Question

 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

solve for degrees of freedom, sum of squares and f values

Answer 1

Two factor ANOVA with replication analysis is performed here to test whether short term memory scores are affected by the type of medication in hyperactive children.

The two factor ANOVA test for three null hypothesis

H₀₁: There is no difference in the means of factor gender

H₀₂: There is no difference in means of factor medication type

H₀₃: There is no interaction between factors gender and medication type

The test is performed in excel by using following steps,

Step 1: Write the data values in excel. The data values are,

	Girl	Boy
Cylert	5	12
	6	10
	2	13
	4	10
	3	9
	2	12
	4	13
	6	10
	2	11
	4	12
Ritalin	12	3
	9	2
	14	5
	13	6
	9	1
	12	4
	8	2
	15	6
	12	1
	11	5
Placebo	4	5
	6	6
	7	7
	6	6
	5	4
	4	5
	5	6
	6	7
	7	5
	7	7

Step 2: DATA > Data Analysis > ANOVA: Two Factor With Replication > OK.  The screenshot is shown below,

Step 3: Select Input Range: All the data values column, Rows per Sample: 10, Alpha = 0.05. The screenshot is shown below,

The result is obtained.  The screenshot is shown below,

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	40.83333	2	20.41667	7.769556	0.001083	3.168246
Columns	0.416667	1	0.416667	0.158562	0.692054	4.019541
Interaction	593.4333	2	296.7167	112.9154	5.11E-20	3.168246
Within	141.9	54	2.627778
Total	776.5833	59

From the ANOVA table,

ANOVA
Source of Variation	SS	df	F	P-value			Decision
Medication type	40.83333	2	7.769556	0.001083	<	0.05	Significant
Gender	0.416667	1	0.158562	0.692054	>	0.05	Not Significant
Medication type*Gender	593.4333	2	112.9154	5.11E-20	<	0.05	Significant
Within	141.9	54
Total	776.5833	59

There is a significant difference in Medication type and significant interaction between medication type and gender.