test is not recommended because your data set will give poor approximation to normality (the test is only valid with a large enough data set).

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