Non-parametric Statistics

Question 1

What is non-parametric statistics?

Answer 1

That data is not normally distributed so you cant make any assumptions

Question 2

To define the shape and spread of a data set (e.g. define the distribution) need:

Answer 2

 A measure of central tendency (e.g. mean)
 A measure of variance (e.g. standard deviation or standard error)

Question 3

What is Chi-Square and what does it measure? Whats are degrees of freedom?

Answer 3

Compares the empirical probability vs. theoretical probability across mutually exclusive groups across within a single grouping variable

Null

HO: Observed Frequency = Expected Frequency

Alternate Hypothesis

HA: Observed Frequency ≠ Expected Frequency

df=# of categories -1

Question 4

How do you interpret a chi square?

Answer 4

A Chi-square analysis was run to determine if the frequency of Freshman, Sophomore, Junior and Senior students using the PAC facilities was different. The chi-square was not significant (χ2 =7.50, 𝑑f= 3, p > 0.05). Therefore, use of the CCRB is not tied to a particular academic standing.

Question 5

What are the 3 prime differences between t-test equivalents, ANOVS, and correlation with their parametric equivalents?

Answer 5

Prime differences:
 No normality assumption
 Data are measured (or transformed) on the ordinal scale
 For interval and ratio scales means are replaced by rankings

Question 6

What is the independent samples t-test equivalent?

Answer 6

Mann-Whitney U-Test

Rank both groups as a single group, then divide back into groups and see if one group is consistently ranked higher than the other

Question 7

What is the paired samples t-test equivalent?

Answer 7

 Calculate difference scores for each individual and then rank independent of sign.

 Put sign back in and calculate test statistics –> If ranks sum to 0 (or < than critical value) then fail to reject Ho

Question 8

What is the between groups ANOVA equivalent?

Answer 8

Kruskal-Wallis ANOVA

Rank all groups as a single group, then divide back into groups and see if at least one group is consistently ranked higher than the other

Question 9

What is the Repeated mesuares ANOVA equivalent?

Answer 9

Friedman ANOVA

Calculate difference scores between each time point for each individual and then rank independent of sign.

• Put sign back in and calculate test statistics  If ranks sum to 0 (or < than critical value) then fail to reject Ho

Question 10

What is the Pearson product moment equivalent?

Answer 10

Spearman Rank Order Correlation

Associate rank on one variable with rank on another

 If participants have a high rank on X and a high rank on Y (or vice versa) then 𝜌𝜌 is positive

 If relationship is inverse such that participants who have high ranks on X have low ranks on Y then 𝜌𝜌 is negative

Question 11

What are the two clinical measures of association?

Answer 11

Relative Risk or Risk Ratio and Odds ratio or relative odds

Question 12

What is Risk ratio?

Answer 12

A ratio of proportion who have the condition versus those that do not

Question 13

What is odds ratio?

Answer 13

A ratio of the odds that an individual in a given group will have trait