Question

A study examined the effects of Ritalin (for attention deficit hyperactivity disorder) and age of participants on a simple memory task. Carry out the correct hypothesis test with α = .05. Do include a summary table. Provide a conclusion for each effect found. If there is a significant effect: 1) How much variance is explained for that effect? 2) You may skip the post hoc tests.

5 mg 10 mg 20 mg 9 8 11 5 5 9 4 5 9 4 8 9 10 yr 6 7 10 Mean 6.60 9.60 5.60 28 Total 33 48 SS 17.20 9.20 3.20 8 9 6 6 5 4 8 6 7 5 8 20 yr 8 4 4 8 6.20 7.20 5.80 Mean Total 31 29 36 10.80 SS 12.80 12.80

N = 30

Σ X T o t a l 2 = 1 , 521

Answer 1

Solution:

Given the information on the effects of Ritalin (for attention deficit hyperactivity disorder) and age of participants on a simple memory task. we have to carry out the correct hypothesis test with α = .05.

We perform two way ANOVA to test the hypotesis.

1) Ho: There is no difference between the Ritalin.

   H1: At least one of the Retalin is significantly different from the others.

2) Ho: There is no difference between the age.

    H1: there is a significant difference between the age.

5 mg 10 mg 20 mg age 10 yr 9 8 11 5 5 9 4 5 9 4 8 9 7 10 6 8 20 yr 9 6 6 4 5 6 7 8 5 4 8 8 8 4

Anova: Two-Factor With Replication SUMMARY 5 mg 10 0 mg 20 mg Total 10 yr 5 33 48 Count Sum Average Variance 5 28 5.6 4.3 5 15 109 9.6 7.266667 0.8 5.209524 6.6 2.3 20 yr 5 LA 5 36 Count Sum Average Variance 31 6.2 15 29 96 5.8 6.4 3.2 2.971429 7.2 3.2 2.7 Total 77 Count Sum Average Variance 10 10 10 59 69 5.9 6.9 3.433333 2.322222 5.788889 7.7 df ANOVA Source of Variation SS Sample 5.633333 Columns 16.26667 Interaction 32.26667 Within 66 MS F P-value Fcrit 1 5.633333 2.048485 0.165252 4.259677 2 8.133333 2.957576 0.071095 3.402826 2 16.13333 5.866667 0.008427 3.402826 24 2.75 Total 120.1667 29

From the summary table of 10 year people, we see that the mean of 20 mg is maximum 9.6 with a variance of 0.8, while the mean 5 mg is minimum 5.6 with a variance of 4.3.

From the summary table of 20 year people, we see that the mean of 10 mg is maximum 7.2 with a variance of 2.7 while the mean 20 mg is minimum 5.8 with a variance of 3.2

From the ANOVA table, We see that the p-value of Age is 0.1653, which is greater than 0.05, so we fail to reject Ho at 5% level and conclude that there is no significant effect between the ages.

The p-value od Retalin is 0.0711 which is greater than 0.05, so we fail to reject Ho at 5% level and conclude that there is no significant effect between the Retalin.