t-test
(for Independent and Dependent Samples)
The t-test is the most commonly
used method to evaluate the differences in means between two groups. The
groups can be independent (e.g., blood pressure of patients who were given
a drug vs. a control group who received a placebo) or dependent (e.g.,
blood pressure of patients "before" vs. "after" they
received a drug, see below). Theoretically, the t-test
can be used even if the sample sizes are very small (e.g., as small as
10; some researchers claim that even smaller n's are possible), as long
as the variables are approximately normally distributed and the variation
of scores in the two groups is not reliably different (see also Elementary
Concepts).
Dependent samples test. The
t-test for dependent samples
can be used to analyze designs in which the within-group variation (normally
contributing to the error of the measurement) can be easily identified
and excluded from the analysis. Specifically, if the two groups of measurements
(that are to be compared) are based on the same sample of observation
units (e.g., subjects) that were tested twice (e.g., before and after
a treatment), then a considerable part of the within-group variation in
both groups of scores can be attributed to the initial individual differences
between the observations and thus accounted for (i.e., subtracted from
the error). This, in turn, increases the sensitivity of the design.
One-sample test. In the so-called
one-sample t-test, the observed
mean (from a single sample) is compared to an expected (or reference)
mean of the population (e.g., some theoretical mean), and the variation
in the population is estimated based on the variation in the observed
sample.
See Hays, 1988. See also the Basic
Statistics Introductory Overviews: t-test
for Independent Samples - Introductory Overview, t-test
for Dependent Samples - Introductory Overview, and t-test
for Single Means - Introductory Overview.