Directions for using SigmaStat
Two-sample t-test

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
23.1                    24.0
24.2                    22.3
23.7                    24.0
23.7                    23.3
26.1                    24.2
24.6                    21.3
24.4                    24.3
25.2                    22.3
24.4                    23.5
24.6                    24.3
26.0                    24.5
26.4                    23.2
25.4                    24.8
24.0                    25.3
25.6                    24.6
23.3```
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.

The output:
 ```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 Difference 0.942 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 distribution.
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 at 0.05.

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.

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