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One-way Analysis of Variance (ANOVA) - 4 Groups

Last modified by
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Jul 24, 2020, 6:28:07 PM
Created by
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Jun 20, 2016, 1:31:14 PM
=a+b+c+d-(((T1)+(T2)+(T3)+(T4))2(n1)+(n2)+(n3)+(n4)-((a-((T1)2n1))+(b-((T2)2n2))+(c-((T3)2n3))+(d-((T4)2n4))))3/((a-((T1)2n1))+(b-((T2)2n2))+(c-((T3)2n3))+(d-((T4)2n4)))n1+n2+n3+n4-4)=a+b+c+d−(((T1)+(T2)+(T3)+(T4))2(n1)+(n2)+(n3)+(n4)−((a−((T1)2n1))+(b−((T2)2n2))+(c−((T3)2n3))+(d−((T4)2n4))))3/((a−((T1)2n1))+(b−((T2)2n2))+(c−((T3)2n3))+(d−((T4)2n4)))n1+n2+n3+n4−4⎞⎟ ⎟ ⎟⎠
Number of groupsNumber of groups
Sample size 1Sample size 1
Sum of values in factor 1Sum of values in factor 1
Sum of squared values in factor 1Sum of squared values in factor 1
Sample size 2Sample size 2
Sum of values in factor 2Sum of values in factor 2
Sum of squared values in factor 2Sum of squared values in factor 2
Sample size 3Sample size 3
Sum of values in factor 3Sum of values in factor 3
Sum of squared values in factor 3Sum of squared values in factor 3
Sample size 4Sample size 4
Sum of values in factor 4Sum of values in factor 4
Sum of squared values in factor 4Sum of squared values in factor 4
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Analysis of Variance (ANOVA) evaluates mean differences between two or more treatments or populations (Gravetter and Wallnau, 2013). Functionally, it performs the same kind of analysis as a t-test, but the advantage of an ANOVA is that an ANOVA can compare more than two groups at once, whereas a t-test is limited to two groups. 

Changing Number of Groups

Below are variations on the ANOVA for different groups.

ANOVA with 3 groups

ANOVA with 5 groups

Computing Sum of Values and Sum of Squared Values

Below are various calculators that supply descriptive statistics for sets of data. It is compatible with groups between n=6 and n=12.
This equation, One-way Analysis of Variance (ANOVA) - 4 Groups, references 1 page
This equation, One-way Analysis of Variance (ANOVA) - 4 Groups, is used in 2 pages
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