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Anova Calculator

ANOVA calculator is used to calculate the difference between two or more means or components through significance tests.

How to use ANOVA calculator:

To use the ANOVA calculator, follow these steps.

Enter the data in the input boxes (Group wise)
You can add or delete groups by clicking the "Add group" or "Delete group" buttons.
Click on calculate button to get the step-by-step solution.

What is ANOVA?

ANOVA stands for Analysis of Variance, a statistical technique used to analyze and compare the means of two or more data groups.

The ANOVA test measures whether there is a significant difference between the means of the groups being compared or if the differences are simply due to chance.

Formulas for ANOVA:

All the following formulas are used while calculating the analysis of variance (ANOVA).

Formula for sum of squares between the group:

SSB = ∑_i=1^kn_i(X̄_i- X̄)²

∑ n_i: the sum of the number of observations in each group
X̄_i: the mean of the ith group
X̄: the overall mean of all the groups

Formula for sum of squares within the group:

SSW = ∑_i=1^K(n_i– 1) S_i²

X̄_i: the mean of the ith group
X̄: the overall mean of all the groups

Formula for the total sum of squares:

SST = SSB + SSW

SST represents the total sum of squares

Formula for mean square between groups:

MSB = SSB / (k – 1)

SSB represents the sum of squares between the group
K – 1 represents the degree of freedom of the group

Formula for mean square within the group:

MSW= SSW / (n – k)

SSW represents the sum of squares within the group
n represents the total sample size
k represents the total number of groups

Formula for test Statistics F:

F = MSB/MSW

MSB represents the mean square between groups
MSW represents the mean square within a group

Applications of ANOVA:

The analysis of variance helps us a lot in various fields. Some applications of ANOVA are as follows:

Medical research
Social sciences
Manufacturing
Agriculture
Business

Example section:

In this section, we’ll learn how the ANOVA table helps us solve our daily problems.

Example 1:

The times required by three workers to perform an assembly-line task were recorded on five randomly selected occasions. Here are the times, to the nearest minute.

Jim	Kane	John
5	0	6
1	1	9
4	4	8
2	6	7
8	3	5

Construct the one-way ANOVA table for the data. Compute SSB, SSW, MSB, MSW, and Static test F using the defining formulas.

Solution:

Step 1: Sum of squares between group

SSB = ∑_i=1^kn_i(X̄_i- X̄)²

SSB = 5 × (4 - 4.6)²+ 5× (2.8 - 4.6)²+ 5 × (7 - 4.6)²

SSB = 46.8

Step 2: Sum of squares within the group

SSW = ∑_i=1^K(n_i-1) Si²

SSW = (5 - 1) × (2.7386)²+ (5 - 1) × (2.3875)²+ (5 - 1) × (1.5811)²

SSW = 62.8

Step 3: Total sum of squares

SST = SSB + SSW

SST = 46.8 + 62.8

SST = 109.6

Step 4: Mean square between group

MSB = SSB / (k - 1)

MSB = 46.8 / (3 - 1)

MSB = 46.8 / 2

MSB = 23.4

Step 5: Mean square within the group

MSW = SSW / (n - k)

MSW = 62.8 / (15 - 3)

MSW = 5.233

Step 6: Test statistics F

F = MSB / MSW

F = 23.4 / 5.233

F = 4.472