Nonparametric Tests: Chi-Square Tests
6 important questions on Nonparametric Tests: Chi-Square Tests
The one sample z-test, one sample t-test, and two sample t-test are examples of significance tests that fall in the category of 'parametric tests'.
What are parametric tests and how do we call significance tests that do not meet the criteria of parametric tests?
- Parametric tests.
- Tests about a population parameter (such as the mean) of a normally distributed variables that are either interval/ratio variables.
- Non-parametric tests.
- Tests for significance when you're dealing with nominal/ordinal level data.
- These tests do not require the data to be normally distributed.
- Which is useful because categorical variables will not be normally distributed.
- E.g., You can't search for the standard deviation on questions about what someone's favourite movie is.
What are the two most commonly applied non-parametric tests?
- Chi-square goodness-of-fit test.
- Tests the H₀ that a nominal/ordinal variable has a certain distribution in the population.
- Chi-square test of independence.
- Tests the H₀ that two nominal/ordinal variables are not related to each other in the population.
When you use a Chi-square test for hypothesis testing, your alternative hypothesis (H₀) is always non-directional.
Why is this the case?
- Squared formula: as the place in the formula, where you subtract the expected frequency from the observed frequency is squared (i.e., ( f₀ - fₑ )² ), you will always get positive values and therefore will never find out whether something is higher or lower.
- Categorical variables.
- With the Chi-test you're dealing with categorical variables (e.g., what is your favourite movie, which party will get your vote, etc.). For these questions, you are primarily concerned with whether your expected pattern holds, not if it is more/less than what you have expected.
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Can you describe what crosstabs are?
- A crosstab is a table that depicts a possible relationship between an independent and dependent variable.
- It is used for nominal and ordinal data.
- Percentages are calculated vertically.
- You can compare the percentages of the dependent variable horizontally.
- E.g., in our sample, a greater percentage of women (75.7%) are inspired by dance than men (53.7%).
This crosstab shows the relationship between the degrees of feeling safe when walking alone in a local area after dark and four European countries.
Can you explain why, when we want to do a significance test, we need a Chi-Square Test for-Independence, instead of:
- A Chi-Square Goodness-of-Fit Test.
- Pearson's r.
- Chi-Square Test for-Independence:
- You want to test the statistical significance between two categorical variables.
- Not Chi-Square Test for-Independence:
- Here we have two variables, instead of one.
- I.e., if it were only about the degrees of feeling safe, you would use this test.
- Not Pearson's r:
- The variables in this table are categorical variables, which are either nominal or ordinal.
- Pearson's r relies on means, which categorical variables don't have.
Consider the following crosstab and the corresponding Chi-Square Test for Independence.
How would you report the results of this Chi-Square test if you had to write it in an academic article?
- A Chi-square test-for-independence was performed between country of residence and feeling of safety walking alone at night. The results (X2 = 341.96, df = 9, n=7,746, p<0.001) suggest that there is a statistically significant relationship between the two variables: feelings of safety differ between the populations of Germany, France, Belgium, and the Netherlands.
- What to report:
- The test you've used.
- The degrees of freedom.
- The number of cases in the sample.
- The Actual score.
- The p value provided by SPSS.
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