Parametric vs Nonparametric Tests: When to use which

There are several statistical tests which can be categorized as parametric and nonparametric. This presentation will help the readers to identify which type of tests can be appropriate regarding particular data features.

1. PARAMETRIC vs NONPARAMETRIC TESTS Gonenc DALGIC Yasar University PhD in Business Administration

2. When to use which statistical tests : Parametric or nonparametric ?? 14.10.2014 2

3. To find the answer , start with the scale of measurement 14.10.2014 3 Nonparametric Nonparametric * Parametric * P arametric * may be used

4. In addition to scale of measurement, we should look at the population distributio n . 14.10.2014 4

5. Normal Distribution a very common continuous probability distribution All normal distributions are symmetric . bell-shaped curve with a single peak . 68% of the observations fall within 1 standard deviation of the mean 95% of the observations fall within 2 standard deviations of the mean 99.7% of the observations fall within 3 standard deviations of the mean for a normal distribution, almost all values lie within 3 standard deviations of the mean

6. 14.10.2014 6 To use parametric tests, stay tuned…  Interval or ratio data are required .  Normal distribution is required . + Homogeneity of variance

7. Homogeneity of Variance The variance is a measure of the dispersion of the random variable about the mean . In other words , it indicates how far the values spread out . It refers to that variance within each of population is equal . Homogeneity of Variances is assessed by Levene’s test. (T-test and ANOVA use Levene’s test .)

8. Parametric or nonparametric – Determination In cases where the data which are measured by interval or ratio scale come from a normal distribution Population variances are equal parametric test s are used . In cases where the data is nominal or ordinal the assumptions of parametric tests are inappropriate nonparametric test s are used . 14.10.2014 8

9. Parametric or nonparametric – Determination 14.10.2014 9 Type of data Categorical Metric Are the data approximately normal ly distributed ? Yes No Are the variances of populations equal ? Nonparametric Tests Parametric Tests Nonparametric Tests No Nonparametric Tests Yes

10. Statistical Test Alternatives : Parametric - Nonparametric 14.10.2014 10 Output variable Nominal Ordinal Interval - Ratio Input variable Nominal Chi-square Mann Whitney Kruskal – Wallis Unpaired t-test or Mann Whitney Paired t-test or Wilcoxon Analysis of variance or Kruskal – Wallis Ordinal Chi-square Mann Whitney Spearman Rank Linear regression or Spearman Interval Ratio Logistic regression Poisson regression Pearson ’s r , L inear regression or Spearman

11. Thank you for your attention . 14.10.2014 11