# t-test for Single Means - Introductory Overview

Purpose and arrangement of data. The t-test for a single mean enables us to test hypothesis about the population mean when our sample size is small and/or when we do not know the variance of the sampled population. In so-called one-sample t-tests, 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. To compute a one-sample t-test when raw data are not available (i.e., when only the sample mean, sample standard deviation, sample size and the hypothesized mean are known), use the Other significance tests option in the Basic Statistics and Tables dialog box.

Assumptions. The theoretical assumption for the one-sample t-test is that the sampled population is normally distributed. You can evaluate the normality of the variable using a variety of graphs (e.g., histograms, probability plots) which are available on the Advanced tab of the T-Test for Single Means dialog box. Tests of normality (Lilliefors test, Kolmogorov-Smirnov test, Shapiro-Wilk W test) are also available using the Descriptive statistics option from the Basic Statistics and Tables dialog box.

Graphical techniques. In addition to the histograms and probability plots that can aid you in determining whether the normality assumption is met, a box-and-whisker plot can be used in a one-sample t-test analysis to visualize the mean and variability of a variable.

Other t-tests. In addition to testing hypothesis about a single mean, the t-distribution can be used to test differences between two independent or two dependent samples. For more information see the overview topics on Independent t-tests and Dependent t-tests.