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Nonparametric Tests and Parametric Statistics, Exams of Business Statistics

Academy For Nursing And Health OccupationsBusiness Statistics

The differences between nonparametric tests and parametric statistics. Nonparametric tests do not require the same stringent assumptions as parametric tests and can be used when assumptions of parametric tests are not met. The document also explains how ranking data works and how nonparametric tests handle outliers and statistical power. It then goes on to describe various nonparametric tests and their parametric counterparts, including the Mann-Whitney/Wilcoxon rank-sum test, Wilcoxon signed rank test, Kruskal-Wallis test, and Friedman's test. The document also includes information on effect sizes and an example of how to obtain the median using SPSS.

Typology: Exams

2022/2023

Available from 10/05/2023

eloy-hermann
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Nonparametric Tests
Parametric Statistics - -Use sample statistics to estimate
population parameters requiring underlying assumptions be met
-e.g., normality, homogeneity of variance
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
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.
The analysis is carried on... - the ranks rather than the actual data
Non parametric tests and outliers - -Instead of being an outlier it's
a rank
-Not a value
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
Mann-Whitney/Wilcoxon rank-sum Test - Compares two
independent groups of scores
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Nonparametric Tests

Parametric Statistics - -Use sample statistics to estimate population parameters requiring underlying assumptions be met -e.g., normality, homogeneity of variance 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 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. The analysis is carried on... - the ranks rather than the actual data Non parametric tests and outliers - -Instead of being an outlier it's a rank -Not a value 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 Mann-Whitney/Wilcoxon rank-sum Test - Compares two independent groups of scores

Mann-Whitney/Wilcoxon rank-sum Test: Parametric Counterpart - -Independent t-test Wilcoxon signed rank Test - -Compares two dependent groups of scores Wilcoxon signed rank Test: Parametric Counterpart - -Paired sample t-test/dependent t-test Kruskal-Wallis Test - -Compares > 2 independent groups of scores Kruskal-Wallis Test: Parametric Counterpart - -One Way ANOVA Friedman's Test - Compares > 2 dependent groups of scores Friedman's Test: Parametric Counterpart - -Repeated Measures Anova Wilcoxon rank-sum test and Mann-Whitney test - -Use either to test differences between two conditions in which different participants have been used. Mann-Whitney and Wilcoxon rank sum tests - Effect size - The equation to convert a z-score into the effect size estimate & r Effect Sizes z & n - -z is the z-score that SPSS produces -N is the size of the study Example - -We had 10 Elective students and 10 Advanced Psych Seminar so the total number of observations was 20. In SPSS obtain... - Run Descriptive Statistics to obtain the median (more adequate than mean for non-parametric tests)

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). 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. Kruskal-Wallis test: R1 - -The sum of ranks for each group. Kruskal-Wallis test: N - -The total sample size. Kruskal-Wallis test: n1 - -The sample size of a particular group. For the Kruskal-Wallis test, we need only report (3) - the test statistic (H), its degrees of freedom and its significance: Friedman's ANOVA - -Test differences between several related groups (2+ conditions) 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. Chi-Square - -Statistical test commonly used to compare observed data with data we would expect Chi-Square- One way/single sample: - Are responses/outcomes distributed as would be expected across a variable with 2+ categories? Chi-Square- Two way - -Determine whether there's a relationship between two categorical variables

Goodness-of-fit test: - a.k.a., Pearson's chi-square Goodness-of-fit test: Equation - [df = (# of rows - 1)(# of columns -

Chi-squared test (i & J) - -i represents the rows in the contingency table

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