F-test analysis - created from Mind Map

Seite 1

One Way ANOVA

Factorial ANOVA

Manually

R- Studio

1. Set the Hypothesis

2. Analyze the degree of freedom and determine the critical value of F

3. Analyze the Sum of the Square

5. Find the F stats

4. Calculate the variance Between and Variance Within

6. Conclusion

H0 and H1

df between and df within

Critical value of F : from the F table

Calculate the mean for each sample

Grand Mean

Sum of Square

SStotal

SSwithin

SSbetween

F=Variance Between/Variance Within

Variance= Sum of Sample/Degree of freedom

Fail the hypothesis or Accept the hypothesis

1.Calculate the group means and the overall mean.

2. Calculate Regression Sum of Squares (SSR) using formula:

3. Calculate the error Sum of Squares (SSE) using :

5. Fill in the ANOVA table

4. Calculate the total Sum of Square (SST)

6. Interprets the results

nΣ(Xj – X..)2

Σ: a greek symbol that means “sum” Xj: the mean of group j X..: the overall mean

Σ(Xij – Xj)2

Σ: a greek symbol that means “sum” Xij: the ith observation in group j Xj: the mean of group j

df treatment: k-1 = 3-1 = 2 df error: n-k = 30-3 = 27 df total: n-1 = 30-1 = 29 MS treatment: SST / df treatment = 192.2 / 2 = 96.1 MS error: SSE / df error = 1100.6 / 27 = 40.8 F: MS treatment / MS error = 96.1 / 40.8 = 2.358

SST = SSR + SSE

Manually

R- Studio

4. Estimate the F ratio for

3. Estimate the degrees of freedom and mean square for

2. Estimate the Sum of Squares

1.Calculate for each cell,

5. Calculate F critical values for

6. Compare F ratio and F critical for each effect and do a conclusion

If the result of interaction factor (AB) is

Factor A

Factor B

AB interactions

Factor A

Factor B

AB interactions

SStotal

SSab

SSb

SSbetween

SSa

SSwithin

Squared score total (T2)

Sum of Squares Within (SSw)

Total (T)

Factor A, Factor B , AB interactions

Significant

Not Significant

Simple main effect

Simple Comparison (if simple main effect is significant

Main effect

Simple Comparison (if main effect is significant)

1. Set Woking directory

2. Load the libarary

3. Import the datafile into the Rstudio

4. Test the assumptions

5. Run the analysis

Specifying the location of the folder

Determine and activate the packages to be used

Bringing the datafile into Rstudio platform

a. Test for normality

b. Test of independence

c. Homogeneity of variance

Examine the distribution of the dependent variable

Assume met (believe that when collecting data , one's response is not affected by another)

By Factor A( test for equality of variance for 2 groups

By Factor B (test for equality of variance for 3 groups or more

Run factorial ANOVA and get the output