Directions for using SigmaStat
Start SigmaStat as before.
Enter data into the spreadsheet. These are condylobasal length measurements of Microtus
mexicanus. Population #1 is from Arizona and population #2 is from New Mexico. Be sure to
label your columns.
pop #1 pop #2
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 t-test: To do a two-sample t-test, go to Statistics, then Compare two groups, then 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 t-test are then displayed on the screen.
Export the file if you want to use the output in another program.
t-test Friday, July 16, 1999, 10:21:57
Normality Test: Passed (P = 0.643)
Equal Variance Test: Passed (P = 0.651)
Group N Missing
arizona 16 0
new mexico 15 0
Group Mean Std Dev SEM
arizona 24.669 1.018 0.254
new mexico 23.727 1.085 0.280
t = 2.494 with 29 degrees of freedom. (P = 0.019)
95 percent confidence interval for difference of means: 0.170 to 1.715
The difference in the mean values of the two groups is greater than would
be expected by chance; there is a statistically significant difference
between the input groups (P = 0.019).
Power of performed test with alpha = 0.050: 0.596
The power of the performed test (0.596) is below the desired power of
0.800. You should interpret the negative findings cautiously.
Explanation of the output:
Normality Test: This is the results of the K-S distance value that would have been
calculated if we had run basic statistics. The P value, in this case, is equal to
0.643, thus we fail to reject the null hypothesis that the populations have a normal
Equal Variance Test: This is the variance ratio test, where the larger sample
variance is divided by the smaller sample variance. The P value, in this case, is
equal to 0.651, thus we fail to reject the null hypothesis that the variances of the
two population are equal.
Group is the labels that you gave your columns.
N is the sample size for each sample.
Missing is the number of blank cells in your data set. In this case missing values
will have no affect on the results of your test.
Mean is the Xbar for each sample.
Std Dev is the standard deviation for each group.
SEM is the standard error of the mean.
Difference is the value from Xbar1 - Xbar2. It is the
difference between the means. If it is positive, it means that group #1 had a larger
Xbar than group #2. The difference, in this case, equals 24.669 - 23.727 = 0.942.
t is the calculated t-value from equation 8.1 in Zar. The degrees of freedom is the
((sum of the N) - 2) = (16 + 15 -2) = 29. This value would be compared to a
critical t-value from table B3. talpha(2)=0.05, 29 = 2.045. As our
calculated t-value is greater than the critical value, we would reject our null
hypothesis (Ho: mu1 = mu2)
95% confidence interval: We did not discuss this in the notes but see chapter 8.2
for a discussion of this quantity.
The difference in the mean value ... This is simply a statement about wether to
reject your null hypothesis that the means of the two populations are equal. The
phrase "greater than would be expected by chance" means that you reject your null
hypothesis. The P value is equal to 0.019, which is less than the level to reject
Power: This is a statement about the power of the test using equation 8.27 from
Zar. This along with the next statement is helpful when you fail to reject a null
hypothesis ("negative findings"). If you fail to reject the null hypothesis and the
power is low, you should consider the possibility that you made a type II error.
Return to two-sample t-test .