Understanding t-tests (W2) ✅

Question 1

What contribute to variance?

Answer 1

1. Between IVs:
   - manipulation of IV
   - individual difference
   - experimental error (random and/or constant)
2. Within IVs:
   - individual difference
   - experimental error

t-ratio = variance between IVs / variance within IVs
-> t-value close to 0 => small variance between IV levels

=> For repeated measure: NO individual difference

Question 2

What is the t-distribution?

Answer 2

• The t-distribution represents the distribution of sampled mean differences when the null hypothesis is true -> AKA no difference in means when IV is manipulated
• The t-distribution has mean = 0
• deviations from the mean (t=0) can be expressed in standard error units

Question 3

What is effect size?

Answer 3

• Reporting it WHENEVER you use t-test
• Cohen’s d: The magnitude of difference between two IV level means, expressed in
  standard deviation units
• d = means difference/SD (ignore the sign)
• Interpreting effect size:
  small = 0.1 - 0.3
  medium = 0.4 - 0.6
  large = 0.7-0.9

Question 4

Why can’t t-test be used for IV with more than 2 levels?

Answer 4

• Overall Type 1 error rate across all t-tests would be higher (> 5% chance wrong)
• Familywise Error rate: the probability that at least one of a ‘family’ of comparisons, run on the same data, will result in a Type I error -> provide corrected significant level
• Formula:
  α’ = 1 - (1 - α)^c
  -> α’ = corrected error rate
  -> c = number of comparisons

=> ANOVA can control this error rate

Question 5

Calculate df for t-tests?

Answer 5

Independent: N - 2
Paired: N - 1