Download One-Way ANOVA with 3 groups Analysis and Power

data cta2x3;
input group pass score;
pass3=0;
if score > 70 then pass3 =1;
if score > 80 then pass3 = 2;
datalines;
0
0
55
0
0
59
0
0
59
0
0
60
0
0
49
0
0
65
0
0
48
0
0
54
0
0
69
0
0
55
0
0
56
0
0
48
0
0
42
0
0
56
0
0
67
0
0
68
0
0
69
0
0
70
0
0
71
0
0
72
0
0
74
0
0
71
0
0
68
0
0
64
0
0
49
0
1
75
0
1
76
0
1
76
0
1
77
0
1
78
0
1
80
0
1
84
0
1
86
0
1
87
0
1
88
0
1
89
0
1
90
0
1
91
0
1
77
0
1
83
0
1
86
0
1
89
0
1
93
0
1
79
0
1
86
0
1
80
0
1
84
0
1
86
0
1
87
0
1
88
0
1
89
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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1
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1
1
1
2
2
2
2
2
2
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
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1
1
0
0
0
0
0
0
0
0
90
91
77
92
65
66
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68
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70
70
71
72
73
63
74
63
71
72
73
63
74
63
70
93
79
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80
84
86
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90
92
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95
93
83
86
90
84
86
88
92
93
90
92
34
56
68
44
58
70
55
59
2
2
2
2
2
2
2
2
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2
2
2
2
2
2
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2
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2
2
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2
2
2
2
2
2
2
2
;
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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1
1
1
1
1
1
1
1
1
66
57
75
76
77
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79
79
80
81
82
77
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77
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90
91
92
93
77
proc glm data=cta2x3;class group;
model score = group;means group;means group /tukey ;run;
***** Means are form the Output *****;
***** The Root MSE from Output is used as the commond stddev **;
***************************************************************;
***** Observed Power at alpha = 0.05
****************************************;
proc power;
onewayanova test=overall
alpha = 0.05
groupmeans = 73.67 | 79.78 | 75.94
stddev = 12.27
groupns = (55 45 50)
power = .;
run;
***** Future Total Sample Size for study to have 80%
*** at alpha=.01 Assuming balanced design *****************;
proc power;
onewayanova test=overall
alpha = 0.01
groupmeans = 73.67 | 79.78 | 75.94
stddev = 12.27
ntotal = .
power = .80;
run;
**** Contingency Table Analysis *************;
proc freq data=cta2x3 order=data;
tables pass*group / chisq measures expected deviation cellchi2 ;
run;
proc freq data=cta2x3 order=data;
tables pass3*group / chisq measures expected deviation cellchi2;
run;
The GLM Procedure
Class Level Information
Class
Levels
Values
group
3
0 1 2
Number of Observations Read
Number of Observations Used
150
150
Dependent Variable: score
Source
Model
Error
Corrected Total
R-Square
0.040338
Level of
group
0
1
2
Sum of
Squares
930.15313
22128.70687
23058.86000
DF
2
147
149
N
55
45
50
Coeff Var
16.08876
Mean Square
465.07657
150.53542
Root MSE
12.26929
F Value
3.09
Pr > F
0.0485
score Mean
76.26000
------------score-----------Mean
Std Dev
73.6727273
79.7777778
75.9400000
14.0185783
10.7044784
11.4951809
Tukey's Studentized Range (HSD) Test for score
NOTE: This test controls the Type I experimentwise error rate.
Alpha
0.05
Error Degrees of Freedom
147
Error Mean Square
150.5354
Critical Value of Studentized Range 3.34848
Comparisons significant at the 0.05 level are indicated by ***.
group
Comparison
1 - 2
1 - 0
2 - 1
Difference
Between
Means
3.838
6.105
-3.838
Simultaneous
95% Confidence
Limits
-2.132
9.807
0.266 11.944
-9.807
2.132
***
***** Means are form the Output *****;
***** The Root MSE from Output is used as the commond stddev **;
***************************************************************;
***** Observed Power at alpha = 0.05 ****************************************;
The POWER Procedure
Overall F Test for One-Way ANOVA
Fixed Scenario Elements
Method
Alpha
Group Means
73.67 79.78
Standard Deviation
Group Sample Sizes
55
Exact
0.05
75.94
12.27
45 50
Computed Power
Power
0.589
***** Future Total Sample Size for study to have 80%
*** at alpha=.01 Assuming balanced design *****************;
The POWER Procedure
Overall F Test for One-Way ANOVA
Fixed Scenario Elements
Method
Alpha
Group Means
73.67 79.78
Standard Deviation
Nominal Power
Group Weights
Computed N Total
Actual
Power
N
Total
0.804
336
Exact
0.01
75.94
12.27
0.8
1 1 1