Independent Groups ANOVA - analysis of variance

Question 1

Why use ANOVA rather than t-tests?

Answer 1

It guards against the family wise error; investigates the relationship between two or more levels of an IV

Question 2

In what way does a one-way ANOVA differ from the t-test?

Answer 2

It compares multiple groups means rather than just 2; doesn’t tell us direction of differences, only that there is a difference

Question 3

In what way is ANOVA like the t-test?

Answer 3

They both deal with quantitative measurements, hypothesis testing & comparisons between groups

Question 4

What is partitioning?

Answer 4

Separating the total variance into 2 components (treatment & error) to calculate how much variability there is between scores & determine whether there is a treatment effect

Question 5

Under what conditions will MS error = MS treat?

Answer 5

If null is true; any difference is due to chance

Question 6

Under what conditions will MS error /= MS treat?;

Why?

Answer 6

If null is false, MS treat will be larger than MS error;

There will be more variation among the means than can be accounted for by chance

Question 7

How does MS relate to variance?

Answer 7

Mean squared error is the average variability within each treatment group (unrelated to any treatment); Mean squared treat is the variability between the groups

Question 8

The F test has 2 types of degrees of freedom. Why?

Answer 8

Because we use df treat (k-1) & df error ((n1-1) + (n2-1) + (n3-1), etc) to account for both; so we look up df for numerator (treat) & df for denominator (error)

Question 9

What does “omnibus” mean?

Answer 9

It analyses ALL the variance; tells us if there’s a difference but not where the difference is

Question 10

What are the statistical hypotheses?

Answer 10

Null: mew 1 = mew 2=…mew k; Alternative: mew 1 /= mew k prime

Question 11

What are the conceptual hypotheses?

Answer 11

Null: there’s no difference between the means; Alternative: at least 2 means are different

Question 12

What is the logic of Analysis of Variance?

Answer 12

We analyse the variance of the groups to tell us something about the differences between the means; same logic as previous tests: observed differences relative to expected differences

Question 13

What value should F be if the null is true?;

What if the null is false?

Answer 13

Around 1;

Greater than 1 (values are always positive)

Question 14

List the order of calculations

Answer 14

1) calculate SS total; 2) calculate SS treat; 3) deduct to find SS error; 4) calculate mean squared treatment & error; 5) calculate F ratio; 6) construct a summary/source table; 7) use tables to find critical F & compare; 8) reach decision; 9) interpret results

Question 15

What are the assumptions of the independent groups ANOVA?

Answer 15

Normality - each set of scores is drawn from a population that is normally distributed; Homogeneity of variance - the scores are drawn from populations with equal variances; Independence of observations - the observations are all independent of one another

Question 16

What happens if the assumptions are violated?;

When are unequal variances a problem?

Answer 16

It’s a robust test, so provided the populations are fairly symmetric & the largest variance is no more than 4 times the smallest, ANOVA is likely to be valid;
If sample sizes are also unequal

Question 17

How do we calculate SS total?;
How do we calculate SS treat?
What about SS error?

Answer 17

Sum of: (each score minus grand mean) squared;
Sum of: number of participants from group, times (mean of group minus grand mean) squared;
SS total minus SS treat

Question 18

How do we calculate MS treat?
What about MS error?
How do we calculate F?

Answer 18

SS treat divided by df treat;
SS error divided by df error;
MS treat divided by MS error