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Introduction to Analysis of Variance - Coggle Diagram
Introduction to Analysis of Variance
Analysis of variance (ANOVA)
- a hypothesis-testing procedure that is used to evaluate mean differences between two or more treatments (or populations).
Levels
- The individual conditions or values that make up a factor
Two-factor design or a factorial design
- A study that combines two factors
Single factor designs
- studies that have only one independent variable (or only one quasi-independent variable).
Test wise alpha level
- the alpha level you select for each individual hypothesis test.
Experiment wise alpha level
- the total probability of a Type I error accumulated from all of the separate tests in the experiment.
The Logic of Analysis of Variance
- a statistical method used to determine whether there are significant differences between the means of three or more independent groups.
Between-Treatments Variance
- measuring the differences between sample means.
Within-Treatments Variance
- provides a measure of the variability inside each treatment condition.
Treatment effects
- the impact that a specific condition or treatment has on the dependent variable.
F-ratio
- the test statistic used in Analysis of Variance (ANOVA) to determine whether there are any statistically significant differences between the means of three or more groups.
Error term
- the variability within each treatment group that cannot be explained by the treatment or group differences.
Total Sum of Squares-
a measure of the overall variability in the data — how much the individual scores differ from the grand mean.
Within-Treatments Sum of Squares
- measures the variability of individual scores within each treatment group essentially, how much the scores deviate from their own group mean, not the grand mean.
Between-Treatments Sum of Squares
- measures how much the group means differ from the grand mean. It captures the effect of the treatment (or independent variable)
Total Degrees of Freedom
-the total number of data points minus 1. It reflects the total amount of variability in your entire dataset.
Within-Treatments Degrees of Freedom
- (also called the error degrees of freedom) tells us how much variation exists within each group. It accounts for random error within each treatment group.
Between-Treatments Degrees of Freedom
-represent the number of independent comparisons you can make between treatment means. It's based solely on the number of groups.
Mean square-
a measure of the variability between the groups or within the groups. It is calculated by dividing the sum of squares (SS) by the corresponding degrees of freedom (df).
Hypothesis Testing and Effect Size with ANOVA
- allows us to compare the means of multiple groups and determine if there is a significant difference between them.
Distribution of F-ratios
- all the possible F values that can be obtained when the null hypothesis is true
ANOVA summary table
- summarizes the results of an ANOVA test, which is used to determine if there are statistically significant differences between the means of three or more groups
eta squared-
a measure of effect size that quantifies the proportion of total variance in the dependent variable that is explained by the independent variable(s) in an ANOVA. It provides a way to understand how much of the variability in the outcome is due to the treatment or grouping factor.
Post hoc tests (or posttests)-
are additional hypothesis tests that are done after an ANOVA to determine exactly which mean differences are significant and which are not.
Pairwise comparisons
- statistical tests used to determine whether the means of two specific groups or conditions are significantly different from each other after conducting an ANOVA.
Tukey’s HSD test
- a post-hoc analysis used after performing an ANOVA when you have more than two groups
Scheffé test-
a post-hoc analysis used in the context of Analysis of Variance (ANOVA) when you want to make pairwise comparisons between multiple groups means after finding a significant result.