A researcher reports df = 18 for a repeated-measures t statistic. This research study used a total of n = 19 participants.

Question

​A researcher reports df = 18 for a repeated-measures t statistic. This research study used a total of n = 19 participants.

BlackTom AI · Accepted Answer

The prompt presents a statement about a repeated-measures t statistic, noting df = 18 and a total of n = 19 participants.

First, restating the core idea: in a typical repeated-measures design analyzed with a paired (dependent-samples) t-test, the degrees of freedom are calculated as df = n − 1, where n is the number of paired observations (i.e., participants). This is because each pair contributes one piece of information after accounting for the mean of the differences.

Next, applying the numbers: if there are 19 participants, and each participant provides a paired observation (pre- and post-measure, for example), then df = 19 − 1 = 18. This aligns perfectly with the given df of 18.

Additionally, it’s helpful to contrast other related cases to avoid confusion. In a repeated-measures ANOVA or a mixed-design analysis, df calculations can differ and depend on the specific tests and factors involved, but for a simple paired t-test with n participants, df = n − 1 is the standard rule.

Since the statement specifies df = 18 with n = 19 in a repeated-measures context, this is consistent with the common paired t-test degrees of freedom calculation.

If an option set were present, one would evaluate each choice by checking whether df = n − 1 holds under the described design, whether the term "repeated-measures t statistic" is being used in the context of a paired samples t-test, and whether there are any caveats (such as misinterpreting df as based on the number of conditions rather than participants).

In summary, under the conventional interpretation of a repeated-measures (paired) t-test, df = n − 1, so with n = 19, df = 18 is exactly what one would expect. This alignment reinforces that the reported df value is compatible with the stated sample size in a paired design.

A researcher reports df = 18 for a repeated-measures t statistic. This research study used a total of n = 19 participants.单项选择题

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​A researcher reports df = 18 for a repeated-measures t statistic. This research study used a total of n = 19 participants.单项选择题