What is the ANOVA Test
The ANOVA (Analysis of
Variance) test is a statistical method used to determine if there are any
statistically significant differences between the means of three or more
independent (unrelated) groups. The test compares the variability within each
group to the variability between the groups to ascertain if the group means are
significantly different from each other.
Key
points about ANOVA:
Purpose:
To test for significant differences among group means in a sample.
Hypotheses:
Null
hypothesis (H0): Assumes that all group means are equal.
Alternative
hypothesis (H1): Assumes that at least one group mean is
different.
Types
of ANOVA:
One-way
ANOVA: Compares means across a single factor with multiple
levels (e.g., comparing test scores across different teaching methods).
Two-way
ANOVA: Examines the influence of two different categorical
independent variables on one continuous dependent variable (e.g., studying the
effect of teaching method and student gender on test scores).
Assumptions:
Independence of
observations.
Normally distributed
populations.
Homogeneity of variances
(equal variances among groups).
ANOVA produces an
F-statistic, which is used to determine the p-value. If the p-value is below a
predetermined significance level (e.g., 0.05), the null hypothesis is rejected,
indicating that there is a statistically significant difference between the
group means.
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