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Introduction to Analysis of Variance - Coggle Diagram
Introduction to Analysis of Variance
Intro: An Overview of Analysis Variance
What is it?
ANOVA: hypothesis=testing procedure that's used to evaluate mean differences between two or more treatments (or populations)
We must decide between 2 interpretations
There are no differences between populations. They observed differences between sample means are caused by random, unsystematic factors that differentiate one sample from another
The populations really do have different means, and these population mean differences are responsible for causing systematic differences between the sample means
Terminology in Analysis Variance
Factor: the variable (independent or quasi) that designates the groups being compared
Levels: individual conditions or values that make up a factor
Two-Factor Design: a study that combines two factors
Single Factor Design: ANOVA
Statistical Hypotheses for ANOVA
The purpose is the determine whether there are significant differences between the treatment conditions
Type I Errors and Multiple-Hypothesis Tests
The testwise alpha level is the rise of a Type I error, or alpha level, for an individual hypothesis test
The experimentwise alpha test is the total probability of a Type I error that's accumulated from all of the individual tests in the experiment
Test Statistic for ANOVA
The Logic of Analysis of Variance
Between Treatment Variance
Measures how much difference exists between the treatment conditions
the differences between treatments are not caused by any treatment effect but are the result of sampling error
the differences between treatments have been caused by the treatment effects so the scores in one treatment should be systematically different from scores in another condition
Within-treatment Variance
Provide a measure of how big the differences are when H0 is true
random, unsystematic factors
The F-Ratio
F = vairance between treatments/variance within treatments = differences including any treatment effects/differences with no treatment effects
F = systematic treatment effects + random and unsystematic differences/random and unsystematic differences
ANOVA Notations and Formulas
ANOVA Formulas
F = variance between treatments/variance within treatments
Final calculation for ANOVIA is the F-ratio
Sample variance = s^2 = SS/df
Total Sum of Squares
SSwithin treatments
Between-treatments sum of squares
SSbetween = SS total- SS within
Analysis of Degrees of Freedom (df)
Calcluation of Variances (MS) and the F-Ratio
Examples of Hypothesis Testing and Effect Size with ANOVA
Distribution of F- Ratios
The F-ratio is constructed so the numerator and denominator of the ratio are measuring exactly the same variance when the null hypothesis is true
There are 2 obvious characteristics
F-values are always positive numbers
when H0 is true, the numerator and denominator of the F-ratio are measuring the same variance
Post Hoc Tests
Enables you to go through the data and compare the individual treatments two at a time
Turkey's HSD Test
Scheffe Test
Uses the F-ratio to evaluated the significance of the difference between any two treatment conditions
