Parametric and Nonparametric Tests

Question 1

Population Parameter

Answer 1

A number that describes something about an entire group or population

The number in the population is usually high, so it will probably have a normal distribution!

Question 2

How is the sample size distributed when a parametric test is used?

Answer 2

Normally distributed

Question 3

Which parameters should be used for skewed data?

Answer 3

Median, IQR (25th percentile, 75th percentile)

Question 4

Data: Sex number in %
Parametric or Non-parametric

Answer 4

Non-parametric
-bc it is a yes or no answer and no means are used and there represented in categories

-means are continuous and more likely to be represented in a normally distributed curve

Question 5

What is considered descriptive statistics?

Answer 5

Mean, median, SD, IQR
-used to describe data

Question 6

What are Inferential Statistics?

Answer 6

Inference = Conclusion (reached based on evidence)
-used to test hypotheses and draw interferences

-Inferential Statistics can be parametric or non-parametric

Question 7

What are the criteria for Parametric Tests?

Answer 7

-Samples are drawn from a normal distribution

-Variances (SD) in both groups compared are approximately equal (both normally distributed)

-Data are continuous (BP, LDL) !!!

Question 8

What are non-parametric Tests?

Answer 8

-Statistics that do not test hypotheses concerning population parameters

-assumptions for parametric tests are not met

-they do not assume normal distribution and are distribution-free tests

Question 9

What type of data is used in non-parametric Tests?

Answer 9

-Nominal data (Male/female, race, dead/alive)
-Ordinal data
-small sample size -> likely to have skewed data

Question 10

What are common Parametric Tests?

Answer 10

-Student’s T-Test -> often used for continuous data
-Analysis of Variance (ANOVA)

Question 11

What are common Non-Parametric Tests?

Answer 11

-Mann Whitney U
Nonparametric form of Student’s t-test

-Chi-Square Test / Fisher’s Exact Test
Used for nominal data

Question 12

Students T-test

Answer 12

-parametric
-comparing two population means (or drug and placebo group)
-most common in the medical literature (more than 50%)

Question 13

What are the assumptions of the Student t-test?

Answer 13

-Normal distribution
-SD in the 2 groups is approximately equal
-continuous data
-Randomly selected, independent samples

-> There are two different groups (drug vs placebo, compared to dependent in cross-over studies - with the same patients used for drug and placebo -> paired data)

Question 14

Purpose of Student T-test

Answer 14

-determine the probability of the findings being due to chance
-creating a p-value

Question 15

What is a t-score?
not on EXAM

Answer 15

-similar to Z-score
-Z-score is the number of SD away from the mean
-t-score is expressed in an estimated SD away from the mean

-Z-scores are stable
-t-scores will vary depending on sample size

Question 16

Example:
randomized, placebo-controlled, double-blinded study (n=300)

the drug arm of the study reduced LDL by 18±4% and the placebo arm reduced LDL by 13±3%

Student’s t-test was used to compare lipid
reduction, p =0.02

Is the student’s t-test appropriate?

Answer 16

Criteria:
Normally distributed - Y bc the SD is not high relative to the mean
Variances should be approximately equal - Y
Continuous data Y- LDL values are continuous data
Independent groups - Y bc placebo-controlled

Question 17

Why are Student t-tests not appropriate when comparing multiple groups?

Answer 17

Because the probability of committing a type I error (alpha) sums up each time we compare different groups

Question 18

Which test is appropriate to test multiple groups?

Answer 18

ANOVA

Question 19

When to use Non-parametric t-tests?

Answer 19

-When the assumptions for a Student’s t-test (parametric test) are not me
-when we have ordinal data

Question 20

What are the Non-parametric t-tests?

Answer 20

-Mann Whitney U
-Wilcoxon Rank Sum

-with median
-they tell us whether the medians are different

Question 21

Which test should be used when the conditions for a parametric t-test are not met?

Answer 21

Mann Whitney U

Question 22

Which test to use for a nonparametric paired t-test

Answer 22

Wilcoxon Signed Rank test

Question 23

ANOVA

Answer 23

-ANOVA = Analysis of Variance
-ANOVA is a “group comparison”
-ANOVA is a parametric test

Question 24

When is an ANOVA test appropriate?

Answer 24

-When comparing the means of three or more groups
-parametric tests
-normally distributed data

Question 25

What is the null for 3 or more groups?

