The following data are from an experiment comparing three different treatment conditions    Treatment          I II III P     6 9 12 27 N = 18   8 8 8 24 G = 108   5 7 9 21 ΣX2 = 800   0 4 8 12     2 3 4 9     3 5 7 15     M = 4 M = 6 M = 8       T = 24 T = 36 T = 48       SS =42 SS = 28 SS = 34       Assume that the data are from an independent- measures study using three separate samples, each with n = 6 participants. Ignore the column of P totals and use an between-subjects ANOVA with α = .05 to test the significance of the mean differences. (follow the four-step procedure) Now assume that the data are from a repeated- measures study using the same sample of n = 6 participants in all three treatment conditions. Use a repeated-measures ANOVA with α = .05 to test the significance of the mean differences. (follow the four-step procedure) Explain why the two analyses lead to different conclusions Compute partial eta square for problem 2. Report your results of the hypothesis test and effect size in APA format Conduct a post hoc analysis for Problem 2 using HSD.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...