Non-Parametric Statistics

Assumptions

• Data are normally distributed across groups
• Homogeneity of variance across groups
• Independence of data observations

If your data violate assumptions, what are your options for data analysis?

– Transform the data (e.g., corrections of normality)
and perform the data analysis using parametric
statistics
– Perform the data analysis using non-parametric
statistics

What are the pros of computing non-parametric statistics rather than parametric statistics?

• Can be used when the variable of
  interest is not normally distributed

• Can be used when data are nominal
  or ordinal

• Can be used to test hypotheses that
  do not involve population parameters

• Computations are easier than those
  for parametric counterparts

• Easy to understand

• Fewer assumptions that have to be
  met (easier to verify assumptions)

What are the cons of computing non-parametric statistics rather than parametric statistics?

• Less sensitive than parametric
  counterparts when assumptions are
  met

• Tend to use less information than
  parametric tests

• Less efficient than parametric
  counterparts when assumptions are
  met

Chi-Square

Categories, Nominal Data
Two or more groups
Frequency of more than 5 occurrences in 80% of cells.
Non-parametric

Fisher Exact

Categories, Nominal Data
Two or more groups
Frequency of less than 5 in one cell (Rare Events!)
Non-parametric

McNemar

Categories, Nominal Data
Two or more groups
Matched or Paired Groups

Mann-Whitney U - Test

• Compares variable by ranking outcomes to
“best/top” ranks
• Two variables from unmatched samples
• Assumes a random & independent sample

Wilcoxon Signed Rank Test

• Compares variable by ranking outcomes to
“best/top” ranks
• Two variables from matched samples
• Assumes a random sample

Kruskal-Wallis

• Compares medians of three of more samples
(groups) on some variable.
• Assumes a ‘LARGER’ random sample, and
independent.

What are the non-parametric alternatives to Independent t-test

Mann-Whitney U

What are the non-parametric alternatives to ANOVA

Kruskal-Wallis

What are the non-parametric alternatives to Dependent t-test

Wilcoxon Signed Rank Test

What are the non-parametric alternatives to Person’s correlation

Spearman’s Rank Correlation

Spearman’s Rank Correlation

• Uses ranks to determine if there is a relationship
between two variables - medians (ordinal)

• Assumptions: random sample, data consist of two measurements or observations collected from the same individual