Question

In Chapter 12 Problem 1: A statistician for a drug company wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines which are CNS stimulants). Their short-term memory was tested on a 20-point scale (where 0 - no memory and 20 - perfect memory) Boys Cylert: 12, 10, 13, 10, 9, 12, 13, 10, 11, 12 Boys Placebo: 5, 6, 7, 6, 4, 5, 6, 7, 5, 7 Boys Ritalin: 3, 2, 5, 6, 1, 4, 2, 6, 1,5 Girls Cylert: 5, 6, 2, 4, 3, 2, 4, 6, 2, 4 Girls Placebo: 4, 6, 7, 6, 5, 4, 5, 6, 7,7 Girls Ritalin: 12, 9, 14, 13, 9, 12, 8, 15, 12, 11 the q value at p = .05 for Tukey's HSD test for the main effect for drug levels is

The q value at p = .05 for Tukey's HSD test for the main effect for drug levels is

3.44

4.37

3.79

2.86

Question 2 In Problem 1, Tukey's HSD value at p = .05 for the main effect for drug levels is

3.44

4.37

2.86

1.25

Question 3 In Problem 1, the results of Tukey's test for the main effect of drug levels reveals that

short-term memory is not different between Cylert and Ritalin conditions, but both are better than the placebo

short-term memory is better for Cylert than the placebo or Ritalin

short-term memory for Ritalin is better than for Cylert or the placebo

short-term memory is poorer for Cylert and Ritalin than for the placebo

Question 4 In Problem 1, the q value at p = .05 for Tukey's HSD for the interaction between gender and drug levels is

3.44

4.23

5.11

5.24

Question 5 In Problem 1, Tukey's HSD value for the interaction between gender and drug levels (at p = .05) is

3.44

4.23

2.17

1.17

Question 6 In Problem 1, the results of Tukey's test for the boys in the interaction revealed

Ritalin worked best

Cylert worked best

the placebo worked best

none of the above

Question 7 In Problem 1, the results of Tukey's test for the girls in the interaction revealed

Ritalin worked best

Cylert worked best

the placebo worked best

none of the above

Question 8 In Problem 1, overall, for the interaction, which of the following is true?

Boys' short-term memory is better on Ritalin.

Girls' short-term memory is better on Cylert.

Boys' short-term memory is better on Cylert.

none of the above

Question 9 In Problem 1, when comparing boys and girls in the interaction, which of the following is true?

Boys do better on Cylert and girls do better on Ritalin.

Boys do better on Ritalin and girls do better on Cylert.

There is a significant difference in short-term memory between girls on Cylert and boys on Ritalin.

none of the above

Question 10: In an Effect Size Analysis in a two factor ANOVA for a main effect, k is equal to

the number of levels for the main effect

the number of levels times 2

the number of levels minus 2

the number of levels for the interaction

Answer 1

Question 2 In Problem 1, Tukey's HSD value at p = .05 for the main effect for drug levels is

Option: 3.44.

(Note that this is not the exact value and the exact value is 3.41 (Use R code: round(qtukey(0.95,3,54),2)).

Question 3:

MSE HSD = 3.44 1.25 20 where, MSE = mean sum of squares due to error = = 2.6278 Tcylert T Ritalin = 7.5, T Placebo - 5.75. since T Placebo – Teylert= T Placebo – T Ritalin) = 1.75 > HSD,

Option: short-term memory is not different between Cylert and Ritalin conditions, but both are better than the placebo.

Question 4 In Problem 1, the q value at p = .05 for Tukey's HSD for the interaction between gender and drug levels is

Option: 3.44.

(Note that this is not the exact value and the exact value is 3.41 (Use R code: round(qtukey(0.95,3,54),2)).

Question 6:

$HSD=3.44\sqrt{\frac{MSE}{10}}=1.76\\\\ where,~MSE=mean~sum~of~squares~due~to~error=2.6278\\\\ \bar{x}_{boy,cylert}=11.2 ,~\bar{x}_{boy,Ritalin}=5.8 ,~\bar{x}_{boy,Placebo}=3.5.~since\\ |\bar{x}_{boy,cylert}-\bar{x}_{boy,Ritalin}|=5.4>HSD,\\ |\bar{x}_{boy,Placebo}-\bar{x}_{boy,cylert}|=7.7>HSD,\\ |\bar{x}_{boy,Placebo}-\bar{x}_{boy,Ritalin}|=2.3>HSD,\\\\$

Option: Cylert worked best

Question 7:

$\bar{x}_{girl,cylert}=3.8,~\bar{x}_{girl,Ritalin}=5.7,~\bar{x}_{girl,Placebo}=11.5.~since\\ |\bar{x}_{girl,cylert}-\bar{x}_{girl,Ritalin}|=1.9>HSD,\\ |\bar{x}_{girl,Placebo}-\bar{x}_{girl,cylert}|=7.7>HSD,\\ |\bar{x}_{girl,Placebo}-\bar{x}_{girl,Ritalin}|=5.8>HSD,\\\\$

Option: the placebo worked best.

Excel output:

Anova: Two-Factor With Replication
SUMMARY	Boys	Girls	Total
Cylert
Count	10	10	20
Sum	112	38	150
Average	11.2	3.8	7.5
Variance	1.955555556	2.4	16.47368
Placebo
Count	10	10	20
Sum	58	57	115
Average	5.8	5.7	5.75
Variance	1.066666667	1.344444	1.144737
Ritatin
Count	10	10	20
Sum	35	115	150
Average	3.5	11.5	7.5
Variance	3.833333333	5.166667	21.10526
Total
Count	30	30
Sum	205	210
Average	6.833333333	7
Variance	12.90229885	13.86207
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	40.83333333	2	20.41667	7.769556	0.001083	3.168246
Columns	0.416666667	1	0.416667	0.158562	0.692054	4.019541
Interaction	593.4333333	2	296.7167	112.9154	5.11E-20	3.168246
Within	141.9	54	2.627778
Total	776.5833333	59