Question

This exercise focuses on the difference between Parametric and Nonparametric statistics.
1. Define parametric statistics.
2. Define nonparametric statistics.
3. What is referred to by the term “scale of measurement”?
4. What are the four common scales of measurement?
5. Which scale(s) of measurement are associated with parametric statistics?
6. Which scale(s) of measurement are associated with nonparametric statistics?
7. Identify the scale that would be associated with each of the following measurements.
a. Gender
b. Percentiles on a standardized achievement test
c. Highest academic degree earned (e.g., B.S., Master’s, etc.)
d. Raw scores on a standardized test
e. Letter grades assigned in class
f. Ethnicity
8. List at least three common assumptions associated with parametric statistics?
9. For each of the following parametric statistics, indicate the corresponding nonparametric statistic:
a. Independent Samples t-test
b. Dependent Samples t-test
c. Oneway Analysis of Variance
10. Which statistic is commonly used when the data are reported in the form of frequencies?

Answer 1

1. Define parametric statistics.

Answer: Parametric statistics is the type of statistics in which we assume that the sample comes from a probability distribution with parameters. It mainly assumes the normal distribution.

2. Define nonparametric statistics.

Answer: Nonparametric statistics is the type of statistics in which we do not assume that the sample comes from a probability distribution.

3. What is referred to by the term “scale of measurement”?

Answer: Scale of measurement defines the nature or characteristics of a variable.

4. What are the four common scales of measurement?

Answer: Four scales of measurements are: Nominal, Ordinal, Interval, and Ratio

5. Which scale(s) of measurement are associated with parametric statistics?

Answer: Interval and Ratio

6. Which scale(s) of measurement are associated with nonparametric statistics?

Answer: Nominal and Ordinal

7. Identify the scale that would be associated with each of the following measurements.

a. Gender - Nominal

b. Percentiles on a standardized achievement test – Ratio

c. Highest academic degree earned (e.g., B.S., Master’s, etc.) - Ordinal

d. Raw scores on a standardized test - Ratio

e. Letter grades assigned in class - Ordinal

f. Ethnicity - Nominal

8. List at least three common assumptions associated with parametric statistics?

Answer: Three common assumption associated with parametric statistics:

1. Normality

2. Independence

3. Homogeneity of variance

9. For each of the following parametric statistics, indicate the corresponding nonparametric statistic:

a. Independent Samples t-test – Mann-Whitney Test

b. Dependent Samples t-test – Wilcoxon Signed-rank Test

c. One-way Analysis of Variance – Kruskal Wallis H Test

10. Which statistic is commonly used when the data are reported in the form of frequencies?

Answer: Non-parametric