Constant Sound Random Sound No Sound Subject’s Gender 7 5 2 M 4 5 2 M...

Constant Sound	Random Sound	No Sound	Subject’s Gender
7	5	2	M
4	5	2	M
6	3	3	F
8	4	1	M
6	4	2	F
6	7	1	F
2	2	4	F
9	2	4	M

If each subject participated in all the three conditions, and we now know about the gender of the subjects too.

Could you write down the test statistics for the gender variable?

What is the p-value of the gender variable?

What is the degree of freedom of the test statistics of the interaction effect?

If we denote them in terms of F(x, y), what is x?

What is y?

Solutions

Expert Solution

Anova: Two-Factor With Replication

SUMMARY	Constant Sound	Random Sound	No Sound	Total
M
Count	4	4	4	12
Sum	28	16	9	53
Average	7	4	2.25	4.416667
Variance	4.666667	2	1.583333	6.44697

F
Count	4	4	4	12
Sum	20	16	10	46
Average	5	4	2.5	3.833333
Variance	4	4.666667	1.666667	3.969697

Total
Count	8	8	8
Sum	48	32	19
Average	6	4	2.375
Variance	4.857143	2.857143	1.410714


ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	2.041667	1	2.041667	0.659193	0.427452	4.413873
Columns	52.75	2	26.375	8.515695	0.002497	3.554557
Interaction	6.083333	2	3.041667	0.982063	0.393731	3.554557
Within	55.75	18	3.097222

Total	116.625	23

test stat for gender variable = 0.659

p value = 0.427452

df for the test statistics of the interaction effect=2

x=2, y=18

orchestra answered 1 year ago

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