The t-test is a fundamental tool in scientific research, frequently used to examine relationships between two variables. It helps answer key questions, such as whether changes in one variable necessitate changes in another, or whether different levels of one variable are associated with different outcomes in another. This section introduces the basic concepts, applications, and assumptions underlying the t-test.

The one-sample t-test is a statistical method used to determine whether the mean of a single sample differs significantly from a known or hypothesized population mean. This test is useful for evaluating if a sample’s mean is consistent with an expected value. In this tutorial we shall use a hypothetical data to test if the sample mean significantly deviates from a specified population mean.

The independent sample t-test is a statistical method used to compare the means of two independent groups, assessing whether their differences are statistically significant. This test is typically applied when comparing outcomes across two distinct groups, such as treatment and control groups in an experiment. We shall use the given data to evaluate whether observed differences are due to chance or a true effect.

The paired sample t-test is a statistical method used to compare the means of two related groups to determine if there is a statistically significant difference between them. This test is often applied in before-and-after studies or in situations where the same subjects are measured under different conditions. To illustrate this test, we use the hypothetical data to assess if there is a mean difference between two related conditions or time points.