The two-sample t-test

If we don t have one stated value, but two independent sets of data (e.g. two analytical results from different laboratories or methods) we have to use the two-sample t-test, because we have to consider the dispersion of both data sets. In the same way as above we have to look carefully, what our question is it may be two-tailed (are the results significantly different ) or one-tailed (is the result from method A significantly lower than that from method B )... 

The mathematics for the two-sample t-test looks somewhat more complex. Beneath the difference between the two means the standard deviations of both data sets and the number of data are involved in the formula. The degree of freedom is given by ni+n2-2. 

But there is a prerequisite that has to be fulfilled, before we can apply the two-sample t-test. It is valid only, if the standard deviations of the data sets are not significantly different. This has to be tested using the F-test. 

The two-sample t-test is valid only if there Is no significant difference between the both standard deviations s, and S2... 

The two-sample t-test is only applicable, if the data are collected from analysing the same sample several times. If the data come from the analysis of different samples where the differences between the samples are much greater than the differences between the two methods or the two laboratories, it is necessary to apply the paired t-test. 

More generally the test statistic is constructed as the signal/noise (signal-to-noise) ratio or something akin to this. We will develop this methodology in relation the comparison of two independent means for a between-patient design. The resulting test is known as the unpaired t-test or the two-sample t-test. 

Which statistical test was to be used for the comparison of the treatment groups in terms of the primary endpoint do you think This is a comparison between two independent groups in a parallel group trial and the primary endpoint is continuous so the sample size calculation will undoubtedly have been based on the two-sample t-test (although this is not specified). 

Describe the use of the two-sample t-test to determine whether there is a real difference in a measured (interval scale) end-point between two sets of observations... 

Aspects taken into account by the two-sample t- test... 

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

The two-sample t-test (3). False negatives, power and necessary sample sizes... 

The two-sample t-test (4). Statistical significance, practical significance and equivalence... 

Demonstrate that the paired t-test has greater power than the two-sample t-test when dealing with paired data... 

There are many cases where we are faced with two columns of measured values and, as with previous examples, we want to see whether values are generally higher in one column than the other. Thus far, the situation is familiar. However, the data in the two columns may be related - they form natural pairs. In that case, the paired /-test provides a superior alternative to the two-sample t-test. An example follows ... 

Table 12.3 Distinctions between the paired and the two-sample t-test...

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