Week 2 ANOVA (Text books)

Question 1

Rather than run an ANOVA, why don’t we simply use multiple t-tests when we have more than 2 groups/conditions?

Answer 1

• because of an increased type 1 error rate - each time we test a group the probability of falsely rejecting the null hypothesis is 5%; which with 3 groups would rise to 14.3%
• ANOVA hold the risk of a type 1 error at 5%
• If 5 conditions rather than 3 error rate rises to 40% if run t-tests!

Question 2

What is the name for this error rate across statistical tests conducted on the same experimental data?

Answer 2

*Familywise error rate
or
*Experimentwise error rate

Question 3

What is the equation for the familywise error rate?

Answer 3

familywise error = 1 - (-.95) to the power of n

n = number of groups

Question 4

In a nutshell, what does ANOVA do?

Answer 4

• ANOVA tells us whether 3 or more means are the same
• so it tests the null hypothesis that all group means are equal
• ANOVA tests for an overall experimental effect
• ANOVA is a special type of regression

Question 5

The F ratio of ANOVA tells us if there is an overall experimental effect, what next?

Answer 5

Post hoc tests, such as Tukey’s HSD, tell us if where the significance is

Question 6

So, what does ANOVA do?

Answer 6

ANOVA compares the ratio of systematic variance to unsystematic variance in an experimental study (using the F ratio)
*The F ratio assesses how well a regression model can predict an outcome compared to the error within that study

Question 7

Why is it important to have a control group in social science experiments?

Answer 7

• They act as a baseline for other groups, which is a reference point.
• when I compare the results, I will see how different each treatment condition is to the control/baseline group to determine if that treatment is effective

Question 8

What are Andy’s wise words regarding the difference between balanced (equal) and unbalanced (unequal) groups when running ANOVA’s?

Answer 8

*In unbalanced designs, it is important to have a fairly large number of cases to ensure that the estimates of the regression coefficients are reliable.

Question 9

Post hoc tests are designed to reduce the likelihood of a type 1 error rate, but what is the downside according to Pallant?

Answer 9

With post hoc tests the approach is stricter making it more difficult to obtain statistically significant differences

Question 10

How do G & W partition the degrees of freedom for an independent measures ANOVA?

Answer 10

df total = N - 1
df between = k - 1
df within treatments = N - k

Question 11

According to G & W what do SSbetween & MSwithin provide?

Answer 11

SSbetween and MSwithin provide a measure of how much difference there is between treatment conditions

Question 12

What are the H0 and H1 for ANOVA?

Answer 12

• The Null hypothesis (H0) is that in the general population there are no mean differences among the treatments
• The H1 (Experimental hypothesis) is that at least one mean is different from another

Question 13

What are the effect sizes for Cohen’s d?

Answer 13

d = 0.2: Small effect (mean difference around 0.2 standard deviation)
d = 0.5: Medium effect (mean difference around 0.5 standard deviation)
d = 0.8: Large effect (mean difference around 0.8 standard deviation)

Question 14

When is ANOVA considered to be robust?

Answer 14

When n is large (20-30+ in each group)
Therefore, violation on the normality assumption would have little effect on its accuracy.
P.93

Question 15

Characteristics of large sample sizes in ANOVA

Answer 15

With large and equal groups in ANOVA =
Also robust against heterogenous variances.
P.93

Question 16

When is Kruskal-Wallace test used?

Answer 16

When the assumptions underlying ANOVA are not met:
Normality and homogeneity
Sample size small and unequal
DV measured on an ordinal scale

Question 17

What is the null hypothesis in ANOVA?

Answer 17

Is that the population means for the groups are equal;

the alternative hypothesis is that they are unequal.

Question 18

When is the F ratio close to 1?

Answer 18

If the variation BETWEEN groups is of the same order of magnitude as the naturally occurring level among individuals WITHIN GROUPS (I.e. Individual differences or error variance).

The F-ratio will be close to 1 and the null hypothesis of no real difference between the groups will be retained.
P.93.

Question 19

What if the variation between groups is much higher than the variation within groups?

Answer 19

The F ratio will be much greater than 1 and the null hypothesis of no difference between the groups will be rejected.
P.93

Question 20

Variance between groups is also known as…

Answer 20

ERROR VARIANCE

Question 21

What is an OMNIBUS F?

Answer 21

A significant or overall omnibus F indicates that there is a difference SOMEWHERE among the groups.

To find out where the differences are… Post hoc analytical comparisons must be conducted.