MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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STEP 1: State the hypotheses and select an alpha level.
H0: µ1 = µ2 = µ3 (There is no treatment effect.)
H1: At least one of the treatment means is different.
We use α = .05
STEP 2: Locate the critical region.
df total = N - 1 =
df between = k - 1 = (Numerator)
df within = N – k = (Denominator)
look up in the f table: df = Numerator, Denominator, Critical region =
STEP 3: Compute the F-ratio.
SS total = ΣX^2-G^2/N =
SS within = ΣSS inside each treatment =
SSbetween = SStotal – SSwithin
=
Calculation of
MS between=(SS between)/(ⅆf between)
MS within=(SS within)/(ⅆf within)
Calculation of F.
F=(MS between)/(MS within)
=
STEP 4 : MAKE A DECISION
Transcribed Image Text:The following data were obtained from an indepen-
dent-measures research study comparing three treat-
ment conditions. Use an ANOVA with a = .05
to determine whether there are any significant mean
differences among the treatments.
Treatment
II
n = 8
n = 6
n = 4
N = 18
T = 16
T = 24
T = 32
G = 72
SS = 40
SS = 24
SS = 16
EX = 464
%3D
Transcribed Image Text:The F Distribution*
*Table entries in lightface type are critical values for the 05 level of significance.
Boldface type values are for the .01 level of significance.
Criticał
Degrees of
Freedom:
Denominator
Degrees of Freedom: Numerator
3.
4
7
8
9
10
11
12
14
16
20
1
239
200
4999 5403 5625
216
230
5764
161
225
234
237
241
242
243
244
246
6106 6142 6169 6208
245
248
4052
5859
5928
5981
6022
6056
6082
19.36
19.37
19.38
19.41 19.42 19.43 19.44
99.42 99.43 99.44 99.45
2
18.51 19.00 19.16 19.25 19.30 19.33
19.39
19.40
98.49 99.00 99.17 99.25 99.30 99.33
99.34
99.36 99.38
99.40 99.41
8.88
28.24 27.91 27.67
8.94
8.84
8.81
8.69 8.66
27.23 27.13 27.05 26.92 26.83 26.69
10.13 9.55 9.28
9.12
9.01
8.78
8.76
8.74
8.71
3.
34.12 30.92 29.46 28.71
27.49 27.34
6.04
5.96
14.54 14.45 14.37 14.24 14.15 14.02
6.94
6.59
6.39
6.26
6.16
6.09
6.00
5.91
5.87
7.71
21.20 18.00 16.69 15.98
4
5.93
5.84
5.80
15.52 15.21 14.98
14.80 14.66
6.61
5.79
5.19
5.05
4.95
4.88
4.82
4.78
4.74
4.70
1.68
1.61
1.60 1.56
9.68
5
5.41
16.26 13.27 12.06 11.39 10.97 10.67 10.45
10.27 10.15
10.05
9.96
9.89
9.77
9.55
4.15
8.10
5.14 4.76
4.53
4.10
4.06
4.39
8.75
4.00
7.72
6
5.99
4.28
4.21
4.03
3.96
3.92 3.87
13.74 10.92 9.78
9.15
8.47
8.26
7.98
7.87
7.79
7.60
7.52
7.39
3.79
3.73
6.84
4.74 4.35
3.97
3.87
3.68
3.63
3.60
5.59
12.25
3.49
6.27
7
4.12
3.57
3.52
3.44
9.55 8.45
7.85
7.46
7.19
7.00
6.71
6.62
6.54
6.47
6.35
6.15
3.50
6.19
3.28
5.67
4.46 4.07
3.69
3.58
6.37
3.39
5.91
3.34
3.31
3.23
5.56
5.32
3.84
3.44
3.20
5.48
3.15
5.36
8
11.26
8.65 7.59
7.01
6.63
6.03
5.82
5.74
5.12
3.37
3.23
3.29.
5.62
3.18
3.13
3.10
3.07
5.11
4.26 3.86
3.02
3.63
6.42
9.
3.48
2.98
2.93
10.56
8.02 6.99
6.06
5.80
5.47
5.35
5.26
5.18
5.00
4.92
4.80
3.07
5.06
2.97
3.02
4.95
2.91
4.71
2.94
4.96
10.04
3.48
3.33
5.64
3.22
3.14
5.21
2.86
4.60
4.10 3.71
2.82
4.52
10
2.77
7.56 6.55
5.99
5.39
4.85
4.78
4.41
3.09
5.07
2.95
2.90
4.84
9.65
3.59
6.22
3.20
5.32
2.82
4.46
I 1
3.98
3.36
3.01
2.86
2.79
2.74
2.70 2.65
7.20
5.67
4.88
4.74
4.63
4.54
4.40
4.29
4,21
4.10
3.26
5.41
3.00
4.82
2.80
4.39
2.76
4.30
3.49
2.69
3.11
5.06
2.92
2.85
4.50
2.72
4.22
2.64
2.60 2.54
4.75
9.33
3.88
6.93 5.95
12
4.65
4.16
4.05
3.98
3.86
2.67
4.10
2.63
3.02
4.86
2.92
2.84
2.77
2.72
2.60
4.67
9.07
3.80
6.70 5.74
2.55
3.85
3.18
2.51
3.78
13
3.41
2.46
5.20
4.62
4.44
4.30
4.19
4.02
3.96
3.67
2.85
2.65
4.03
14
4.60
3.74
3.34
3.11
2.96
2.77
2.70
2.60
2.56
2.53
2.48
2.44
2.39
8.86
6.51
5.56
5.03
4.69
4.46
4.28
4.14
3.94
3.86
3.80
3.70
3.62 3.51
2.79
2.59
2.55
2.70
4.14
2.64
2.48
2.43
2.39
3.56 3.48
2.90
2.51
2.33
4.54
8.68
15
3.68
3.29
3.06
6.36
5.42
4.89
4.56
4.32
4.00
3.89
3.80
3.73
3.67
3.36
2.66
2.59
3.89
2.54
2.8.5
4.44
2.74
2.49
2.45
2.42
2.37
2.28
3.37 3.25
16
4.49
3.63
3.24
3.01
2.33
8.53
6.23
5.29
4.77
4.20
4.03
3.78
3.69
3.61
3.55
3.45
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