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 mean squares 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

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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 mean squares
MS between=(SS between)/(f between)
MS within=(SS within)/(f within)

Calculation of F.

F=(MS between)/(MS within)
=
STEP 4 : MAKE A DECISION

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 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
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
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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