Matched Pairs Design Test for Equality of Means

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Brief Instructions

Press STAT and ENTER. Clear lists L1, L2 and L3. Enter one set of measurements under L1 and the other set of measurements under L2. Next put the cursor on L3 in the data entry window and press "2ND", "1", "-" minus sign, "2ND", "2" and "ENTER".

Now press STAT, choose TESTS, choose T-Test and press "ENTER". To the right of "Inpt:" choose "Data" and press "ENTER". Next to "m0:" enter "0"; next to List:, enter L3; check that "1" is next to "Freq:"; and then next to "m:", highlight "m0" and press "ENTER". Put the cursor on "Calculate" and press "ENTER".

The test statistic is next to "t =" and the P-value is next to "p =".

Detailed Instructions

This test is used to decide whether the means of the same measurements made under two different conditions on the same group of individuals are the same. To demonstrate this procedure we will test whether the means of the following two tests given to the same eight students are the same at the 95% confidence level.

 Subject 1 2 3 4 5 6 7 8 Test 1 39 50 58 43 26 48 56 50 Test 2 40 44 52 48 32 26 50 44

Press "STAT" and "ENTER". Clear lists L1, L2 and L3. Enter the Test 1 data under L1, and the Test 2 data under L2. When you are finished, the data entry screen should look as shown below. Notice that the numbers in the two lists are still paired with the same numbers they were in the original data.

 L1 L2 L3 39 40 50 44 58 52 43 48 26 32 48 26 56 50 50 44

Next put the cursor on L3 in the data entry window, and press "2ND", "1", "-" (minus sign), "2ND", "2" and "ENTER". The result should look like the following.

 L1 L2 L3 39 40 -1 50 44 6 58 52 6 43 48 -5 26 32 -6 48 26 22 56 50 6 50 44 6

You can find the differences manually and just enter them in a list, but with longer lists or numbers with more significant digits, doing so may be take a lot of time.

Now press "STAT", choose "TESTS" and use the down-arrow to select "T-Test" and press "ENTER".

For this particular setup, we will choose "Data" instead of "Stats" to the right of "Inpt:". Press the "ENTER" button to make sure the "Data" option is selected.

Next to "m0:", enter "0"; enter "L3"; next to "List:", and make sure that "1" is to the right of "Freq:" Next to "m:", highlight the option "m0", since this is the alternative hypothesis to m = m0 where m0 = 0. Then press "ENTER" to make sure this option is selected. Finally, put the cursor on "Calculate" and press "ENTER". You should see the following results.

The most important values given here are the test statistic, t ≈ 1.36, and the P-value, p ≈ 0.215. Even though the calculator gives ten significant digits for each of these, three significant digits are usually enough. When in doubt, use enough digits of the P-value so you can decide whether it is bigger or smaller than the significance level.

In this case, the P-value is more than the significance level, 1 - 0.95 = 0.05, so we would keep the null hypothesis. With 95% confidence, the evidence is not strong enough to say the means of the two tests are different.

If you select "Draw" instead of "Calculate", the calculator will draw a normal curve and shade in the area representing the P-value. The drawing process takes a little longer, but the test statistic and P-value are still shown at the bottom of the screen.

In the "Draw" screen, the P-value is only given to 4 decimal places. So if the P-value is less than 0.00005, the "Draw" screen would say the P-value is .0000. If this is the case, go back and use the "Calculate" option to give the P-value in scientific notation, because the P-value is usually not zero.