Non-Parametric Statistics Flashcards
Non-parametric vs parametric stats
non-parametric makes no assumptions about distribution of data
more general but less statistical power
define ordinal and nominal data
ordinal: order. ranked.
nominal: categories.
ranking rules
rank lowest to highest
in the case of ties, assign AVERAGE rank
two methods to test for normality
- kurtosis / skewness
- Kolmogorov-Smirnov one-sample test (not discussed)
outline method of using kurtosis/skewness to test for normality
unbiased estimator of population excess kurtosis: G2, the adjusted Fisher-Pearson standardised moment coefficient
G1 used for estimator of skewness
define z scores for each, with the null hypothesis that the distribution CAN be described as normal.
what are the non-parametric tests used for two related samples?
Wilcoxon Signed Rank test
OR Sign Test (simpler, less statistical power)
related samples: eg. measurements before and after a treatment
what is the non-parametric test used for two unrelated samples?
Mann-Whitney U-test
(this is the non-parametric equivalent to the t-test for independent samples)
outline the method for the Wilcoxon signed rank test
Calculate absolute differences between pairs, remove 0’s.
Rank differences in order (lowest to highest)
Note the sign of the differences. sum +ves and -ves. Choose the SMALLER sum to be the test statistic.
evaluate on Wilcoxon table for T values.
outline the general procedure for a sign test
simpler test for two related samples.
consider the NUMBER of positive and negative changes (ignore 0’s)
use binomial to calculate the probability distribution of the given numbers of changes happening by chance (p=0.5).
for large samples, approximate binomial as normal w continuity correction
describe the procedure for a Mann-Whitney U test for two unrelated samples
combines rank values of two samples and measures whether the ranks are randomly mixed.
calculate the U-statistic for each sample. choose the SMALLER of the two.
for smaller samples, consult U-statistic tables.
For larger samples, convert to z-score to evaluate.
what is a Spearman rank correlation used for?
non-parametric test to measure strength and direction of MONOTONIC relationship between two variables, even if non-linear relationship
used to compare ORDINAL data
outline the general method for a Spearman rank correlation.
rank data for both variables, ranks xi and yi.
plug into appropriate formula for rs depending on whether there are ties present.
t-statistic (found from rs) used to evaluate, with n-2 degrees of freedom.
