One Way ANOVA Calculator

Analysis Of Variance

tails: for ANOVA test you can use only right tail
One Way ANOVA tutorial

Target: To check if the diffrence between the average (mean) of two or more groups (populations) is significant, using sample data
ANOVA is usually used when there are at least three groups, since for two groups you can use t tests.

Example1: A farmer use four differnt fertilizers in four fields. The farmer compare sample average of apples' weight from each field to decide if the difference between the fertilizers is significant.

Assumptions

Independent Independent samples
Normal Distribution Normal distribution of the analyzed population
equal standard deviation Equal standard deviation, σ12=...=σk

Required Sample Data

average Sample data from all compared groups

Parameters

k - Number of groups.
ni - Sample side of group i.
n - Overall sample side, includes all the groups (Σni, i=1 to k).
xi - Average of group i.
x - Overall average (Σxi,j / n, i=1 to k, j=1 to ni).
Si - Standard deviation of group i.

Results calculations

Source Degrees of Freedom Sum of Squares Mean Square F statistic p-value
Groups
(between groups)
k - 1 Number of groups minus one
average Represents the difference between the groups
[Sum of Squares Between Groups, the squared differences of each groups' average from the overall average]
MSG = SSG / (k - 1) The bigger MSG is, the higher the chance that not all the group's averages equal
F = MSG / MSE The bigger F is, the higher the chance that not all the group's averages equal
1 - P(x ≤ F) The smaller p-vlaue is, the higher the chance that not all the groups' averages equal
Error
(within groups)
n - k Overall sample side minus number of groups
average Represents the differences within the groups
[The squared differences of each observation average from the overall average]
MSE = SSE / (n - k) The smaller MSE is, the higher the chance that not all the groups' averages equal
Total
n - 1 Overall sample side minus one, includes observations in all the groups
SS(total) = SSG + SSE Sum of Squares for all observations, not group related
Sample Variance = SS(total) / (n - 1) Regular sample variance for all observations, not group related

Hypotheses

H0: μ1 = .. = μk
H1: not(μ1 = .. = μk)

Test statistic

F statistic

F distribution

F distribution right tailed

Test calculation

Statistic Data

α: Significant level (0-1), maximum chance allowed rejecting H0 while H0 is correct (Type1 Error)
Outliers: It is not recommended to exclude outliers unless you know the reasons

Enter raw data directly
Enter raw data from excel

Enter sample data directly

Header: You may change groups' name to the real names.
Data: When entering data, press Enter after each value.

It is okay to leave empty cells, empty cells or non numeric cells won't be counted

Enter sample data from excel

You may copy data from Excel, Google sheets or any tool that separate data with Tab and Line Feed.
Copy the data, one block of consecutive columns includes the header, and paste below. . click to see example: example from excel


It is okay to leave empty cells, empty cells or non numeric cells won't be counted


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