2022 Introduction to Statistics in Research Mitchell 2nd ed

I N T R O T O R E S E A R C H : D A T A V I S U A L I Z A T I O N & C O M M O N S T A T T E S T S

Parametric Vs. Non-parametric tests

Before we move forward to the tables to use as a guide for the test to use, let’s define parametric and non-parametric. By far, a parametric test is the most powerful statistic. But if we use a parametric statistic and the assumptions are violated , we increase the risk that we will reject the null hypothesis when it is true. Adams & McGuire (2022) define parametric statistics as “Statistics used to analyze interval and ratio data and that assume a normal distribution and homogeneity of variance between groups ” (p. 457). Nonparametric statistics is defined as the “Statistics used to analyze nominal and ordinal (ranked) data or used when the assumptions of parametric statist ics are violated” (Ibid, p. 457). Nonparametric tests are usually based on rands or signs

Essentially, to use the parametric test, you must meet ALL four assumptions: normal distribution, at least 10 participants, interval or ratio data, and homogeneity of variance.

Parametric tests must meet four criteria

Key Component

Parametric Test

Non-parametric Test

#1 Shape of Distribution

Data normally distributed

Data skewed our outlier influence At least five in each group Nominal or ordinal data Samples have very different variances Test for independence between variables but not interaction Less powerful – more chance of Type I errors.

#2 Sample size

At least ten participants in each group

#3 Scale of measurement

Interval or ratio data

#4 Homogeneity of variance Variance in each group the same

Comparisons

Interactions

Test for interactions (like factorial designs) More powerful – greater probability of correctly rejecting a null hypothesis

Power

Computations

More complicated

Less complicated

Table 109: Key components for parametric Vs non-parametric tests

That’s why it is so important to visualize the data before you choose your test . And that’s why what you write in your proposal might change somewhat after you collect your data! The next few tables will help you quickly determine which test to use.

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