Note: Use the data below for this question and use the Example given below to report your answer.

Also Include SAS codes used

Suppose you are interested in assessing whether peoples musical tastes tend to change as they grow older. You assemble two groups of people (45 people in each group): one group containing young people (i.e. first independent variable, age, and it has two categories. These groups were each subsequently split into three smaller groups of 15 and then assigned to listen to either Hip-Hop/Rap, R&B, or Classical music. This is the second independent variable, music, and it has three categories. There were different participants in all conditions, which means that of the 45 people under 40, 15 listened to Hip-Hop/Rap, 15 listened to R&B and 15 listened to Classical; likewise, of the 45 over-forties, 15 listened to Hip-Hop/Rap, 15 listened to R&B, and 15 listened to Classical. After listening to the music, each person was asked to rate it on a scale ranging from -100 (this music is awful!) through 0 (completely indifferent) to +100 (this music is great!). This is the dependent variable and is called liking.

Perform an appropriate analysis of variance on this data to evaluate:

• the main effect of age (two categories) on liking ratings
• the main effect of type of music listened to (3 categories) on liking ratings
• whether there is interaction between age and type of music on the liking ratings

If appropriate, include a figure that visually displays your most pertinent results.

For this question, you do NOT need to include the 5 steps of hypothesis testing.

Example write-up of results:

A twoway ANOVA was applied to evaluate the effects of treatment (A, B, C), sex (M, F), and the potential interaction between treatment and sex on time to pain relief in 30 patients with osteoarthritis. There was a statistically significant interaction between treatment and sex on time to pain relief [F(2,24) = 27.91, p = indicating that the treatment effects differed by sex.

In males, those who received treatment C had significantly shorter time to pain relief [mean=15.40, 95%CI = (12.58, 18.22)] than those who received treatment A [mean=24.80, 95%CI = (21.98, 27.62), p=0.0009] but not compared to those who received treatment B [mean=17.40, 95%CI = (14.58, 20.22), p=1.0]. In addition, treatment B resulted in significantly shorter time to pain relief than treatment A (p=0.0122) in males.

In females, those who received treatment C had significantly longer time to pain relief [mean=32.40, 95%CI = (29.58, 35.22)] than those who received treatment B [mean=23.20, 95%CI = (20.38, 26.02), p=0.0012] or treatment A [mean=21.40, 95%CI = (18.58, 24.22), p=0.0001]. There was no statistically significant difference in mean time to pain relief for treatment B vs. treatment A in females.

These findings indicate that, in males, treatments C and B were the most beneficial in terms of shortening time to pain relief compared to treatment A. In females, treatments A and B were the most beneficial in shortening time to pain relief compared to treatment C (see Figure above).

Music liking rating by age group and type of music Factor B (Music Type) Factor A (Age Category) Hip-Hop/Rap R&B