12 - Hypothesis Testing For Differences Between Means Amd Proportions

Question 1

Tests for difference between means and proportions

Answer 1

• one sample t-test: 1 group,test (n>120)
  Ex: sample mean = pop mean?
• independent group t-test: 2 groups compared
  Ex: sampled from the same pop?
• repeated or paired sample measure t-test: related samples
  Ex: individuals are matched by pairs and allocated at random

Question 2

Assumptions for parametric t-test

Answer 2

Compare 2 groups:

• equal interval or ratio
• normal distribution
• homogeneity of variance
• sample randomly selected

Question 3

Assumption for non-parametric t-test

Answer 3

Compare two populations:
- do not depend on the form of the underlying population distribution
- use nominal or ordinal data
(Basically when 1 or more assumptions of parametric t-test is violated)

=> more widely applicable but less powerful and sensitive to real differences between groups

Ex:

1) Mann-Whitney U test compares mean rank of 2 independent group (ORDINAL -> should be able to rank data)
2) Wilcoxon signed tank test compare observations across two occasions in a repeated measure scheme

Question 4

Degrees of freedom

Answer 4

Indicates the number of values free to vary in a set of values.

Important when sample size is small because it has the effect of increasing the probability level to achieve significance.

Question 5

Degrees of freedom

Answer 5

N-k

K= number of groups

Question 6

Paired sample more precise

Answer 6

Greater control of sources of error stemming from individual differences.

Question 7

Levene test

Answer 7

Test variance homogeneity.

If significant=> equal variance is not assumed and we have to look at the 2nd row