Question

Imagine you performed a “beer goggling” experiment and randomly assigned participants to drink either 0, 1, or 3 beers, and then had all participants rate the attractiveness of the same fellow college student on a scale from 0 to 50, with higher scores indicating greater perceived attractiveness. There was a total of 21 participants in this study, divided evenly among the three coding conditions. Assume p < .05. Use these data to answer the following questions.

Group	/ Mean Attractiveness Rating
0 beer =	21.57
1 beer	= 26.57
3 beers	= 35.71

Source	SS	df	MS	F
Between	720.096	2	360.048	21.54
Within	300.857	18	16.714

A. in a post-hoc what is HSD value and what is the effect size of this data?

thank you for the help

Answer 1

Let's perform Tukey's Post hoc HSD test for above three groups

M₀ = group with 0 beer

M₁ = group with 1 beer

M3 = group with 3 beers

From above Anova Tales,

MS_within =16.714;

M0 = 21.57;

M1 = 26.57;

M₃ = 35.71;

df_within = 18;

n = 7(21 participants are equally divided into 3 groups)

Now, formula for HSD statistic is:

Where:

• Mi – Mj is the difference between the pair of means. to calculate this, M,i should be larger than Mj
• MSw is the Mean Square Within, and n is the number in the group or treatment

Applying Above formula we get,

Now, HSD(M₃ vs M₀) = 9.150

Similarly, HSD(M₃ vs M1) = 5.915

HSD(M1 vs M₀) = 3.235

From Tukey critical value table, HSD score df =18 and n = 7 for alpha = 0.05 is: 4.67

Now HSD values of M₃ vs M1 and M₃ vs M₀is more than HSD score from table. Hence both the means are significantly different. So, M3-M1 and M3-M0 are significant.

On the other hand, HSD for M1 vs M₀ is less than critical score. Hence we can say that mean for M1 and M0 is significantly same.