4. Unpaired Continuous Data (Unpaired T-Test, Mann-Whitney, 20 Patients)

Double-blind placebo-controlled studies often include two parallel groups receiving different treatment modalities. Unlike crossover studies (Chap. 3), they involve independent treatment effects, i.e., with a zero correlation between the treatments. The two samples t-test, otherwise called the independent samples t-test or unpaired samples t-test, is appropriate for analysis.

Is one treatment significantly more efficaceous than the other.

In a parallel-group study of 20 patients 10 of them are treated with a sleeping pill, 10 with a placebo. The first 11 patients of the 20 patient data file is given underneath.

We will start with a graph of the data. The data file is entitled “chapter4unpairedcontinuous”, and is in extras.springer.com. Start by opening the data file in SPSS.

The above graph shows that one group (the placebo group!!) performs much better than the other. The difference must be statistically significant, because the 95 % confidence intervals do not overlap. In order to determine the appropriate level of significance formal statistical testing will be performed next.

For analysis the module Compare Means is required. It consists of the following statistical models:

In the output sheet the underneath table is given.

It shows that a significant difference exists between the sleeping pill and the placebo with a p-value of 0.002 and 0.003. Generally, it is better to use the largest of the p-values given, because the smallest p-value makes assumptions that are not always warranted, like, for example in the above table, the presence of equal variances of the two sets of outcome values.

Just like with the Wilcoxon’s test (Chap. 3) used for paired data, instead of the paired t-test, the Mann-Whitney test is a nonparametric alternative for the unpaired t-test. If the data have a Gaussian distribution, then it is appropriate to use this test even so. More explanations about Gaussian or parametric distributions are given in Statistics applied to clinical studies 5th edition, 2009, Chap. 2, Springer Heidelberg Germany, 2012, from the same authors. For analysis Two-Independent-Samples Tests in the module Nonparametric Tests is required.

The nonparametric Mann-Whitney test produces approximately the same result as the unpaired t-test. The p-value equals 0,005 corrected for multiple identical values and even 0,003 uncorrected. The former result is slightly larger, because it takes into account more, namely, that all tests are 2-tailed (not a single but two sides of the Gaussian distribution is accounted). Which of the two results is in your final report, will not make too much of a difference. Ties are rank numbers with multiple values.

Statistical tests for assessing parallel-groups studies are given, both those that assume normality, and those that account nonnormality. It may be prudent to use the latter tests if your data are small, and, if nonnormality can not be ruled out. Normality of your outcome data can be statistically tested by goodness of fit tests, and can be graphically assessed with quantile-quantile plots (see Sect. 8).

More explanations about Gaussian or parametric distributions are given in Statistics applied to clinical studies 5th edition, 2012, Chaps. 1 and 2, Springer Heidelberg Germany, from the same authors.

Normality of your outcome data can be statistically tested by goodness of fit tests (Statistics applied to clinical studies 5th edition, 2012, Chap. 42, Springer Heidelberg Germany, from the same authors), and can be graphically assessed with quantile-quantile plots (Machine Learning in Medicine a Complete Overview, 2015, Chap. 42, pp 253–260, Springer Heidelberg Germany, from the same authors).