Parametric vs Nonparametric Tests: When to use which
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The document discusses the appropriate use of parametric and nonparametric statistical tests based on the scale of measurement and population distribution. It explains the characteristics of different data types (nominal, ordinal, interval, and ratio) and the conditions required for using parametric tests, including normal distribution and homogeneity of variance. The document provides a decision-making framework for selecting the appropriate statistical tests, detailing alternatives for various input and output variable types.
Parametric vs Nonparametric Tests: When to use which
- 1. 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 • define an attribute Nominal • e.g. gender, matital status • rank or order the observations as scores or categories from low to high in terms of «more or less» • e.g. education, attitude/opinion scales Ordinal • interval between observations in terms of fixed unit of measurement • e.g. measures of temperature Interval • The scale has a fundamental zero point • e.g. age, income Ratio Nonparametric Nonparametric *Parametric *Parametric *may be used 14.10.2014 3
- 4. In addition to scale of measurement, we should look at the population distribution. Population is normally distributed • Nonparametric • (have to be used) Not normally distributed population or no assumption can be made about the population distribution • Parametric • (may be used) 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. To use parametric tests, stay tuned… Interval or ratio data are required. Normal distribution is required. + Homogeneity of variance 14.10.2014 6
- 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 tests are used. In cases where the data is nominal or ordinal the assumptions of parametric tests are inappropriate nonparametric tests are used. 14.10.2014 8
- 9. Parametric or nonparametric – Determination Type of data Categorical Metric Are the data approximately normally distributed? No Yes Are the variances of populations equal? Nonparametric Tests Nonparametric Tests No Nonparametric Tests Parametric Tests Yes 14.10.2014 9
- 10. Statistical Test Alternatives: Parametric - Nonparametric Output variable Nominal Ordinal Interval - Ratio 14.10.2014 10 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, Linear regression or Spearman
- 11. Thank you for your attention. 14.10.2014 11