Review Question - QID 103895

When comparing the means of two groups in respect to a continuous variable, a t-test should be utilized.

T-tests are one of the most commonly used statistical tests in the medical literature. They are usually the easiest and most powerful test to employ when the following conditions are met: 1) No more than two groups are being compared (e.g. runner vs sedentary individuals). 2) The variable of interest is continuous. For example, blood calcium level is a continuous variable because each observation can take on any value within the range of physiologic plausibility. Presence or absence of a malignant tumor would not be a continuous variable because only two values are possible. 3) The two samples are independent of each other. In this example the blood calcium of a runner should have no bearing on the blood calcium level of a randomly-selected sedentary individual.

Rosner discusses how to treat variance when conducting two group t-tests. Under the null hypothesis the variance of both groups is considered to be the same. The actual variances of the two groups are almost never identical, and thus they are pooled in order to determine the variance used in the t-test itself. If, however, the groups' variances are very different they cannot be pooled and the t-test must be performed with an assumption of unequal variances instead of with a pooled estimate.

Guyatt describes a situation in which the assumption of independence is not met. In some instances the two groups are not independent, but are in some way paired. For example, the blood values can be from the same patient or each patient can have a specific matched control. A simple test to compare the pairs would be to determine which of the two in each pair performed better. The binomial distribution can determine how likely the observed number of superior pairs is. This analysis, however, ignores the magnitude by which each individual in a pair outperforms the other. A paired t-test can be used instead, and its ability to preserve the magnitude of the differences makes it a more powerful test of differences between paired groups of data.

Illustration A is a flowchart outlining when to use which of three commonly employed statistical tests.

Incorrect Answers:
Answer 2: ANOVA is most commonly utilized for the same questions as a t-test but when MORE than two groups are being compared.

Answer 3: Linear regression does not compare means, but instead explores the degree of linear association between one variable on another.

Answer 4: Chi-square tests are used when the data is not continuous.

Answer 5: F-tests compare the variances, not the means, of two groups.