STATS 13- ANOVA

Question 1

Reminder: normal distribution

Answer 1

Question 2

What do Z and t tell you

Answer 2

• z tells you how different an individual was from the group
• t tells you how different the means of 2 groups are

Question 3

Do you need analysis of variance (ANOVA)

Answer 3

• t-tests: compare 2 groups
• ANOVA: compare as many groups as you like
  
  • Better description: analysis of variance of group MEANS
  • Looking at variability between and within group

Question 4

ANOVAs and t-tests

Answer 4

• What happens when you have more than 2 groups (A, B, C, D)
  
  • We need to be able to see where the overall variability comes from (e.g. A may be very different to BCD)
• Why not just do lots of t-tests?
  
  • Massively increased probability of accepting something as different when it is not
  • Every time we do a t-test we accept there is the probability that it is due to chance, the greater number of t-test we do this chance accumulates
• Get lots of possible combinations
• A-B, A-C, A-D, B-C, B-D, C-D

Question 5

ANOVA

Answer 5

• F= Variability due to factor (means) / Variability due to error
  *

Question 6

Sources of variation

Answer 6

• The important this to realise is that you can divide the variability of a set of data into
• A: variation BETWEEN groups
  
  • The effect of the FACTOR
  • Calculate the mean square between groups
• B: variation WITHIN groups
  
  • The ERROR
  • Calculate the mean square within groups

Question 7

F value and Jargon

Answer 7

• F= Variability due to factor (S_b²) / Variabiltiy due to error (S_w²)
• Mean square (S) is the same as variance (sum squares/ df)
• Sum of squares (SS) is just another measure of variability

Question 8

Degrees of freedom

Answer 8

• For the ANOVA we’re making 2 estimates: variability due to factor (IV) and variability due to error
• The significance of an F value, just like t, depends on the number of measurements or degrees of freedom (DF)
• So when quoting ANOVA resulting need to give 2 degrees of freedom values
  
  • Between groups, DF, then WITHIN groups DF
  • k-1, N-k
  • k= Number of groups
  • N= total data set

Question 9

Reporting results

Answer 9

• We found that the choice of lecturer had a significant effect on final exam scores
• (3,12) = df: 3= df due to factor; 12=df due to error
• Highly significant difference between the scores
  *

Question 10

ANOVA summary from SPSS

Answer 10

Mean square = Sum of squares / df

F = Mean square (factor)/ Mean square (error)

Question 11

ANOVA between-subjects design

Answer 11

• Differences between participants make up a large portion of the error term
• The effect of the factor has to be large before it is significant
  
  • Low statistical power (probability of rejecting a false null hypothesis is low, see lecture)
  • Sample sizes, or effect size, need to be large to be detected

Question 12

ANOVA: within-subject design

Answer 12

• Every participant is tested in each condition
  
  • Differences used: removes between- subject (not very interesting) variation from the error term
• Small factor (IV) effects are more likely to be detected as significant
• High statistical power
• Fewer participants needed