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Anova Calculator

Anova Calculator helps you to solve the analysis of variance of different subject groups. So, provide the subject groups as input in the below box and hit the calculate button next to the input box to get the output within no time.

Anova Calculator: Anova (Analysis of Variance) Calculator is a handy online tool that displays the significant difference between the means of different groups. Our free handy calculator tool performs all required statistical operations i.e mean and standard deviation much easier and faster. This tool will give the result within fraction of seconds in addition to the step by step solution provided taking examples.

How to Calculate One Way Analysis of Variance?

The below provided step by step procedure is useful for you while solving the One way anova. Use these steps and get the result easily.

  • Take any number of groups with data values
  • Know the mean and standard deviation for those groups
  • Now calculate sum of squares between groups and sum of squares within groups.
  • The formulae to find the SSb and SSw are here
  • SSb=∑i=1 to k ni(xi-x)2, where ni is the number of subjects in the ith group
  • SSw=∑i=1 to k (ni-1)Si2, where Si is the standard deviation of the ith group
  • Total sum of squares SSt=SSb+SSw
  • Mean square between groups MSb=SSb/(K-1)
  • Mean square within groups MSw=SSw/(N-k)
  • F-Statistic or F-ratio F=MSb/MSw
  • Substitute your values in the above formulae and do mathematical calculations

Example

Question: Solve the one way anova of the following groups Group 1={5,1,11,2,8}, Group 2={0,1,4,6,3}, Group 3={13,9,8,15,7}?

Solution:

Given data is Group 1={5,1,11,2,8}, Group 2={0,1,4,6,3}, Group 3={13,9,8,15,7}

Mean of Group 1=5+1+11+2+8/5=27/5=5.4

Mean of Group 2=0+1+4+6+3/5=14/5=2.8

Mean of Group 3=13+9+8+15+7/5=10.4

SD of Group 1=4.1593

SD of Group 2=2.3875

Standard Deviation of Group 3=3.4351

Total Number of subjects in each group (N)=5

SSb=∑i=1 to k ni(xi-x)2

SSb= [(5-5.4)2+(1-5.4)2+(11-5.4)2+(2-5.4)2+(8-5.4)2+(0-2.8)2+(1-2.8)2+(4-2.8)2+(6-2.8)2+(3-2.8)2+(13-10.4)2+(13-10.4)2+(9-10.4)2+(8-10.4)2+(15-10.4)2+(7-10.4)2]*5=149.2

SSw==∑i=1 to k (ni-1)Si2

=(5-1)*(4.1593)2+4*(2.3875)2+4*(3.4351)2

=139.1994

SSt=SSb+SSw = 149.2+139.1994=288.3994

MSb=SSb/(K-1)=149.2/(3-1)

=149.2/2=74.6

MSw=SSw/(N-k)

=139.1994/(15-3)= 11.5999

F ratio=MSb/MSw

=74.6/11.5999=6.4311

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Anova Calculator

Frequently Asked Questions on Anova Calculator

1. How to know the analysis of variance of a sample with a calculator?

You must provide the sample, means of those samples and standard deviation separated by comma in the input and click on the calculate button to get the result in the respective field of Anova Calculator.


2. What is meant by One way Anova?

One way Anova is used to determine the difference between the means of independent groups. It checks the impact of many factors by comparing the means of various samples.


3. What are the types of tests in Anova?

The two types of tests in Anova are One way anova and two way anova with replication or without replication.


4. When to use a one way ANOVA?

You can use the one way anova in this situation. When you have a group of individuals randomly split into smaller groups and completing different tasks.