Question

Also briefly answer these questions in your own words:

- In general, when should you use non-parametric vs. parametric tests?

- Specifically, what are the parametric equivalents of: the Mann-Whitney, Wilcoxon rank-sum & signed-rank, Kruskal-Wallis, and Friedman's tests? what type of variables or research design would call for each of these tests (i.e. how do know which test to use)?

- When would you use a chi-square test, what are its assumptions, and what does the textbook recommend for reporting its effect size?

2. Psy 259

Answer 1

Answer) When should parametric and non parametric tests be used:

We use parametric tests when the form of distribution of parent population from which the samples are drawn is assumed to be known and we are concerned in testing statistical hypothesis about the parameter. In almost all test of significance, the parent distribution is normal and we are concerned in testing or estimating the mean and variance of the population.

Whereas

Non parametric tests are used when we don't have any information about the form of the frequency distribution and are used when the measurements are nominal or ordinal. These are not used for estimating the parameters.

-The parameter equivalent of Mann Whitney test is t distribution. This test is used when we do not make the assumption about the parent population. It is used to compare two independent groups when the dependent variable is ordinal or continuous but not normally distributed.

The parameter equivalent of Wilcoxon rank sum test is two sample t test and is used to compare two unmatched groups. The Wilcoxon signed rank is used to test difference in median of two matched samples. This is done by computing the difference between two matched groups and using signed rank test to test if the median of these differences differs from zero. This is equivalent to paired t test.

The parameter equivalent of Kruskal wallis test is one way analysis of variance(ANOVA) and is used when assumptions of one way ANOVA are not met. It is used to assess the significant differences on a continuous variable by a categorical independent variable.

The parameter equivalent of Friedman test is one way analysis of variance(ANOVA) and is used to test the differences between groups when the dependent variable is ordinal.

- The chi square test is used for testing relationship between categorical variables, to test the goodness of fit that is to test how well the observed distribution of data fits with the distribution that is expected when the variables are independent.

The assumption of this distribution are:

1. Two variables should be measured at an ordinal or nominal data that is the variable must be categorical.

2. Two categorical variables must consist of two or more independent groups, if it has less than two groups then chi square cannot be computed as degrees of freedom becomes zero.

3. The categories must be mutually exclusive.

The expected frequency of each must be atleast 5.