Below is an example of a 2x3 contingency table examining the relationship between diabetes and gender fake data. The Chi-Square Goodness of Fit Test is used when you want to determine whether the data follow a particular distribution. For this test, you have categorical data for one variable. The parametric statistics we have worked with so far involve ratio or interval data. However, there may be cases where the data you collect is ordinal.
Or, the data you collect is interval or ratio, but it does not meet the assumptions of the general linear model for example: it is highly skewed, not normally distributed and therefore tests like t-tests, ANOVA, or regression are not appropriate. In these cases, you can rank-order the data and use non-parametric tests to examine hypotheses about differences between groups. Here are a few important non-parametric tests and how they can be used to answer different types of research questions:.
Mann-Whitney U Test : Evaluates the difference between two independent groups; analogous to independent samples t-tests. Null hypothesis is that there no difference between the two groups.
If there is a significant difference between conditions, the MW-U will be small. Closer to 0 is better—a value of 0 indicates that there is no overlap in the rank order between the two groups. Wilcoxon Signed Rank Test : Evaluates differences between two conditions using data from a repeated measures design; analogous to a paired samples t-test.
This test involves rank ordering the difference scores. A small T indicates a difference between treatments. Friedman Test : evaluates differences between three or more conditions in a repeated measures design analogous to single factor repeated measures ANOVA. For both the K-W and Friedman tests, the resulting test statistic is an omnibus one—it tells you there is at least one difference between the groups, but not which specific groups are different.
You will need to perform follow-up analyses to determine which groups are different. Pairwise comparisons are made using the Mann-Whitney U or Wilcoxon test. For the stepwise stepdown procedure, the groups are ranked by the sum of their ranks. Then the first and second groups are compared. If they are not different, then the third group is entered, and so on.
When a significant difference is found, the procedure is stopped. If there are any remaining groups that need to be compared, then the same procedure continues using the group that was significantly different in the previous step, and then adding in additional groups until another significant variable pops. Since this is the final week of classes and a bit shorter than a usual week, this assignment is meant to be shorter and quicker than the other assignments.
This assignment is a good opportunity to use your own data, if you wish. If you do want to use your own data, just replace the variables in the instructions below with variables from your own dataset. This is only possible if your own data has at least two categorical variables in it. If you want to use data provided by me, you should use the smoking dataset. You can click here to download the dataset.
The smoking. For the purpose of this assignment, we will assume the variables of interest are not normally distributed and therefore we need to use non-parametric tests to answer the research questions. There are two research questions that you need to answer this week. For each one, please include a contingency table two-way table , the code and result you used to test the question, and your interpretation of the result.
Is there a relationship between gender and whether someone is a current smoker? Some examples: You could use a two-sample proportions test basically, normal approximation to binomial. You could do a two sample binomial test the same thing, but based off the fact that the data are actually binomial.
You could do a Fisher exact test conditions on both margins, giving a hypergeometric. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Alternative nonparametric test for chi-square test for independence Ask Question. Asked 8 years, 7 months ago.
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