Nonparametric Tests and Their Applications, Exams of Statistics

An overview of nonparametric tests and their applications. It explains the differences between parametric and nonparametric tests, and how nonparametric tests can be used when assumptions of parametric tests are not met. The document also covers ranking data, nonparametric tests and outliers, and statistical power. It provides examples of nonparametric tests such as Mann-Whitney/Wilcoxon rank-sum Test, Wilcoxon signed rank Test, Kruskal-Wallis Test, Friedman's Test, and Chi-Square. The document also discusses the issue of multiple comparisons.

Typology: Exams

2022/2023

Available from 11/08/2023

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Nonparametric Tests 2023
Parametric Statistics - Correct answer -Use sample statistics
to estimate population parameters requiring underlying
assumptions be met
-e.g., normality, homogeneity of variance
Nonparametric test statistics (3) - Correct answer -Don't
have the same stringent assumptions (fewer assumptions)
-Can be used when assumptions of parametric tests are not
met
-Data is ranked
Ranking Data (3) - Correct answer -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.
The analysis is carried on... - Correct answer the ranks
rather than the actual data
Non parametric tests and outliers - Correct answer -Instead
of being an outlier it's a rank
-Not a value
Non parametric tests and statistical power. - Correct answer
-Information about the magnitude is lost-> less power
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Nonparametric Tests 2023

 Parametric Statistics - Correct answer -Use sample statistics to estimate population parameters requiring underlying assumptions be met  -e.g., normality, homogeneity of variance  Nonparametric test statistics (3) - Correct answer -Don't have the same stringent assumptions (fewer assumptions)  -Can be used when assumptions of parametric tests are not met  -Data is ranked  Ranking Data (3) - Correct answer -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.  The analysis is carried on... - Correct answer the ranks rather than the actual data  Non parametric tests and outliers - Correct answer -Instead of being an outlier it's a rank  -Not a value  Non parametric tests and statistical power. - Correct answer -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  Mann-Whitney/Wilcoxon rank-sum Test - Correct answer Compares two independent groups of scores  Mann-Whitney/Wilcoxon rank-sum Test: Parametric Counterpart - Correct answer -Independent t-test  Wilcoxon signed rank Test - Correct answer -Compares two dependent groups of scores  Wilcoxon signed rank Test: Parametric Counterpart - Correct answer -Paired sample t-test/dependent t-test  Kruskal-Wallis Test - Correct answer -Compares > 2 independent groups of scores  Kruskal-Wallis Test: Parametric Counterpart - Correct answer -One Way ANOVA  Friedman's Test - Correct answer Compares > 2 dependent groups of scores  Friedman's Test: Parametric Counterpart - Correct answer - Repeated Measures Anova  Wilcoxon rank-sum test and Mann-Whitney test - Correct answer -Use either to test differences between two conditions in which different participants have been used.  Mann-Whitney and Wilcoxon rank sum tests - Effect size - Correct answer The equation to convert a z-score into the effect size estimate & r

 Wilcoxon signed-rank test- Examples: 1 - Correct answer For the elective class, depression levels were significantly higher on Wednesday compared to Sunday  Wilcoxon signed-rank test- Examples: 2 - Correct answer For the advanced positive psychology class, depression levels were significantly lower on Wednesday compared to Sunday  Kruskal-Wallis test - Correct answer Differences between several independent groups  Kruskal-Wallis test: based on - Correct answer -ranked data  Kruskal-Wallis test: Ranked Data denoted by - Correct answer The sum of ranks for each group is denoted by Ri (where i is used to denote the particular group).  Kruskal-Wallis test: Example - Correct answer 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.  Kruskal-Wallis test: R1 - Correct answer -The sum of ranks for each group.  Kruskal-Wallis test: N - Correct answer -The total sample size.  Kruskal-Wallis test: n1 - Correct answer -The sample size of a particular group.  For the Kruskal-Wallis test, we need only report (3) - Correct answer the test statistic (H), its degrees of freedom and its significance:

 Friedman's ANOVA - Correct answer -Test differences between several related groups (2+ conditions)  For Friedman's ANOVA we need only report..(3) - Correct answer -the test statistic (χ2), its degrees of freedom and its significance  -No need to do any post hoc tests for this example.  Chi-Square - Correct answer -Statistical test commonly used to compare observed data with data we would expect  Chi-Square- One way/single sample: - Correct answer Are responses/outcomes distributed as would be expected across a variable with 2+ categories?  Chi-Square- Two way - Correct answer -Determine whether there's a relationship between two categorical variables  Goodness-of-fit test: - Correct answer a.k.a., Pearson's chi- square  Goodness-of-fit test: Equation - Correct answer [df = (# of rows - 1)(# of columns - 1)  Chi-squared test (i & J) - Correct answer -i represents the rows in the contingency table

  • j represents the columns.  Chi-squared test- observed data & model - Correct answer - The observed data are the frequencies the contingency table  -The 'Model' is based on 'expected frequencies'.  Don't forget - Correct answer -Issue of multiple comparisons still relevant