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What is a simple ANOVA used for?

Used for when you have three or more groups, but one independent variable.


What are the three basic steps in logic of ANOVA?

1. Scores on the DV are not all the same, they vary.
2. Measure the amount of variability (i.e. the size of the differences between scores).
3. Compare the component parts (sources) of variability.


Where does variability come from?

- Individual differences
- Experimental error (random error)
- Treatment effect


How do you explain where this variability comes from in Logic step 2?

a) calculate the total amount of variability in the entire data set.
b) decompose the total variability into its component parts (or separate components).


Describe where total variability comes from

Variability within groups --> due to individual differences
Variability between groups --> Individual differences, experiment error, and treatment effect.


How do you compare the components (sources) of variability? (Logic step three)

Through the F ratio
F = Variability between groups/variability within groups


Describe the F ratio in more detail

F = treatment effect + ID's + experiment error/ID's + experiment error = Variability between/variability within


What is unsystematic variability?

Unexplained variability, aka uncontrolled variability, aka unsystematic variability.
ID's and experiment error are unsystematic variability.
AKA: variability of subjects treated alike, AKA: variability in scores on DV not attributed to the IV.


What is another term for unsystematic variability?

Random error


What would be the F ratio if the treatment had NO effect?

0 + ID's + exp. error/ID's + exp. error ~> 1 (approx. 1), not exactly 1 because of sampling error.


What would the F ratio be if the treatment did have an effect?

F = some # >0 + ID's + exp. error/ID's + exp. error = >1


What is the new term variance gets in ANOVA?

"Mean Square", or MS (official acronym of Mean Square)


Explain the term Mean Square

New name for variance in ANOVA, it's the mean of the squared deviation scores)
So Sigma(squared) = Sum of Squares/N


There are many ways to notate F ratio then. Provide a few examples.

MS between/MS within = MStrt/MSerror = MS(subscript A, which stands for between groups))/MS(subscript S/A (which stands for within groups))


List the calculations for a simple ANOVA

a) Begin with Sums of Squares, SStotal = Σ(X(subscript ij) - Xbar..)²
b) Next, sum of squares between groups SSb = Σn(Xbarj - Xbar..)²
c) Last, sum of squares within groups, SSw = SStotal - SSb


What is the logic behind the progression of calculations for ANOVA?

Need to calculate σ² (or s²) = SS/df, then decompose it.


What does the "ij" stand for for the Xij?

i = subject, j = group. So the ith score in the jth group.


What does the ".." stand for in Xbar..?

Summed over all of the subjects, and summed over all of the groups. These dots mean that we've summed all of the subjects in all of the groups.
Mean summed over all subjects and summed over all groups --> i.e. its the mean for all scores from subjects in all groups. i.e. the mean of everyone's scores, our GRAND MEAN.


what does X12 mean? X31?

The first score in the second group.
Third score in the first group.


For the first calculation (SStotal = Σ(X(subscript ij) - Xbar..)²), what do you do for all subjects in all groups?

Subtract each raw score from the grand mean, then square them, and sum them.
i.e. sum of squared deviations within each group added together.


What are we doing in the second calculation (SSb = Σn(Xbarj - Xbar..)²) for ANOVA?

Finding the sum of squares between groups, we are looking at the variability between the groups.
- Between group deviations
- Deviations of the treatment means from the grand mean.


Because each individual treatment mean represents a sample of n scores, each of the squared deviation scores has to be multiplied by n to obtain a complete measure of SSb.

Because each individual treatment mean represents a sample of n scores, each of the squared deviation scores has to be multiplied by n to obtain a complete measure of SSb.


Explain SSw = SStotal - SSb

= within groups deviations, or SS.
= Deviations of raw scores from their respective group means