Which two scales of measurement always require nonparametric procedures and why?
The two scales of measurement that always require nonparametric procedures are the nominal scale and the ordinal scale.
1. Nominal Scale: The nominal scale is the simplest scale of measurement and is used for categorizing data into distinct categories or groups. The categories in the nominal scale do not have any inherent order or ranking. Examples include gender, ethnicity, or marital status. Since there is no numerical value associated with the categories, nonparametric procedures are used to analyze nominal data. Nonparametric tests such as the chi-square test or Fisher's exact test are often used to compare frequencies or proportions between different categories.
2. Ordinal Scale: The ordinal scale of measurement involves assigning data into categories that have a meaningful order or ranking. Although the categories can be ranked, the differences between the categories may not be equal or quantifiable. For example, a Likert scale (Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree) is an example of ordinal data. Nonparametric procedures are used for analyzing ordinal data because they do not assume that the intervals between different categories are equal. Nonparametric tests such as the Mann-Whitney U-test or the Wilcoxon signed-rank test are commonly used for analyzing ordinal data.
In summary, nonparametric procedures are required for the nominal and ordinal scales of measurement because these scales do not adhere to the assumptions of parametric statistics, which assume equal intervals and normally distributed data.
The two scales of measurement that always require nonparametric procedures are nominal and ordinal scales.
Nominal scale variables are categorical variables that represent classes or categories, such as gender, race, or types of sports. The values on a nominal scale do not have any inherent order or numerical meaning. For example, if we have a variable representing types of sports, like basketball, soccer, and tennis, we cannot assign any numerical significance to the values. Since nonparametric tests do not assume any specific underlying distribution or measurement properties, they are suitable for analyzing nominal scale data.
Ordinal scale variables represent ordered categories or rankings. They have an inherent order, but the intervals between categories may not be equal. Examples of ordinal scale variables include rankings like 1st, 2nd, and 3rd place in a race or survey responses with options like strongly agree, agree, neutral, disagree, and strongly disagree. Nonparametric procedures are used with ordinal data because they do not require assumptions about the shape or distribution of the data and can operate based solely on the order or ranking of the values.
Nonparametric procedures are more flexible and robust to violations of assumptions compared to parametric procedures, which rely on assumptions about the shape and distribution of the data, such as normality. Therefore, when working with nominal or ordinal scale variables, nonparametric tests are used to analyze and draw conclusions from the data.