Overview H0 Hypothesis for different tests:
- Always about the population, never about the sample.
- One specific situation: ‘equal to’ – ‘no difference’ – ‘no relation’.
1. Single sample Z-test:
- Population mean is equal to the test value.
Example: Number of cars in households in declining areas is equal to 0.93.
2. Single sample T-test:
- Population mean is equal to the test value.
Example: Desired age at retirement in the population, is equal to 65 years.
3. Paired sample T-test:
- In the population, the mean difference in hours worked between woman and their partners is equal to 0.
- In the population, there is no difference between the mean hours worked between woman and their
partners.
4. Two sample T-test:
- Means for two populations are equal.
- Mean income is equal in the populations of Spain and Portugal.
5. Normality test/ Kolmogorov Smirnov test:
- In the population, the mean distribution is equal to the normal distribution.
- In the population, the hours difference is equal to the normal distribution.
6. Levene’s test:
- Variances of the 2 populations are equal.
7. Sign-test:
- In the population, the number of negative differences is equal to the number of positive differences.
- In the population, the median of differences is equal to 0.
Example: In the population the number of dual earners where woman works more than their partner is
equal to the number of dual earners where partner works more than their woman.
8. Wilcoxon-rank-signed test:
- In the population, the sum of ranks in the group based on positive differences is equal to the sum of
ranks in the group based on negative differences.
Example: In the population the sum of ranks in the group “hrs woman > hrs partner” is equal to the sum
of ranks in the group “hrs partner > hrs woman”.
9. Mann-Whitney test:
- In the population, the mean ranks in both groups are equal.
- In the population, the medians are equal.
Example: The levels of tension between classes are equal between Spaniards and Portuguese
populations.
10. Binomial test:
- In the population, the proportions of …. is equal to a test proportion.
- Always about the population, never about the sample.
- One specific situation: ‘equal to’ – ‘no difference’ – ‘no relation’.
1. Single sample Z-test:
- Population mean is equal to the test value.
Example: Number of cars in households in declining areas is equal to 0.93.
2. Single sample T-test:
- Population mean is equal to the test value.
Example: Desired age at retirement in the population, is equal to 65 years.
3. Paired sample T-test:
- In the population, the mean difference in hours worked between woman and their partners is equal to 0.
- In the population, there is no difference between the mean hours worked between woman and their
partners.
4. Two sample T-test:
- Means for two populations are equal.
- Mean income is equal in the populations of Spain and Portugal.
5. Normality test/ Kolmogorov Smirnov test:
- In the population, the mean distribution is equal to the normal distribution.
- In the population, the hours difference is equal to the normal distribution.
6. Levene’s test:
- Variances of the 2 populations are equal.
7. Sign-test:
- In the population, the number of negative differences is equal to the number of positive differences.
- In the population, the median of differences is equal to 0.
Example: In the population the number of dual earners where woman works more than their partner is
equal to the number of dual earners where partner works more than their woman.
8. Wilcoxon-rank-signed test:
- In the population, the sum of ranks in the group based on positive differences is equal to the sum of
ranks in the group based on negative differences.
Example: In the population the sum of ranks in the group “hrs woman > hrs partner” is equal to the sum
of ranks in the group “hrs partner > hrs woman”.
9. Mann-Whitney test:
- In the population, the mean ranks in both groups are equal.
- In the population, the medians are equal.
Example: The levels of tension between classes are equal between Spaniards and Portuguese
populations.
10. Binomial test:
- In the population, the proportions of …. is equal to a test proportion.
