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ANOVA Essentials
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ANOVA
Analysis of Variance, a statistical method used to compare means of three or more samples to find out if at least one sample mean is significantly different from the others.
Between-group Variability
The variance that is attributed to the differences between the mean of each group, indicating how much the group means deviate from the overall mean.
Within-group Variability
Measurement of the variance within individual groups, reflecting how much the individual observations deviate from their respective group means.
F-statistic
A ratio used in ANOVA to determine if between-group variability is significantly larger than within-group variability, calculated as the mean square between (MSB) divided by the mean square within (MSW).
Degrees of Freedom (DF)
The number of independent values or quantities which can be assigned to a statistical distribution. For ANOVA, DF is split into DF for between-group and within-group.
Mean Sum of Squares Between (MSB)
The average of the sum of squared deviations of the group means from the overall mean, an essential component in calculating the F-statistic.
Mean Sum of Squares Within (MSW)
It represents the average variance within the groups, an essential component in calculating the F-statistic.
Homogeneity of Variances
The assumption in ANOVA that the variances within each of the groups are approximately equal.
Post-hoc Tests
Additional tests conducted after an ANOVA when the null hypothesis is rejected to identify precisely which means are significantly different from each other.
Type I Error
The error made when a true null hypothesis is incorrectly rejected.
Type II Error
The error that occurs when a false null hypothesis is not rejected.
Power of the Test
The probability that the test correctly rejects a false null hypothesis, which is (1 - beta), where beta is the probability of a Type II error.
Factor
In the context of ANOVA, a factor is an independent variable that categorizes the groups being compared.
Levels
The different conditions or values of a factor in an ANOVA.
One-way ANOVA
A type of ANOVA that involves one independent variable with two or more levels to understand if there is a significant difference in the dependent variable.
Two-way ANOVA
ANOVA that involves two independent variables, examining both the individual and interactive effects on the dependent variable.
Interaction Effect
In a two-way ANOVA, the combined effect of two factors on the dependent variable that is different from the effects each factor would produce on its own.
Main Effect
The effect of an independent variable on the dependent variable averaged across the levels of any other independent variables.
Null Hypothesis in ANOVA
The hypothesis stating that there are no differences between the group means and any observed variation is due to random chance.
Assumptions of ANOVA
The conditions that must be met for the results of the ANOVA to be valid, including independence of observations, normality, and homogeneity of variances.
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