# 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.