*t*-test

This is a two-part problem in which you will analyze the same data set in two different ways. Read the instructions for each part carefully and be sure to show your work. Use the six-step procedure you learned in lecture and lab for determining statistical significance. You should explain your results for each part and why they are the same as -- or different from -- the other part.

1. A researcher evaluates the differences between two different methods of displaying information to fighter pilots about incoming fire from enemy aircraft. The dependent measure consists of pilot reaction time in milliseconds to the correct readout of the displayed information. Analyze the findings using a __t__-test for independent samples (i.e., assume that there are 10 different pilots in each group). Use a
= .05, 2-tailed test. Show null and alternative hypotheses. Report means and standard deviations for both displays. Report t, df, and the significance level. Is there a statistically significant difference between the two displays? What does this mean in terms of the mean reaction times?

__Display # 1__: 455, 470, 395, 465, 543, 480, 508, 548, 586, 613

__Display # 2__: 548, 449, 528, 496, 656, 527, 612, 581, 604, 795

2. Re-analyze the data using a __t__-test for dependent samples, assuming the scores under each display are given in order by participant (e.g., pilot 1 scored 452 on display # 1 and 544 on display # 2, pilot 2 scored 480 on display # 1 and 449 on display # 2, etc., so there are 10 pilots total, not 20). Use a
= .05, 2-tailed test. Show null and alternative hypotheses. Report means and standard deviations for both displays. Report t, df, and the significance level. Is there a statistically significant difference between the two displays? What does this mean in terms of the mean reaction times?

On the basis of your analysis, which display would you recommend? Explain. Why do the two analyses (independent vs. dependent) produce different results?

**Using SPSS for the Independent t-test**

1. Dowload the dataset h5.sav from the place where your lab instructor advised you to find it. For this exercise, consider the columns labeled **time** and **display**.

2. Note how the data for this study are recorded in the Data Editor. The data for Display 1 are stacked on top of the data for display 2; both are in the column labeled **time**. The second column (**display**) lists which display type each piece of data (row) belongs to.

3. Choose Analyze from the pull-down menu, then Compare Means, then Independent Samples T Test. The Independent Samples T-test Dialog Box appears.

4. Select Reaction time in MS. Push the (>) button to move it to the Test Variable box. Select Type of Display. Push the (>) button to move it to the Grouping Variable box. The grouping variable box will show display(??). Click Define Groups. The Define Groups Dialog Box appears. Choose Use Specified Values. For group 1, type in 1; for group 2, type in 2. [These are the numbers (1, 2) that appear in the Display column for your data.] Press continue. The Independent Samples T-Test Dialog Box reappears. In the grouping variable box, display(1, 2) now appears. Press OK.

5. The t-test procedure now runs, and the results appear in the Output window.

**Using SPSS for the Dependent t-test**

1. For this exercise, use the data in columns labeled **d1** and **d2**. Note that d1 contains all the times for display 1 and d2 contains all the times for display 2.

2. Choose Analyze from the pull-down menu, then Compare Means and Paired Samples t-test. The Paired Samples T-Test Dialog box appears. Select d1. D1 will appear in the bottom for Current selections. Select d2. D2 will appear in the bottom under Current Selections. Then press the (>) button to place the pair in the Paired Variables Box.

Press OK. The results will appear in the Output window.