T Tests Task: One-Sample t Test :: SAS(R) Studio 3.3: User's Guide

About the One-Sample t Test Task

A one-sample t test compares the mean of the sample to the null hypothesis mean.

To compare an individual mean with a sample size of n to a value m, use $t equals . fraction x with macron above , negative m , over fraction s , over square root of n end fraction end fraction$ where

is the sample mean of the observations and s² is the sample variance of the observations.

For example, you want to perform a one-sample t test on the horsepower values in the Sashelp.Cars data set. The null hypothesis is 300.

To run a one-sample t test, open the T Tests task. From the T test drop-down list, select One-sample test.

Example: One-Sample t Test for Horsepower

To create this example:

In the Tasks section, expand the Statistics folder and double-click T Tests. The user interface for the T Tests task opens.
On the Data tab, select the SASHELP.CARS data set.
From the T test drop-down list, select One-sample test.
To the Analysis variable role, assign the Horsepower column.
On the Options tab, enter 300 in the Alternative hypothesis field.
To run the task, click .

Here is a subset of the results:

Assigning Data to Roles

To run a one-sample t test, select One-sample test from the T test drop-down list. Assign a numeric column to the Analysis variable role.

Setting Options

Option Name	Description
Test
Tails	specifies the number of sides (or tails) and direction of the statistical tests and test-based confidence intervals. You can choose from these options: Two-tailed test specifies two-sided tests and confidence intervals for means. Upper one-tailed test specifies upper one-sided tests in which the alternative hypothesis indicates a mean greater than the null value, and upper one-sided confidence intervals between the lower confidence limit and infinity. Lower one-tailed test specifies lower one-sided tests in which the alternative hypothesis indicates a mean less than the null value, and lower one-sided confidence intervals between minus infinity and the upper confidence limit.
Alternative hypothesis	specifies the value of the null hypothesis. By default, the null hypothesis has a value of 0.
Normality Assumption
Tests for normality	runs tests for normality that include a series of goodness-of-fit tests based on the empirical distribution function. The table provides test statistics and p-values for the Shapiro-Wilk test (provided the sample size is less than or equal to 2000), the Kolmogorov-Smirnov test, the Anderson-Darling test, and the Cramér-von Mises test.
Nonparametric Tests Note: This option is available only for a two-tailed test.
Sign test and Wilcoxon signed rank test	generates the results from these tests: The sign test statistic is , where n⁺ is the number of values that are greater than , and n^- is the number of values that are less than . Values equal to are discarded. The Wilcoxon signed rank statistic S is calculated as $s equals . sum , from , i colon vertical line , x sub i , minus , mu sub 0 , vertical line greater than 0 , to , white square , of . r with subscript i , and with superscript plus , end sub-superscript , minus . fraction n sub t , open , n sub t , plus 1 close , over 4 end fraction$ , where r⁺_i is the rank of after discarding values of , and n_t is the number of x_i values not equal to . Average ranks are used for tied values.
Plots
Histogram and box plot	creates a histogram and box plot together in a single panel, sharing common X axes.
Normality plot	creates a normal quantile-quantile (Q-Q) plot.
Confidence interval plot	creates a plot of the confidence interval for the means.