CASE 1: A habituation task is often used to test memory for infants. In this task, infant’s looking times are measured on successive trials where the experimenter shows them the same stimulus. If the infant remembers the object, looking times decrease across successive trials. Following are data for 5 infants across 3 presentations:

NOTE: Use a =.01

CASE 2 : The following ANOVA summary table gives the results of a research study looking at learning performance under three temperature conditions:

Other details:

1. Temperature conditions= 50 deg, 70 deg, 90 deg
2. \({{M}_{1}}=1,{{M}_{2}}=4,{{M}_{3}}=1\), where M is the mean.
3. \({{n}_{1}}={{n}_{2}}={{n}_{3}}=5\)

For the data above:

1. Complete the summary table
2. Calculate the effect size in two ways
3. If you do an a priori comparison, which test will you use? What would your hypothesis be? Do the appropriate test and say what you concluded.
4. If you do a post-hoc comparison against the control group (assume that group 2, tested under 70 degrees temperature is the control) which test would you use? Do the test and report conclusions.
   CASE 3: Researchers often observe a relationship between the reaction time scores and the number of errors that participants commit on many psychological problem solving tasks. This is known as the speed-accuracy trade-off. Below are data from a reaction time study, where the experimenter recorded average reaction time in ms, and the number of error scores for each individual:
   1. For the data below, calculate Pearson’s correlation [5 points]
   2. Calculate the power for the correlation where \({{\rho }_{1}}\) is the same as the correlation estimated from the sample.

CASE 4: Bahrick and Hall (1991 tested knowledge of high school algebra for t groups of participants, 50 years after they graduated. One group received additional math courses in college, the other did not.

1. Based on the following information, calculate the effect size and power for this study.
   No college math: Mean = 42, n = 8, SS = 100 Additional math: Mean = 50, n = 8, SS = 140
2. If the researchers need power = .80, how many subjects do they need?

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