Directions for using SigmaStat
Paired Sample t-test

Start SigmaStat as before.

Enter data into the spreadsheet. These are measurements of the width of the right hand and the left hand from 10 different persons. Be sure to label your columns.

  ind    Right     Left
   1      8.7      8.6
   2      7.9      7.6
   3      7.6      7.2
   4      8.5      8.2
   5      9.6      9.7
   6      8.7      8.4
   7      9.2      9.0
   8      8.4      8.3
   9      8.9      8.7
  10      8.8      8.6
Save your work: Once you have the data entered and checked, go to File, then Save as, and name the file. Be sure to save the file to the A:\ drive.

Run the Paired Sample t-test: To do a paired sample t-test, go to Statistics, then Before and After, then paired t-test. This brings up another window, which is used to assign columns in your spreadsheet. The box may be too low on your screen, in which case you will need to drag it higher on your screen to be able to see the bottom of the window. Data format is Raw. Then use the cursor to point to the top of column #1; this highlights column #1 as one of your populations. Then click on the Next button at the bottom of the window. Then click on column #2, and then click on the Finish button. The results of the paired sample t-test are then displayed on the screen.

Export the file if you want to use the output in another program.

The output: 
Paired t-test:   Saturday, September 30, 2000, 21:49:30

Normality Test:   Passed   (P = 0.295)

Group    N   Missing   
right   10     0   
left    10     0 .  

Group     Mean    Std Dev   SEM   
right     8.630    0.581    0.184   
left      8.430    0.695    0.220   

Difference    0.200    0.141    0.0447

t = 4.472  with  9 degrees of freedom. (P = 0.002)

 95 percent confidence interval for difference of means:  0.0988 to  0.301

The change that occurred with the treatment is greater than would be
expected by chance; there is a statistically significant change  (P = 0.002)

Power of performed test with alpha = 0.050: 0.978

Explanation of the output:
The explanation of the output is essentially that of a 2-sample t-test, except that you will note that there is no test for the equality of variances.

Also note:
Difference is the sample mean of the deviations. In this case it is equal to 0.200. 0.141 is the sample standard deviation of the ds, while 0.0447 is the standard error of d.

t is the calculated t-value from equation 9.1 in Zar. The degrees of freedom is the ((number of pairs - 1) = (10 - 1) = 9. This value would be compared to a critical t-value from table B3. talpha(2)=0.05, 9 = 2.262. As our calculated t-value is greater than the critical value, we would reject our null hypothesis (Ho: mu1 = mu2)

Return to a paired sample test.