Introduction to MINITAB in the Saint Mary's Microcomputer Lab

X. Inference on the mean of a difference
(Matched pairs data)

The data must be entered in two columns, and the paired values must be kept side-by-side.

Hypothesis tests and confidence interval calculations are done with the same commands.

The process:

1. Select Calc>Basic Statistics>Paired t
2. Select the column containing your first values for the box "First Sample"
3. Select the column containing your second values for the box "Second sample"
4. Click on the "Options" button [so you can set confidence level and alternative hypothesis]
5. If you want a confidence interval for the mean of the differences: type in the confidence level in the "Level" box and make sure the "Alternative" is set to "not equal"
6. If you want to perform a test on the mean difference: select the alternative hypothesis ("less than" "not equal" or "greater than") in the "Alternative" box - for the one-sided alternatives, make sure the alternative says what you mean (the "First" and "Second" labels matter)
7. If you want to test a null hypothesis of the form "Mu(1) - Mu(2) = K" (rather than the usual Mu(1) = Mu(2)) enter K in the "Test Mean" box (usually you will leave this at 0.0 because "Mu(1) - Mu(2) = 0" is equivalent to "Mu(1) = Mu(2)" )
8. Click "OK" for the "options" window and "OK" for the "Paired t" window.

Output to the Session window:

A heading "Paired T-Test and CI: [First column],[Second column]"
A second text line "Paired T for [First] - [Second]"
A table with data on the two groups and on the differences: First a heading line identifying the numbers below
For each group and for the differences: the value (for the "subscript" variable) that identifies the group, the sample size (labeled "N"), the sample mean (labeled "Mean"), Sample standard deviation (labeled "StDev") and the (sample) standard error of the mean (StDev/sqrt(N) - labeled "SE Mean).

A line with the confidence interval:

For a standard confidence interval (or if the test is "not equal") "C% confidence interval for mean difference: ([Lower limit], [Upper limit])
If you performed a test with alternative "greater than" or "less than" : "C% lower bound [or upper bound] for mean difference: [value] " This is the value for which we can say "We can say, with C% confidence that the mean difference is no less than [no more than] [value]" - this is the cutoff for a one-sided confidence interval (all the risk on one side).

"T-Test of difference = 0 [or K, if you put in a K] (vs {">" or "<" or "not ="}): T-value = [number] P-value = [number] DF = [number]" [Degrees of freedom may not be a whole number - Minitab uses the exact calculation rather than our rough rule of thumb]

The printout does not give a yes or no answer - you must determine that, based on the t- or p-value and your decision criteria.The program will give a confidence interval for Mu(1) - Mu(2) and will calculate the t- and p- values for the test with null hypothesis "Mu(1) = Mu(2)"[or Mu(1) - Mu(2) = K, iof you changed that] and alternative as stated. If you have mis-stated the alternative hypothesis, the stated p-value will be wrong; the t-value will be based on the difference "First - Second" - so make sure that matches the order you want.

Method for version 10.5 [Mac] corresponds to hand calculation: [Create a new column containing all the differences, then use one-sample t methods on the new column.]

1. Select Calc>Mathematical Expressions.
2. Type "D" or "diff" into the " Variable(New or Modified)" box.
3. Put the cursor in the " Expression " box.
4. Select the column containing the data from the first sample.
5. Type a "-" sign [no quotqtion marks, of course],.
6. Select the column containing the data from the second variable.
7. Select " OK "
The program will compute the differences, choose a column for 'D' and put the differences in there.
8. Do your hypothesis test or estimation using this column labeled D - remember which column is subtracted from which. (SeeVIII-t-tests and estimation of means ).


Last update 8/21/2000

Maintained by