Non parametric tests

Question 1

Non-normal data

Answer 1

Types of distributions:
- Bi-modal (u shape)
- triangular
- Decaying (negative)

Question 2

Issues with normality testing

Answer 2

Strong relationship between sample size and sensitivity. At large and very large sample sizes, tiny deviation from normality = significant results

Question 3

QQ Plots

Answer 3

Helpful visual tests that compare 2 distributions

Percentiles of normal distribution on x-axis and percentiles of data are on y-axis
If data point are close to being linearly related then the data distributions are a close match.

Question 4

Non-parametric tests

Answer 4

-Work with median rather than mean
-Valid for ordinal interval and ratio data
-Can be used with normal or non normal data sets
-More robust measure of central tendency’s when data is not normally distributed

Question 5

Shapiro-Wilk W

Answer 5

metric indicating how normal the data is, higher value = more normal

Question 6

Shapiro-Wilk p

Answer 6

probability indicating significance of difference from normality

Question 7

Shapiro Wilk at different sample sizes

Answer 7

small sample = weak ethics, more likely to agree with certain distribution

large sample = overly conservative, detect tiny departures from normality, all failing null hypotheses

Question 8

Wilcoxon signed rank test

Answer 8

Alternative for one-samples and paired samples t-tests

ordering and sum data, effectively transforming it into a rank.

tests whether ranks are symmetrical around 0

Test statistic (W), p-value and effect size but no df

Question 9

Man-Whitney U test

Answer 9

alternative to independent samples t-test

ordering and sum data, effectively transforming it into a rank.
- you make note of what group each sum belongs to and add them up

Tests statistic (W), p-value and effect size but no df