Nonparametric Tests

Wilcoxon signed-rank test

-Compare two sets of related scores, when these scores come from the same participants (within group/condition)

Kruskal-Wallis Test

-Compares > 2 independent groups of scores

Wilcoxon signed rank Test

-Compares two dependent groups of scores

Chi-Square- Two way

-Determine whether there's a relationship between two categorical variables

Nonparametric test statistics (3)

-Don't have the same stringent assumptions (fewer assumptions) -Can be used when assumptions of parametric tests are not met -Data is ranked

Mann-Whitney/Wilcoxon rank-sum Test: Parametric Counterpart

-Independent t-test

Non parametric tests and statistical power.

-Information about the magnitude is lost-> less power -When using a non-parametric and parametric tests on the same dataset, the parametric test will have more power to find an effect

Non parametric tests and outliers

-Instead of being an outlier it's a rank -Not a value

Wilcoxon signed-rank test- involves

-Involves calculating the difference between two sets of scores, making a note of the sign of the difference (positive or negative) then ranking the differences from lowest to highest ignoring whether they are positive or negative.

Don't forget

-Issue of multiple comparisons still relevant

Kruskal-Wallis Test: Parametric Counterpart

-One Way ANOVA

Wilcoxon signed rank Test: Parametric Counterpart

-Paired sample t-test/dependent t-test

Friedman's Test: Parametric Counterpart

-Repeated Measures Anova

Chi-Square

-Statistical test commonly used to compare observed data with data we would expect

Friedman's ANOVA

-Test differences between several related groups (2+ conditions)

Chi-squared test- observed data & model

-The observed data are the frequencies the contingency table -The 'Model' is based on 'expected frequencies'.

Kruskal-Wallis test: n1

-The sample size of a particular group.

Kruskal-Wallis test: R1

-The sum of ranks for each group.

Kruskal-Wallis test: N

-The total sample size.

Ranking Data (3)

-These tests work on the principle of ranking the data for each group: -Lowest score=a rank of 1 -Next highest score = a rank of 2, and so on.

Wilcoxon rank-sum test and Mann-Whitney test

-Use either to test differences between two conditions in which different participants have been used.

Parametric Statistics

-Use sample statistics to estimate population parameters requiring underlying assumptions be met -e.g., normality, homogeneity of variance

Example

-We had 10 Elective students and 10 Advanced Psych Seminar so the total number of observations was 20.

Chi-squared test (i & J)

-i represents the rows in the contingency table - j represents the columns.

Reporting (5) Independent t-test

-median -R (effect size) -U or WS -p -z (standardized test statistic)

Kruskal-Wallis test: based on

-ranked data

For Friedman's ANOVA we need only report..(3)

-the test statistic (χ2), its degrees of freedom and its significance -No need to do any post hoc tests for this example.

Effect Sizes z & n

-z is the z-score that SPSS produces -N is the size of the study

Wilcoxon signed-rank test-Example

Imagine the experimenter was interested in the change in depression levels for each course condition.

In SPSS obtain...

Run Descriptive Statistics to obtain the median (more adequate than mean for non-parametric tests)

Goodness-of-fit test: Equation

[df = (# of rows - 1)(# of columns - 1)

Goodness-of-fit test:

a.k.a., Pearson's chi-square

The analysis is carried on...

the ranks rather than the actual data

For the Kruskal-Wallis test, we need only report (3)

the test statistic (H), its degrees of freedom and its significance:

Kruskal-Wallis test: Example

A major food company wants to investigate the difference between three different low-cholesterol cereal brands. They recruit participants and assign them to three different conditions.

Chi-Square- One way/single sample:

Are responses/outcomes distributed as would be expected across a variable with 2+ categories?

Wilcoxon signed-rank test- Examples: 2

For the advanced positive psychology class, depression levels were significantly lower on Wednesday compared to Sunday

Wilcoxon signed-rank test- Examples: 1

For the elective class, depression levels were significantly higher on Wednesday compared to Sunday

Friedman's Test

Compares > 2 dependent groups of scores

Mann-Whitney/Wilcoxon rank-sum Test

Compares two independent groups of scores

Kruskal-Wallis test

Differences between several independent groups

Mann-Whitney and Wilcoxon rank sum tests - Effect size

The equation to convert a z-score into the effect size estimate & r

Kruskal-Wallis test: Ranked Data denoted by

The sum of ranks for each group is denoted by Ri (where i is used to denote the particular group).