Test Assumptions

The final factor that we need to consider is the set of assumptions of the test. All parametric tests assume that the populations from which samples are drawn have specific characteristics and that samples are drawn under certain conditions. These characteristics and conditions are expressed in the assumptions of the tests. Nonparametric tests make assumptions about sampling (random) and the independence or dependence of samples (varies by test) but make no assumptions about the population.

Parametric Assumptions

Listed below are the most frequently encountered assumptions for parametric tests. Statistical procedures are available for testing these assumptions. The Kolmogorov-Smirnov Test is used to determine how likely it is that a sample came from a population that is normally distributed. The Levene test is used to test the assumption of equal variances. If we violate test assumptions, the statistic chosen cannot be applied. In this circumstance we have two options: 1) we can use a data transformation or 2) we can choose a nonparametric statistic. If data transformations are selected, the transformation must correct the violated assumption. If successful, the transformation is applied and the parametric statistic is used for data analysis.


  • Interval or ratio scale of measurement (approximately interval)
  • Random sampling from a defined population
  • Samples are independent/dependent (varies by statistic)
  • Characteristic is normally distributed in the population
  • Population variances are equal (if two or more groups/variables in the design)



It has been traditional for the man rather than the woman to receive the check when a couple dines out. A researcher wondered whether this would be true if the woman was clearly in charge, asking for the wine list, questioning the waiter about dishes on the menu, etc. A large random sample of restaurants was selected. One couple was used in all restaurants, but in half the man assumed the traditional in-charge role, and in the other half the woman was in charge. At each restaurant, the couple recorded whether the check was presented by wait staff to the man or to the woman.

Test the research hypothesis that the check will be presented to the person showing in-charge behavior.


We selected the chi-square test of independence for data analyses because the dependent variable is measured on a nominal scale of measurement and we have two independent groups in our design (in-charge man and in-charge woman). The chi-square test of independence is a nonparametric test, so we make no distributional assumptions about check presentation in the population. The chi-square test of independence does require random sampling and independence of observation. Our study meets both of these assumptions, so we can proceed to data analysis.

We have reviewed the steps needed to correctly select the statistic needed to test our hypothesis. Proceed to the Practice Exercises to test your knowledge.


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