A pharmaceutical research company is studying a new non-addictive sleep medication. Participants who suffered from insomnia for over a year were randomly assigned to one of three groups. Group 1 is given a placebo, Group 2 is given 10 mg of the medication, and Group 3 is given 20 mg of the medication. The scores below represent the nightly average number of hours that the participants slept for a one-week period of time during the study. Conduct a one-way ANOVA using an a = .01. If appropriate, follow up with a measure of effect size and Tukey's HSD.

Placebo (X1) 10 mg (X2) 20 mg (X3)