One-Sample t Test

The TTEST Procedure

One-Sample t Test

A one-sample t test can be used to compare a sample mean to a given value. This example, taken from Huntsberger and Billingsley (1989, p. 290), tests whether the mean length of a certain type of court case is 80 days using 20 randomly chosen cases. The data are read by the following DATA step:

   title 'One-Sample t Test';
   data time;
      input time @@;
      datalines;
    43  90  84  87  116   95  86   99   93  92
   121  71  66  98   79  102  60  112  105  98
   ;
   run;

The only variable in the data set, time, is assumed to be normally distributed. The trailing at signs (@@) indicate that there is more than one observation on a line. The following code invokes PROC TTEST for a one-sample t test:

   proc ttest h0=80 alpha=0.1;
      var time;
   run;

The VAR statement indicates that the time variable is being studied, while the H0= option specifies that the mean of the time variable should be compared to the value 80 rather than the default null hypothesis of 0. This ALPHA= option requests 10% confidence intervals rather than the default 5% confidence intervals. The output is displayed in Figure 67.1.

One-Sample t Test

The TTEST Procedure

Statistics
Variable	N	Lower CL Mean	Mean	Upper CL Mean	Lower CL Std Dev	Std Dev	Upper CL Std Dev	Std Err	Minimum	Maximum
time	20	82.447	89.85	97.253	15.2	19.146	26.237	4.2811	43	121

T-Tests
Variable	DF	t Value	Pr > \|t\|
time	19	2.30	0.0329

Figure 67.1: One-Sample t Test Results

Summary statistics appear at the top of the output. The sample size (N), the mean and its confidence bounds (Lower CL Mean and Upper CL Mean), the standard deviation and its confidence bounds (Lower CL Std Dev and Upper CL Std Dev), and the standard error are displayed with the minimum and maximum values of the time variable. The test statistic, the degrees of freedom, and the p-value for the t test are displayed next; at the 10% $\alpha$ -level, this test indicates that the mean length of the court cases are significantly different from 80 days (t=2.30, p=0.0329).

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