Requirements for applying a two-sample t-test

An important aspect of the two-sample /-test is the ability to off-set the three relevant aspects against one another. A couple of examples are set out below  

1 The two sets of data must approximate to normal distributions and have similar SDs 

The data within each of the two samples should be drawn from populations that are normally distributed and have equal SDs. We have to be aware that the data we are dealing with are small samples. Judgements can be tricky. Even if populations adhere perfectly to the above requirements, small samples drawn from them are unlikely to have perfect, classic, bell-shaped distributions or to have exactly coincident SDs. 

The mathematical basis of the two-sample t-test assumes that the samples are drawn from populations that  

The test is quite robust, but where there is strong evidence of non-normality or unequal SDs, action is required. We may be able to convert the data to normality, for example by the use of a logarithmic transformation (introduced in Chapter 5). Alternatively, we may have to use an alternative type of test ( non-parametric ) which does not require a normal distribution. These are discussed in Chapter 17. 

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