Question

Many of the hypothesis tests we have studied are predicated on requirements to ensure that the sample statistic will have a certain sampling distribution. When these requirements are not met, we typically must use some sort of “backup” (nonparametric test). Complete the table below. For each regular/parametric test shown, please list the requirement(s) that must be met for that test, then list the nonparametric backup test that would be used when the requirements are not met.

Regular Test	Requirements	Backup Test
Independent Samples t-test
Pearson's Product Moment Correlation Coefficient (PPMC)
Chi-Square Test for Independence
ANOVA

Answer 1

ANSWER::

Regular Tests	Requirements	Backup Test
Independent Samples t-Test	1. Parent populations. from which the samples have been drawn are normally distributed. 2. The population variances are equal and unknown. 3. The two samples are random and independent of each other	Mann-Whitney Test
Pearson's Product Moment Correlation Coefficient	1.Two variables should be measured at the interval or ratio level (i.e., they are continuous) 2.There is a linear relationship between the two variables 3.There should be no significant outliers 4.The variables should be approximately normally distributed	Spearman Rank Correlation Test
Chi-Square Test for Independence	1. The sampling method is simple random sampling. 2. The variables under study are each categorical. 3. If sample data are displayed in a contingency table, the expected frequency count for each cell of the table is at least 5.	Fisher's Exact Test
ANOVA	1. Each group sample is drawn from a normally distributed population 2. All populations have a common variance 3. All samples are drawn independently of each other 4. Within each sample, the observations are sampled randomly and independently of each other 5. Factor effects are additive	Kruskal-Wallis Test

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