NON-PARAMETRIC TESTS

Parametric tests

These are statistical tests that make assumptions about the parameters of the population distribution from which the sample is drawn

Non-parametric tests

These are statistical tests that that has no reference to population parameter μ and σ

FALSE; this is for non-parametric tests

TRUE OR FALSE: Parametric tests can be used both for non-normally distributed and normally distributed data and are often called "distribution free."

parameters and confidence intervals

We prefer parametric tests because we would like to say something about the population from which the samples came, and this is best done with estimates of? (two items)

TRUE; this is why we prefer parametric tests

TRUE OR FALSE: It is difficult to do flexible modelling with non-parametric tests

Parametric tests

These types of tests are more likely to detect significant differences when they truly exist

FALSE; this is for parametric tests

TRUE OR FALSE: Non-parametric tests usually have more statistical power

Non-parametric tests

When there are definite outliers and when we have nominal, ordinal, or interval data to analyze, it is more appropriate to use this test

Chi-square test of independence

This common non-parametric test is used for testing independence or association of row and column variables making use of contingency tables

Ho: there is no association/samples are independent from each other

Ha: there is association/samples are not independent from each other

Sample null and alternative hypothesis for chi-square test of independence

xc^2

Test statistic symbol for the chi-square test of independence

xc^2 = (foi - fei)^2/fei

foi = observed frequencies

fei = expected frequencies

Test statistic formula for the chi-square test of independence

sum of rows * sum of columns / grand total

Formula to get the expected frequencies

TRUE

TRUE OR FALSE: The 𝜒𝑐2 approximately follows a chi-square distribution with degrees of freedom (df) = (nrow - 1) (ncolumn-1) if the two-study factors are independent and the observed count of each cell is at least 5

If computed xc^2 is greater than the xc^2 tabular value

Decision rule in rejecting the null hypothesis in a chi-square test of independence

Wilcoxon Signed Rank Test

This is used to compare outcomes between two matched or paired samples; parametric counterpart is the paired t-test

FALSE; median difference is used instead

TRUE OR FALSE: In non-parametric tests, the null hypothesis is that the mean difference is zero

Ho: there is no median difference

Ha: there is median difference

Sample null and alternative hypothesis for Wilcoxon Signed Rank Test

FALSE: for this test, we are only interested in

positive and negative differences so samples with 0 differences are dropped from further analysis.

TRUE OR FALSE: In the first step in computing for the score differences between paired samples , we are interested in the positive, negative, and 0 differences for analysis

rank/ranking

For the second step is Wilcoxon Signed Rank Test, we assign this to the absolute values of the differences obtained

TRUE

TRUE OR FALSE: For the third step in the Wilcoxon Signed Rank test, each assigned rank is given the same sign from the "Difference" column and reported in the "Signed Rank+" and "Signed Rank-" columns.

FALSE; the smaller of the two rank sums

TRUE OR FALSE: For the fourth step in the Wilcoxon Signed Rank test, the signed ranks are summed and reported in the bottom "Total" row. The larger of the two rank sums is used as the test statistic and referred to as W.

W is less than or equal the critical value

Decision rule in rejecting the null hypothesis in a Wilcoxon Signed Rank Test

Mann Whitney U Test

Used to compare two independent samples; parametric counterpart is the independent t-test

samples are random and observations drawn for each sample are

independent from each other

Assumption for the samples of the Mann Whitney U Test

Ho: The distributions of the two populations are identical.

Ha: The distributions of the two populations are not identical.

Or

Ho: MedianA = MedianB

Ha: MedianA ≠ MedianB

Sample null and alternative hypothesis for the Mann Whitney U Test

TRUE

TRUE OR FALSE: Like the Wilcoxon Signed Rank Test, in a Mann Whitney U Test, you start by sorting the data from lowest to highest mpg. Then assigning ranks in the two groups of size n1 and n2 with their combined ranks.

TRUE

TRUE OR FALSE: The test statistic for the Mann Whitney U Test is denoted by U and is the smaller of U1 and U2

R1 and R2

Denotes the sum of the ranks for group1 and group2

U1 = N1*N2 ((N1(N1+1)/2) - R1

Same with R2

Formula in getting U1 or U2

If U is less than or equal the critical value, reject Ho

Decision rule in rejecting the null hypothesis in a Mann Whitney U Test

Kruskal Wallis Test

This is used for comparing ordinal and non-normal variables for more than two independent groups; used to compare medians among k comparison groups; parametric equivalent: One-Way ANOVA with data replaced by their ranks

Ho: The k population medians are equal.

Ha: The k population medians are not all equal.

Sample null and alternative hypothesis for Kruskal Wallis test

H

Symbol for the test statistic of the Kruskal Wallis test (solution for this is in the course notes/learning materials)

Reject Ho if H≥ the critical value.

Decision rule in rejecting the null hypothesis in a Kruskal Wallis Test