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Exercise: Comparing means, 7

Question 7. What are the implications of this for the t test?
What could be done about it?

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Suggested answer

The distribution must be positively skew, which means that the t test is
not strictly speaking valid.
However, the samples are almost the same size and the test is robust.
This means that if the null hypothesis were true,
we would get 5% of tests ‘significant’.
If the null hypothesis were false and there was a difference,
the power to detect it would be reduced by the skewness and
we would have less chance of detecting the difference than if assumptions were met.
The distribution could be made more symmetric by a log transformation,
which we will discuss in the next topic.
Alternatively, we could use a test which does not rely on such assumptions,
such as the Mann Whitney U test, outside the scope of this module.

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Last updated: 27 July, 2009.

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