Lecture 4

Question 1

What is a simple ANOVA used for?

Answer 1

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

Question 2

What are the three basic steps in logic of ANOVA?

Answer 2

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.

Question 3

Where does variability come from?

Answer 3

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

Question 4

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

Answer 4

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

Question 5

Describe where total variability comes from

Answer 5

Variability within groups –> due to individual differences

Variability between groups –> Individual differences, experiment error, and treatment effect.

Question 6

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

Answer 6

Through the F ratio

F = Variability between groups/variability within groups

Question 7

Describe the F ratio in more detail

Answer 7

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

Question 8

What is unsystematic variability?

Answer 8

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.

Question 9

What is another term for unsystematic variability?

Answer 9

Random error

Question 10

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

Answer 10

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

Question 11

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

Answer 11

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

Question 12

What is the new term variance gets in ANOVA?

Answer 12

“Mean Square”, or MS (official acronym of Mean Square)

Question 13

Explain the term Mean Square

Answer 13

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

Question 14

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

Answer 14

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

Question 15

List the calculations for a simple ANOVA

Answer 15

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

Question 16

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

Answer 16

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

Question 17

What does the “ij” stand for for the Xij?

Answer 17

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

Question 18

What does the “..” stand for in Xbar..?

Answer 18

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.

Question 19

what does X12 mean? X31?

Answer 19

The first score in the second group.

Third score in the first group.

Question 20

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

Answer 20

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.

Question 21

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

Answer 21

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.

Question 22

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.

Answer 22

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.

Question 23

Explain SSw = SStotal - SSb

Answer 23

= within groups deviations, or SS.

= Deviations of raw scores from their respective group means