# Single Sample t Test

This function gives a single sample Student t test with a confidence interval for the mean difference.

The single sample t method tests a null hypothesis that the population mean is equal to a specified value. If this value is zero (or not entered) then the confidence interval for the sample mean is given (Altman, 1991; Armitage and Berry, 1994).

The test statistic is calculated as: - where x bar is the sample mean, s² is the sample variance, n is the sample size, µ is the specified population mean and t is a Student t quantile with n-1 degrees of freedom.

Power is calculated as the power achieved with the given sample size and variance for detecting the observed mean difference with a two-sided type I error probability of (100-CI%)% (Dupont, 1990).

Example

Test workbook (Parametric worksheet: Systolic BP).

Consider 20 first year resident female doctors drawn at random from one area, resting systolic blood pressures measured using an electronic sphygmomanometer were:

 128 127 118 115 144 142 133 140 132 131 111 132 149 122 139 119 136 129 126 128

From previous large studies of women drawn at random from the healthy general public, a resting systolic blood pressure of 120 mm Hg was predicted as the population mean for the relevant age group. To analyse these data in StatsDirect first prepare a workbook column containing the 20 data above or open the test workbook and select the single sample t test from the parametric methods section of the analysis menu. Select the column marked "Systolic BP" when prompted and enter the population mean as 120.

For this example:

Single sample t test

Sample name: Systolic BP

Sample mean = 130.05

Population mean = 120

Sample size n = 20

Sample sd = 9.960316

95% confidence interval for mean difference = 5.388429 to 14.711571

df = 19

t = 4.512404

One sided P = .0001

Two sided P = .0002

Power (for 5% significance) = 98.71%

A null hypothesis of no difference between sample and population means has clearly been rejected. Using the 95% CI we expect the mean systolic BP for this population of doctors to be at least 5 mm Hg greater than the age and sex matched general public, lying somewhere between 125 and 135 mm Hg.