# By subjects t test and wilcoxon signed rank test

I am trying to see if people pronounce one kind of word (say nouns like "cat") with a longer duration than another kind (say plural nouns like "cats"). I had $18$ people pronounce words from lists of $20$ word pairs. I would like to apply either a paired t test or a wilcoxon signed rank test.

The question is: Should I use each person's average duration for nouns and compare that to their average duration for plural nouns (meaning that I would be comparing $18$ pairs of words)? Is it possible to just take the raw data (meaning that I would compare $360$ pairs of words- $18\times20$)? Which is the preferred approach?

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This should be in statistics SE. – picakhu Aug 16 '12 at 13:17

## 1 Answer

The preferred test in my view is to pair the raw data and not the averages. The averages mix things together unnecessarily. How a person handles the plural for one noun can be different from what they would do with another. This variability is incorporated when you pair the individual resposnes but gets lost if you pair averages. Also you have a larger sample size for the individual pairs and it is an appropriate sample size to apply to the test. Although duration is a continuous variable it may not turn out to be approximately normally distributed. So I would apply a goodness of fit test like Shapiro-Wilk and look at the quantile - quantile plot to decide if normality is an appropriate assumption. if it is not then apply the signed-rank test.

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That is really helpful, thanks. If you do it that way, can you generalize across people, or are you limited to generalizing across words for the given set of people? I mention this, because often the sample sizes are as small as 3-4 people. – Naomi Aug 16 '12 at 17:35
If you have a lot of nouns and just a few people you have a lot of information about how that group differs in pronunciation of nouns and their plurals. But because the sample size in terms of people is small relative to your target population you do not have a good handle on how much this varies from person to person. You might want to do an anlaysis of variance to see if the difference in duration varies much from one person to the next. You should include a fairly large group of people so that you have good statistical power to detect differences that might exist. – Michael Chernick Aug 16 '12 at 18:09