Statistics > Analysis of Variance > One-Way ANOVA
Statistics > Analysis of Variance > One-Way ANOVA
One-way analysis of variance uses one factor to categorize three or more
populations. It is used to test hypotheses that three or more population means
are equal. The null hypothesis H0 is
μ1 = μ2 = ... = μk,
where μi is the mean of population i of
k populations.
The test statistic F is the ratio of two estimates of the variance
common to the k populations:
When the null hypothesis is true, it has an F distribution
with degrees of freedom given by
numerator degrees of freedom = k - 1
denominator degrees of freedom = N - k
The test statistics F can be expressed as the ratio
MS(treatment) / MS (error).
The mean square (MS) and sum of squares (SS) are computed in order to
obtain F.
SS(treatment) is a sum of squares representing the
variation between the sample means:
where ni is the size of sample i,
is the mean of sample i,
, and N is the sum of all sample sizes.
SS(error) is a sum of squares representing the variation that is assumed to
be common to the populations:
SS(total) is a measure of the total variation in all the sample data:
SS(total) = SS(treatment) = SS(error)
MS(treatment) is the mean square for treatment:
MS(error) is the mean square for error:
To use this utility, you will need to provide sample values for different
populations in separate columns and specify the significance level.
The SS and MS values are displayed along with the test statistic, critical
value, and p-Value.
Dialog Inputs
To include a column in the analysis, select the column name in the
Select the column to be included in the analysis: list and click
the Add to list button. The selected column(s) will be added to the
Responses list. To remove a column from the Responses
list, select it and click the Remove from list button.
Ctrl-click or shift-click to select multiple columns.
Click the Clear Input List button to clear the input list.
Enter the signicance level (a number between 0 and 1) in the
Significance level text box.
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