Question 4

The moon illusion refers to the perception that, even though its dimensions remain constant, the moon appears to be much larger when viewed just over the horizon when compared to viewing it at its zenith. Kaufmann & Rock (1962) developed a procedure to replicate the moon illusion in the lab by having participants adjust a "variable" moon appearing on a horizon to match a "standard" moon at its zenith. The dependent variable is the ratio of the diameter of variable moon divided by the diameter of the standard moon. Thus, a ratio of 1.0 would indicate that the two moons are perceived to be the same size whereas ratios larger than 1.0 would indicate that the variable moon on the horizon was perceived to be larger than the standard moon at its zenith. The researchers conduct a pilot study with six participants to test the effectiveness of their new procedure. The mean ratio for the pilot group was 1.311 with a standard deviation of 0.341.

a) Use a directional hypothesis with = .05 to determine whether the new procedure can induce a moon illusion in the lab.

Step 1: Hypotheses:

Step 2: Decision Criterion:

Step 3: Obtain a Statistic:

Step 4: Make a Decision:

Step 5: Report the result:

b) Report and interpret the effect size usingcohen's d.

c) Report and interpret the 98% confidence interval.

d) What would thet-critical have been if we had used a non-directional hypothesis instead of a directional hypothesis ()? Would this have affected the significance of the test? Explain why this happened in terms of power.