Two-sample t test

In clinical trial analyses you may want to test the means of two independent populations to determine if they are significantly different. For example, let s say that you have the lab test value LDL and you want to know if the change-from-baseline value is significantly different after treatment between active chug and placebo. If you assume the change from baseline for LDL, ldl change, is normally distributed, you can run a two-sample t-test in SAS like this ... 

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). 

When comparing the means from two independent sampies we use the unpaired or two-sample t-test. If the numj)er of observations, means and standard deviations in the respective samples are nl, 1, si and n2, s2, then ... 

The initial specific rates of 02 consumption and C02 production are calculated and interpreted, and the effect of diminishing 02 concentration on its specific consumption rate is investigated. For each test type, the mean and standard deviation of the 02 and C02 specific rates are calculated and tabulated in Table 1. The four types of stoppered culture tests were compared using two-sample t tests on these quantities to determine whether the particular conditions affected the cell metabolism [74]. If either initial rate showed a statistically significant (95 % confidence level) difference between the two test types being compared, then we concluded that the conditions affected metabolism and would be likely to affect bioreactor performance. 

Table 2. Summary of gas exchange data from stoppered culture tests using A. annua. Two sample t test results ...

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... 

Set out the characteristics that data should fulfil if it is to be subjected to a two-sample t-test... 

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... 

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