Question

Scenario: I'm interested in whether there is a relationship between Team (A vs. B) and Outcome (Good vs. Bad). Below are the data. Test the null hypothesis that the categories are independent. α= .05.

	Team A	Team B
Good Outcome	fo = 35 fe=	fo = 55 fe=
Bad Outcome	fo = 15 fe=	fo = 45 fe=

The expected frequency, f_{e ,} for the Team A X Good Outcome category = _____

20

90

30

40

The Chi Square test statistic = _____

3.13

1.25

35.14

7.55

degrees of freedom, df = ______, and the Chi Square critical boundary = ______

1; 3.84

15; 25.00

3; 7.81

2; 5.99

What is the correct result based on the data?

Retain H₀; Not Significant; categories are Not independent

Reject H₀; Significant; categories are Not independent

Retain H₀; Not Significant; categories are independent

Reject H₀; Significant; categories are independent

The correct APA format for the result would include

p > .05

p < .05

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	A	B	Total
	Good outcome	30.0000	60.0000	90
	bad outcome	20.0000	40.0000	60
	total	50	100	150
chi square    χ2	=(Oi-Ei)2/Ei	A	B	Total
	Good outcome	0.833	0.417	1.2500
	bad outcome	1.250	0.625	1.8750
	total	2.0833	1.0417	3.1250
test statistic X2=		3.1250

The expected frequency, f_{e ,} for the Team A X Good Outcome category = 30

The Chi Square test statistic = 3.125

degree of freedom(df) =(rows-1)*(columns-1)=1

Chi Square critical boundary = 3.841

Retain H₀; Not Significant; categories are independent

The correct APA format for the result would include p >0.05