Week 8: One-Way Between-Subjects ANOVA

Question 1

What does ANOVA stand for?

When do you use an ANOVA?

Answer 1

ANOVA = Analysis of Variance
Similar to t-tests, you’re comparing mean differences
However, you’re comparing 3 or more group means, NOT just 2 group means like in a t-test

Question 2

What are categorical variables?

Answer 2

Nominal or ordinal

Question 3

What are continuous variables?

Answer 3

Ratio or interval

Question 4

In an ANOVA, is your IV categorical or continuous?

Is your DV categorical or continuous?

Answer 4

Independent Variable = Categorical
- consists of 3 or more levels or groups
Dependent Variable = Continuous

Question 5

• In an IV, what does it mean by having a between-subjects variable or a within-subjects variable?

Answer 5

Between-subjects = people participate in ONE group only

Within-Subjects = people participate in ALL groups

Mixed = a combination of between and within subjects design

Question 6

• What is an F-test?

Know what the numerator and denominator represents in your F ratio.

Answer 6

instead of calculating mean differences, we calculate variances to get our F-Value

   Variance Between Groups (Mean Square Between) F= \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
   Variance Within Groups (Mean Square Error)

Question 7

• Why is it bad to do multiple comparisons using t-tests when you have 3 or more levels or groups in your IV?

Answer 7

Never use a t-test to compare 3 or more groups
(group 1 v. group 2, group 2 v. group 3, group 1 v. group 3)

Its bad to compare these 3 groups using separate t-tests
= you are likely to inflate -increase- type I error (see a significant difference when there is none)

Use an ANOVA to compare 3 OR MORE groups
-helps to deal with Type I error inflation through post hoc tests

Question 8

• What are the assumptions of an ANOVA?

Answer 8

Normal distribution - make sure your distribution has no skewness or kurtosis

Homogeneity of Variance - make sure the variances of each group are similar

Independent observations - scores from each group or level must come from different people

Question 9

• What does a “one-way” mean? What does a “two-way” mean?

Answer 9

One-way = having 1 IV

Two-way = having 2 IVs

Three- way = having 3 IVs

Question 10

• What is an omnibus test? What does an omnibus test tell us and not tell us?

Answer 10

(when you get your f-test, you’ll be examining an omnibus test)
Omnibus test - tells us overall whether our analysis of our IV and DV is significant

OMNIBUS = LOOKS FOR SIGNIFICANT DIFFERENCE OF IV AND DV

Does not tell us where the mean difference occur within your levels or groups of the IV

Question 11

• What do you want to assess if your p-value in an F statistic is significant? What is a post hoc test?

Answer 11

If your p-value is significant, you want to access the post hoc test
- if not significant, no need to look at post hoc test

Post Hoc Test = examines where you mean differences are in your categorical levels of the IV

POST HOC TEST = MEAN DIFFERENCES OF CATEGORICAL LEVELS

*Remember, a post hoc test in an ANOVA calculates your group mean comparison with Type I Error inflation in mind.

Question 12

• What are Type I and Type II errors? What are other names given to represent these errors?

Answer 12

Type I Error = (Family wise error) Finding a significant difference when there should NOT be one

Type II Error = (Statistical Error)Finding NO significant difference when there should be
*Important because they affect your interpretation of group mean comparisons

Question 13

• What does it mean by having a conservative post hoc test?

What does it mean by having a liberal post hoc test?

Answer 13

When Post Hoc Tests are too CONSERVATIVE (strict in its calculation), Type I error is similar but type II error is greater.

When Post Hoc Tests are too LIBERAL (not strict in its calculation), type I error is greater but Type II error is smaller

*Notice trade off between ^ V or V ^ (arrows)

Question 14

• Know the different post hoc tests discussed in class – which ones are conservative and liberal?

Answer 14

Bonferroni = conservative (reduces Type I Error but increases Type II Error), useful when comparing fewer group means

LSD= Least Significant Difference = liberal (likelihood of Type I error)

Turkey Honest Significant Difference (HSD) = conservative (reduces Type I Error but also increases Type II Error), useful when comparing a lot of group means.

Question 15

Bonferroni

Answer 15

conservative
(reduces Type I Error but increases Type II Error),
useful when comparing fewer group means

Question 16

LSD

Answer 16

Least Significant Difference =
liberal
(likelihood of Type I error)

Question 17

Turkey Honest Significant Difference (HSD)

Answer 17

conservative

(reduces Type I Error but also increases Type II Error), useful when comparing a lot of group means.