Answer 25

H0: Group 1 = Group 2 = Group 3
-no difference between the groups

-if there is a difference between any of the means the p-value will be <0.05 for ANOVA

-but it doesn’t tell me between which group the statistical difference is

Question 26

After discovering a difference between 3 groups

Answer 26

-conduct a “posthoc” test and analyze where the difference in mean between the 3 groups is

-pairwise comparison:
Group 1 vs Group 2
Group 2 vs Group 3
Group 1 vs Group 3

(a priori = before)

Question 27

One-way ANOVA

Answer 27

-assessing the effect of a single variable (factor) on a single response variable (change of condition)
-multiple groups (it is ANOVA)

-f.e.: women with osteoporosis is assigned into 3 groups: std treatment, new drug, placebo

-the response variable is: a change in bone density
-single variable is: the new drug

Question 28

Two-way ANOVA

Answer 28

-assesses the effect of two variables (factors)
-multiple groups

-the response variable is the change in condition
-two variables (factors): f.e. drug and age

Question 29

Multi-way ANOVA - MANOVA

Answer 29

-assesses the effect of multiple variables (factors)
-multiple groups

-the response variable is the change in condition
-two variables (factors): f.e. drug, diet and alcohol consumption

Question 30

Analysis of Covariance - ANCOVA

Answer 30

-same as ANOVA
-but controlling for the effects of some explanatory variable
-f.e. : we have the two variables (factors): drug, age
-the covariable could be: the severity of the disease

Question 31

Repeated Measures ANOVA

Answer 31

-assessing several or repeated measurements of the same participant -> different conditions or different times

-BP taken while sitting, standing, supine
-Measurement of bone density at different times (6 months, 12 months)

Question 32

Multiple Comparison Test or Posthoc Test
(NOT ON EXAM)

Answer 32

-for repeated tests
-Bonferroni t procedure

-prevents aggregation of p-values (alpha) like a Studtent’ds test would do
-increases the critical value -> it makes each comparison more rigorous -> and decreases each p-value
-the sum of the p-values will still be under 0.05 and significant

Question 33

Different Comparison Test, Posthoc Test
(NOT ON EXAM)
important for research

Answer 33

-Bonferroni t Procedure
-Tukey test
-Scheffe’s Procedure
-Dunnett’s Procedure

Question 34

When are posthoc tests done?

Answer 34

-After we determined a difference with the ANOVA
-we want to find out where the difference is with: the post hoc test

Question 35

Nonparametric Comparison of 3 or more Groups

Answer 35

-Remember for parametric test we need: normal distribution, equal SD, continuous data
-for parametric test comparing multiple groups we would use ANOVA

-if one of these criteria is not met or the data is ordinal when comparing multiple groups: we use the nonparametric form of ANOVA

-Kruskal Wallis test: ANOVA on ranks
-Friedman test: ANOVA on ranks for paired (related) data –> f.e. cross-over studies

Question 36

Which test is used for Categorical Variables (nominal data)?

Answer 36

Chi-square test

nominal data: race, color, sex

Question 37

Chi-square test

Answer 37

-compares expected frequency vs observed frequency
-determines a p-value: what is the probability that this frequency of findings is due to chance alone

-2x2 table: 2 groups (drug, placebo) x 2 categories (male, female) -> fill with the percentages

-the test compares the actual numbers (in percentage) vs the expected numbers due to random variation

Question 38

When is a Chi-square test considered statistically significant?

Answer 38

-NOMINAL DATA
-FREQUENCY TEST: is the amount of participants similar enough (significantly equal)

-p-value is less than 0.05 when the observed frequency is outside of the expected frequency

Question 39

When is the Fisher’s Exact Test used?

Answer 39

-Nominal Data
-like Chi-square Test
-if at least one of the cells in the table has a value of 5 or less

-Yates correction for sample size of 25-40

Question 40

What is the McNemar’s Test

Answer 40

-examines the frequency of data when the cases are dependent or related
-Chi-square test for dependent or paired samples

-several data points obtained from the same patient (repeated measures)

Question 41

What is the Mantel-Haenszel test used for?

Answer 41

-adjust for confounding variables when comparing two INDEPENDENT categorial groups

-so it has to be independent groups
-nominal data