General instructions. This assignment is to be done in your lab session. Submit your assignment from the lab computer during lab time. If the assignment involves SPSS, be sure that when you open SPSS, you set it so that commands are displayed in the output: Edit -> Options, Viewer tab, check box Display commands in the log.

Our goal in this lab exercise is to demonstrate how some contrasts can be correlated while other contrasts are independent. To do this, you will adapt the linked SPSS syntax file. This program samples three scores (n=3) from each of three normally distributed groups (a=3). It then computes the value of three contrasts for each sample. Then it determines the correlations of the contrasts across the random sample, and makes scatterplots of the contrasts. Your job is to complete the SPSS syntax (a.k.a. "programming code") and answer the questions below.

* Open the SPSS syntax file. Look closely at the code and find the comments, indicated like this:
/* Here's an SPSS comment. */
Some comments simply explain what the code is doing. Other comments tell you to make some modifications. Carry out the modifications to the code indicated by the comments.

* Run the code. Your output should have (i) a Frequencies table that shows the 95th and 97.5 percentile of the contrasts, (ii) a table of Descriptive Statistics for the contrasts, (iii) a table of correlations for the contrasts, and (iv) two scatterplots. If you try this several times, be sure to clear out all trial runs, and retain only the final run.

* In the top of the first Log textbox, type your full name. After that, type in answers to these questions:

(A) What is the value of Σ_jc_1jc_3j? Are the contrasts Ψ₁ and Ψ₃ orthogonal? What is the correlation across samples of Ψ₁ and Ψ₃?

(B) Suppose a random sample has Ψ₃ (=(M1+M2)/2-M3) greater than the 95th percentile. For such a sample, what is the probability that Ψ₁ (=M1-M2) exceeds its 95th percentile? This question is asking for the conditional probability of getting a false alarm on Ψ₁ given that you have a false alarm on Ψ₃. You can answer this question by counting the number of samples that exceed both 95th percentiles, and dividing by the number of samples that exceed just one 95th percentile. (And you can make those counts by clicking on the interactive scatterplot and setting the axis limits so that the lower limit is at the 95th percentile, which you determine from the output table.) Hint: The conditional probability should be about 5%, because the two contrasts are orthogonal.

(C) What is the value of Σ_jc_2jc_3j? Are the contrasts Ψ₂ and Ψ₃ orthogonal? What is the correlation across samples of Ψ₂ and Ψ₃?

(D) Suppose a random sample has Ψ₃ (=(M1+M2)/2-M3) greater than the 95th percentile. For such a sample, what is the probability that Ψ₂ (=M1-M3) exceeds its 95th percentile? This question is asking for the conditional probability of getting a false alarm on Ψ₁ given that you have a false alarm on Ψ₃. You can answer this question by counting the number of samples that exceed both 95th percentiles, and dividing by the number of samples that exceed just one 95th percentile. (And you can make those counts by clicking on the interactive scatterplot and setting the axis limits so that the lower limit is at the 95th percentile, which you determine from the output table.) Hint: The conditional probability should be much greater than 5%, because the two contrasts are positively correlated.

What to turn in and how to turn it in. Save a copy of the output file for your own records, and upload a copy to the Assignments in Oncourse.