Question

Proficiency of math courses is evaluated using a special departmental assessment. Three different instructors at two different class times are assessed. The data are below. What can the department conclude with an α of 0.01?

1			2
A	B	C	A	B	C
100 88 96 98	85 79 80 90	89 95 89 61	94 81 80 85	72 63 73 77	88 94 96 87

b) Obtain/compute the appropriate values to make a decision about H₀.
Time: critical value =   ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Instructor: critical value =   ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =   ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Time: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect
Instructor: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect

Answer 1

DATA:

	A	B	C
1	100	85	89
	88	79	95
	96	80	89
	98	90	61
2	94	72	88
	81	63	94
	80	73	96
	85	77	87

..........

Anova: Two-Factor With Replication
SUMMARY	A	B	C	Total
1
Count	4	4	4	12
Sum	382	334	334	1050
Average	95.5	83.5	83.5	87.5
Variance	27.66667	25.66667	233	113
2
Count	4	4	4	12
Sum	340	285	365	990
Average	85	71.25	91.25	82.5
Variance	40.66667	34.91667	19.58333	102.0909
Total
Count	8	8	8
Sum	722	619	699
Average	90.25	77.375	87.375
Variance	60.78571	68.83929	125.4107

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	150	1	150	2.3591	0.1419	8.2854
Columns	730.75	2	365.375	5.7464	0.0117	6.0129
Interaction	490.75	2	245.375	3.8591	0.0403	6.0129
Within	1144.5	18	63.58333
Total	2516	23

b)
Time: critical value = 8.2854  ; test statistic =  2.3591
Decision: Fail to reject H0

Instructor: critical value =  6.0129 ; test statistic =  5.7464
Decision: Fail to reject H0

Interaction: critical value = 6.0129  ; test statistic =  3.8591
Decision: Fail to reject H0

.................

C)

Time: η² =0.06 SMALL

Instructor: η² =0.29 MEDIUM

Interaction: η² = 0.19 SMALL

.............

THANKS

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