Explain the ANOVA method
ANOVA method is a statistical method where different components are generated from separated variance data for additional tests. The relationship between independent and dependent variables is explained where a one-way ANOVA is used for more than three groups of data.
Steps Followed for ANOVA Calculation and how those Calculations result in The Respective Table.
- Calculate the mean- calculate all the ways in the question for all the groups then figure the overall means
- Set up the alternative and null hypothesis- the alternative theory states that there is a difference in the means while null hypothesis states that the means are similar.
- Calculate the sum of squares- summing all the group means and subtract to the total means from all the groups
- Calculate the degrees of freedom (df)
- Calculate the mean squares- dividing degree of freedom from sum of squares row by row
- Construct a table and make conclusions- insert all the results in the table and look for F
Example of an ANOVA Table and what is in Every Cell
Source of Variation
Sums of Squares (SS)
Degrees of Freedom (df)
Mean Squares (MS)
F
Between Treatments
2
2510.5
1255.3
93.44
Error (or Residual)
12
161.2
13.4
Total
14
2671.7
The first column is source variation which represents the between treatment and residual or error variation. The between treatment and residual variation are summed up to bring total variation. The second column is named sums of squares. The between treatment sum of squares is computed by adding squared differences between the overall mean and each treatment mean. The error sums of squares is computed by adding the squared differences between the group mean and each observation. The total sums of squares is computed by adding the squared differences between the overall sample and each observation. The third column contains the degrees of freedom (df)—the between treatment degrees of is df1=K-1. Error degrees of freedom is df2=N-K. The total degrees of freedom is N-1. Therefore, (k-1) + (N-K) = N-1). The fourth column contains mean squares (MS) which are computed by dividing degrees of freedom (df) from sums of squares (SS) row by row.
The Type of Analysis ANOVA is Useful for and why
ANOVA helps in testing three or more variables. It is the same as multiple sample t-test with fewer errors and many issues. ANOVA compares the means of every group and spread the variance into different sources.
Disadvantages of Using ANOVA Method
There are several disadvantages of the ANOVA method and the main ones, including; the assumptions should be proved. Also, it may be challenging to determine the differences between multiple groups and one-way ANOVA; therefore, it could be assumed that the groups have similar deviations.
Why ANOVA is used in Regression Analysis
ANOVA helps to assess the effects of a predictor or predictors on a residual and how these predictors can explain the variance in data. In contrast, the regression analysis helps to assess the quantitative relationship between a response and a predictor. Therefore ANOVA is used in regression analysis to determine the relationship between a predictor and a response.
Typical Follow up Analysis After Developing an ANOVA Table