Explain Scales of Measurement and Discuss Assumption of Parametric Statistics

Introduction

In psychological research and statistics, how data is measured determines the type of analysis that can be conducted. The concept of scales of measurement is foundational in selecting appropriate statistical techniques. Furthermore, parametric statistical methods, which are widely used in psychology, rest on certain assumptions that must be satisfied for valid results. This post explains the various scales of measurement and highlights the core assumptions behind parametric statistics.

Scales of Measurement

Scales of measurement refer to the different levels at which data can be categorized and quantified. There are four major types:

1. Nominal Scale

This is the most basic level of measurement. Data are categorized without any order or hierarchy. Numbers may be assigned for labeling, but they hold no numerical value. Examples include gender (male/female), religion, or marital status.

• Only allows for counting frequencies
• No mathematical operations can be performed

2. Ordinal Scale

Data are categorized in a meaningful order, but the intervals between values are not equal. Examples include rankings (first, second, third), satisfaction levels (satisfied, neutral, dissatisfied).

• Median can be calculated
• Differences between rankings are not interpretable

3. Interval Scale

This scale not only categorizes and orders data but also ensures equal intervals between values. However, it lacks a true zero point. A common example is temperature in Celsius or Fahrenheit.

• Allows addition and subtraction
• Ratio comparisons are not meaningful

4. Ratio Scale

The highest level of measurement, which includes all properties of the interval scale, along with an absolute zero point. Examples include height, weight, age, and time.

• All mathematical operations are possible
• Can compute meaningful ratios (e.g., twice as heavy)

Assumptions of Parametric Statistics

Parametric statistical tests are those that make certain assumptions about the data. These methods include t-tests, ANOVA, regression, and Pearson’s correlation. If the assumptions are not met, the results can be misleading.

1. Level of Measurement

Parametric tests require that the data be measured at the interval or ratio level. Nominal and ordinal data are not suitable for these techniques.

2. Normality

Data should follow a normal distribution, especially in the case of small sample sizes. If the data are significantly skewed, non-parametric alternatives may be preferred.

3. Homogeneity of Variance

This means that the variance within each group being compared should be roughly equal. Violations of this assumption can lead to increased Type I or Type II errors.

4. Independence of Observations

The observations should be independent of each other. This means one participant’s score should not influence another’s. This assumption is particularly important in experimental research.

5. Linearity (for correlation and regression)

Parametric tests that examine relationships between variables (like Pearson’s correlation or regression) assume that the relationship is linear.

Conclusion

Understanding the scales of measurement is essential for choosing the correct statistical tools and accurately interpreting psychological data. Simultaneously, being aware of the assumptions that underlie parametric tests ensures that conclusions drawn from data are valid and reliable. If these assumptions are violated, researchers must either transform their data or consider non-parametric alternatives. Hence, a foundational grasp of measurement and assumptions enhances the overall quality of psychological research.