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Anova Calculator
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Anova is a easy way to calculate the variance for a given set of of data. It is more helpful when we do for multiple testing in statistics. Anova Calculator is a online tool to do the statistical test. You just have to enter the items n, mean value x and Standard deviation S separated by commas for each and get the mean, SST, MST, SSE, MSE and F ratio instantly.
The Anova coefficient F is given by
F = $\frac{MST}{MSE}$
Here MST = Mean sum of squares due to treatment
MSE = Mean sum of squares due to error.

## Steps for Anova Calculator

Step 1 :

Read the problem and create a table out of it that has items n, score x, standard deviation S and S2.

Step 2 :

Then calculate the mean score $\bar{x}$ and calculate the value of sum of squares due to treatment (SST) given by
SST = $\sum$ n (x-$\bar{x}$)2

Step 3 :

Using it calculate the Mean sum of squares due to treatment MST given by
MST = $\frac{SST}{p - 1}$
where p = total no of populations
Then Calculate the value of SSE and MSE using below formula
SSE = $\sum$ (n-1)S2
and
MSE =$\frac{SSE}{N-p}$

Step 4 :

The Anova coefficient F ratio is given by
F = $\frac{MST}{MSE}$
that gives you the Anova test.

## Problems on Anova Calculator

1. ### A contracter assign equal amount of work for the 3 group of employees. Each having different potential.Go for the anova test for the following data:Employees  no of employees (n) Score (x)  Standard deviation (S)Group 1      9                            8               5Group 2      9                            8.5            4Group 3      9                            9               6

Step 1 :

Given data is

Employees  no of employees (n) Score (x)  Standard deviation (S) S2

Group 1      9                            8               5                             25

Group 2      9                            8.5            4                              16

Group 3      9                            9               6                              36

Step 2 :

No of employees n = 9,
Total no  of population p = 3,
Total no of observations N = 27

The mean $\bar{x}$ = $\frac{8+8.5+9}{3}$
= 8.33

Step 3 :

The sum of squares due to treatment
SST = $\sum$ n (x - $\bar{x}$)2
= 9(8 - 8.33)2 + 9 (8.33 - 8.5)2 + 9(9-8.33)2
= 6

The mean sum of squares due to treatment is given by
MST = $\frac{SST}{p-1}$
= $\frac{4.5}{3-1}$
= 3

The sum of squares due to error is
SSE = $\sum$ (n-1) S2
= (9-1) (25+16+36)
= 616

The mean sum of squares due to error is
MSE = $\frac{SSE}{N-p}$
= $\frac{616}{27 - 3}$
= 25.67

Step 4 :

The Anova coefficient F is given by
F = $\frac{MST}{MSE}$
= $\frac{2.25}{25.67}$
= 0.117

The Anova coefficient is F = 0.117

2. ### Find the anova coefficient for a given data:Students  no of students (n) Score (x)  Standard deviation (S)    S2Class 1      9                            20             5                          25Class 2      9                            22             7                          49Class 3      9                            19             4                          16

Step 1 :

Given data is

Students  no of students (n) Score (x)  Standard deviation (S)    S2

Class 1      10                          20             5                          25

Class 2      10                          22             7                          49

Class 3      10                          19             4                          16

Step 2 :

No of employees n = 10,
Total no  of population p = 3,
Total no of observations N = 30

The mean $\bar{x}$ = $\frac{20+22+19}{3}$
= 20.33

Step 3 :

The sum of squares due to treatment
SST = $\sum$ n (x - $\bar{x}$)2
= 10 (20 - 20.33)2 + 10 (22 - 20.33)2 + 10 (19 - 20.33)2
= 46.67

The mean sum of squares due to treatment is given by
MST = $\frac{SST}{p-1}$
= $\frac{46.67}{3-1}$
= 23.335

The sum of squares due to error is
SSE = $\sum$ (n-1) S2
= (10 - 1) (25+49+16)
= 810

The mean sum of squares due to error is
MSE = $\frac{SSE}{N - p}$
= $\frac{810}{30 - 3}$
= 30

Step 4 :

The Anova coefficient F is given by
F = $\frac{MST}{MSE}$
= $\frac{23.335}{30}$

= 0.778