Single Sample t Test
Menu location: Analysis_Parametric_Single Sample t.
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.