Null hypotheses are,
There is no interaction between oral hygiene and cortisol
value.
Cortisol value has no effect on number of cavities.
Oral hygiene has no effect on number of cavities.
Source | SS | df | MS | F |
Between Treatment | 12.6905 | 5 | ||
Factor A | 0.0238 | 1 | 0.0238 | 0.12 |
Factor B | 0.9048 | 2 | 0.4524 | 2.19 |
A x B Interaction | 11.7619 | 2 | 5.88095 | 28.50027 |
Within Treatments | 7.4285 | 36 | 0.2063472 |
dfA = a - 1 = 2 - 1 = 1
dfB = b - 1 = 3 - 1 = 2
df Interaction = (a-1)(b-1) = (2-1)(3-1) = 2
df Within = df Total - (dfA + dfB + df Interaction) = 41 - (1 + 2 + 2) = 36
SS A = MS A * dfA = 0.0238 * 1 = 0.0238
SS B = MS B * dfB = 0.4524 * 2 = 0.9048
MS Interaction = SS Interaction / df Interaction = 11.7619/2 = 5.88095
SS Within = SS Total - (SS A + SS B + SS Interaction) = 20.1190 - (0.0238 + 0.9048 + 11.7619) = 7.4285
MS Within = SS Within / df Within = 7.4285 / 36 = 0.2063472
F Interaction = MS Interaction / MS Within = 5.88095 / 0.2063472 = 28.50027
Critical value of F at 0.01 significance level and df = 1, 36 is 7.40
Critical value of F at 0.01 significance level and df = 2, 36 is 5.25
Since the observed F for factor A is less than the critical value (7.40), there is no significant main effect of factor A.
Since the observed F for factor B is less than the critical value (5.25), there is no significant main effect of factor B.
Since the observed F for Interaction is greater than the critical value (5.25), there is a significant Interaction effect of factor A.
Thus,
The main effect due to factor A is not significant.
The main effect due to factor B is not significant.
The interaction between two factors is significant.
W. Thomas Boyce, a professor and pediatrician at the University of British Columbia, Vancouver, has studied...
W. Thomas Boyce, a professor and pediatrician at the University of British Columbia, Vancouver, has studied interactions between individual differences in physiology and differences in experience in determining health and well-being. Dr. Boyce found that some children are more sensitive to their environments. They do exceptionally well when the environment is supportive but are much more likely to have mental and physical health problems when the environment has challenges. You decide to do a similar study, conducting a factorial experiment...
Aa Aa 11. Two-factor ANOVA Emphasis on calculations W.Thomas Boyce, a professor and pediatrician at the University of British Columbia, Vancouver, has studied interactions between individual differences in physiology and differences in experience in determining health and well-being. Dr. Boyce found that some children are more sensitive to their environments. They do exceptionally wel when the environment is suppo「tive but are much more likely to have mental and physical health problems when the environment has challenges. You decide to do...
3. Two-factor analysis of variance Emphasis on calculations Aa Aa W. Thomas Boyce, a professor and pediatrician at the University of British Columbia, Vancouver, has studied interactions between individual differences in physiology and differences in experience in determining health and well-being. Dr. Boyce found that some children are more sensitive to their environments. They do exceptionally well when the environment is supportive but are much more likely to have mental and physical health problems when the environment has challenges You...
A sociologist classified 45 faculty members by subject matter of course (factor A with 4 levels) and highest degree earned (factor B with 3 levels) The first ANOVA table below is from a model including A and B main effects and AB interaction effects. The second one is from a model including B main effects and AB interaction effects but no A main effects Sequential sum of squares ANOVA table with A, B and AB terms. Analysis of Variance Source...
please show work for each!
ΑΙ Factor B B. B2 T = 40 T = 10 M=4 M= 1 SS-50 SS = 30 Factor A A2 T-50 M=5 SS - 60 T = 20 M = 2 SS = 40 N-40 G = 120 EX =640 Use a two-way ANOVA with a=0.05 to evaluate the main effects and the interaction. m Source SS df MS F Between treatments | 1 6.67 I 2.00 Factor A (ROWS) 18.00 Factor B (COLUMNS)...
The following results are from an independent-measures, two-factor study with n = 5 participants in each treatment condition Factor A: Factor B: 3 M=5 M=8 M=14 T=25 T=40 T=70 SS 30 SS 38 SS46 n=5 n=5 n=5 2 T= 15 T-20 T=40 SS 22 SS 26 SS 30 ZX2 = 2,062 Use a two-factor ANOVA with α = .05 to evaluate the main effects and interaction. Source df MS Between treatments A x B Within treatments Total F Distribution Numerator...
The following results are from an independent-measures, two-factor study with n condition. 10 participants in each treatment Factor B Factor A 2 T 40 M=4.00 SS = 50 T=50 M = 5.00 SS = 60 T= 10 M 1.00 SS 30 T=20 M 2.00 SS 40 N = 40; G = 120; Σ? = 640 Use a two-factor ANOVA with α =。05 to evaluate the main effects and the interaction Source df MS Between treatments AxB Within treatments Total For...
4. Measuring effect size for two-factor ANOVA Аа Аа It is projected that approximately 580,000 veterans will take advantage of the GI Bill for the 21st Century. Boots to Books is a course for all veterans, current military members, and their family members, friends, and supporters. The goal of Boots to Books is to assist deployed, postdeployed, and veteran students in making a positive transition from military to civilian life or from deployment to postdeployment life, including the acquisition of...
12. Measuring effect size for two-factor ANOVA It is projected that approximately 580,000 veterans will take advantage of the GI Bill for the 21st Century. Boots to Books is a course for all veterans, current military members, and their family members, friends, and supporters. The goal of Boots to Books is to assist deployed, postdeployed, and veteran students in making a positive transition from military to civilian life or from deployment to postdeployment life, including the acquisition of college survival...
12. Measuring effect size for two-factor ANOVA It is projected that approximately 580,000 veterans will take advantage of the GI Bill for the 21st Century. Boots to Books is a course for all veterans, current military members, and their family members, friends, and supporters. The goal of Boots to Books is to assist deployed, postdeployed, and veteran students in making a positive transition from military to civilian life or from deployment to postdeployment life, including the acquisition of college survival...