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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

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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

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  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               5

    Group 2      9                            8.5            4

    Group 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



    Answer  :  

    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)    S2

    Class 1      9                            20             5                          25

    Class 2      9                            22             7                          49

    Class 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



    Answer  :  

    The Anova coefficient is F = 0.778.



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