The one-sample $$t$$-test is a statistical procedure used to compare a sample mean ($$M$$) against a hypothetical population mean ($$\mu_0$$). It is used to evaluate whether the sample likely comes from a population with that specific mean.

One-Sample $$t$$-Test

Match each type of t-test with the research scenario it is designed to analyze.

There are three primary variations of the $$t$$-test, each suited for slightly different research designs: the one-sample $$t$$-test, the dependent-samples $$t$$-test, and the independent-samples $$t$$-test.

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The $$t$$-test is the most commonly used null hypothesis test for evaluating statistical relationships that focus on the difference between two means.

$$t$$-Test

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KPU Research Methods in Psychology - 4th American Edition

Types of $$t$$-Tests

Once a $$p$$-value is obtained from a $$t$$-test output, it is compared to the alpha level (typically $$\alpha = .05$$). If the $$p$$-value is less than or equal to $$.05$$, the null hypothesis is rejected, concluding a significant difference exists. If it is greater than $$.05$$, the null hypothesis is retained due to insufficient evidence.

Evaluating $$p$$-Values in a $$t$$-Test

When reporting the results of a $$t$$-test using APA style, the format includes the $$t$$ symbol, degrees of freedom, the calculated $$t$$ value, and the $$p$$-value. For instance, a result might be written as: $$t(9) = -3.07, p = .01$$. In this format, the $$t$$ and $$p$$ are italicized, the degrees of freedom appear in parentheses without any decimal remainder, and both the $$t$$ score and $$p$$-value are rounded to two decimal places.

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