Tests of Differences and Nonparametric Alternatives

Question 1

REVIEW

Answer 1

REVIEW

Question 2

When is a student t-test used?

Answer 2

Proper SHT for testing the mean difference between the two independent groups.

Question 3

When is a paired t-test used?

Answer 3

Proper SHT for testing the mean differences between the two related groups.

Question 4

When is a analysis of variance (ANOVA) used?

Answer 4

Extension of a Student’s t-test for multiple groups.

Question 5

When is a repeated measures ANOVA used?

Answer 5

Extension of a paired t-test for multiple points in time.

Question 6

When is a factorial ANOVA used?

Answer 6

Applied when the mean differences were compared by multiple factors.

Question 7

When is a mixed ANOVA used?

Answer 7

Applied when the mean differences were compared by multiple factors over time.

Question 8

When is a analysis of covariance (ANCOVA) used?

Answer 8

Applied when the mean differences were compared controlling for a confounding variable.

Question 9

What are some questions to ask when deciding which statistical test to apply?

Answer 9

1. ) Is the level of measurement continuous?
   - To compare means of continuous.
   - To compare proportions (percent) of categorical.
2. ) How many groups are to be compared?
3. ) Are the data normally distributed with equal variances across groups.
4. ) Are the collected data independent or matched.

Question 10

NON-PARAMETRIC TESTS

Answer 10

NON-PARAMETRIC TESTS

Question 11

When are non-parametric tests used?

Answer 11

When the data is not normally distributed or if the variances of the data in the groups are very different.

Question 12

What are the 3 things that identifies data as parametric?

Answer 12

• Data level of measurement to be continuous.
• Normally distributed.
• Equal variances across groups to compare.

Question 13

• __________ tests (student’s t-test, ANOVA,…) are the most powerful on parametric data.
• ____________ tests are available when data is non-parametric.

Answer 13

• Parametric

- Non-parametric

Question 14

Non-Parametric Tests:

• ______________ test in place of the Student’s t-test.
• _________________ test in place of the paired t-test.
• ________________ test in place of ANOVA.
• ________ test in place of repeated measures ANOVA.

Answer 14

• Mann-Whitney U
• Wilcoxon signed-rank
• Kruskal-Wallis H
• Friedman

Question 15

Non-parametric tests work on the principle of ________ the data.

Answer 15

ranking

Question 16

Non-parametric tests work on the principle of rank ordering of scores.

• Scores are ranked from _________ to ___________.
• With the rank of __ assigned to the smallest score and _ to the highest score.

Answer 16

• smallest to largest

- 1, n

Question 17

Non-parametric test may not be testing the null hypothesis of interest.

• Null hypotheses that can be studied using non-parametric tests tend to be very _________.
• There is not much choice for non-parametric tests.

Answer 17

-restrictive

Question 18

• Non-parametric methods are focused on __________ testing rather than estimation.
• Can non-parametric tests calculate the confidence interval (CI)?

Answer 18

• significance

- No

Question 19

Mann-Whitney U Test:

• A non-parametric alternative to _____________.
• Used to test the _____ difference between the ____ _________ groups.

Answer 19

• Student’s t-test

- mean, two independent

Question 20

Wilcoxon SIgned-Rank Test:

• A non-parametric alternative to ____________.
• Used to test the _____ difference between the ____ ________ groups.

Answer 20

• Paired t-test

- mean, two matched

Question 21

Kruskal-Wallis H Test:

• A non-parametric alternative to _____________.
• Used to test the _____ difference between the ______ or more __________ groups.

Answer 21

• ANOVA (analysis of variance)

- mean, 3 or more independent

Question 22

Friedman Test:

• A non-parametric alternative to ________________.
• Used to test the _____ difference between the _____ or more ________ groups.

Answer 22

• Repeated Measures ANOVA

- mean, 3 or more related

Question 23

Quiz 1:

1. ) Mann-Whitney U test is used to compare (2,3 or more) sets of scores that are (independent,related).
2. )The Kruskal-Wallis H test is used to compare (2,3 or more) sets of scores that are (independent,related).
3. Wilcoxon signed-rank test is used to compare (2,3 or more) sets of scores that are (independent,related).
4. Friedman’s test is used to compare (2,3 or more) sets of scores that are (independent,related).

Answer 23

• 2, independent
• 3 or more, independent
• 2, related
• 3 or more, related

Question 24

Quiz 2:
-A non-parametric test was used to compare the difference between the mean alcohol consumption scores at the two institutions. The non-parametric test was used as a substitute for a Student’s t-test because the assumption of the normal distribution with the alcohol consumption scores is questionable. The mean alcohol consumption for the students at the religious institution was 11.9 (SD=27.6) drinks in the 30 days prior to the survey, which was significantly lower than 26.9 (SD=53.1) drinks per 30 days for students attending the secular university (p-value < 0.05). Which non-parametric test would they have used?

Answer 24

Mann-Whitney U test

Question 25

What are the weaknesses of non-parametric tests?

Answer 25

• Less powerful tan parametric tests on parametric data.
• May not be testing the null hypothesis of interest.
• Null hypothesis that can be studied using non-parametric tests tend to be very restrictive.
• Not much choice for non-parametric tests.
• Can’t be related to the confidence interval (CI).