Parametric and Non-Parametric Statistics

Introduction

In social research, once data is collected, it must be analyzed to draw valid conclusions. The choice of statistical test depends on:

• Type of data (nominal, ordinal, interval, ratio)
• Distribution of data (normal or not)
• Research objectives (comparison, relationship, prediction)

Accordingly, we use either:

• Parametric Statistics (assume normal distribution, require interval/ratio data), or
• Non-Parametric Statistics (distribution-free, work with nominal/ordinal data).

Parametric Statistics

1. Meaning and Definition

• Parametric statistics are statistical methods that make assumptions about the parameters (mean, variance, standard deviation) of the population from which the sample is drawn.
• They usually assume that data comes from a normal distribution and is measured at the interval or ratio level.

Definition (Kerlinger):
“Parametric tests are those which require at least interval-level measurement and make assumptions about the parameters of the population distribution.”

2. Assumptions of Parametric Tests

To use parametric tests correctly, the following assumptions must be satisfied:

• Level of Measurement – Data must be interval (temperature, test scores) or ratio (income, age, height).
• Normality – Population distribution should be approximately normal.
• Homogeneity of Variance – Variances of different groups should be equal (tested using Levene’s test).
• Independence – Observations must be independent of each other.
• Random Sampling – The sample must be randomly selected from the population.

3. Types of Parametric Tests

(A) Tests of Means

1. t-Tests
   • One-sample t-test → compares sample mean with population mean.
   • Independent t-test → compares means of 2 independent groups (e.g., male vs. female income).
   • Paired-sample t-test → compares means of the same group before and after treatment (e.g., farmers’ knowledge before & after training).
2. Z-Test
   • Used when sample size > 30.
   • Compares means or proportions of large samples.
3. Analysis of Variance (ANOVA)
   • One-way ANOVA → compares means across 3 or more groups.
   • Two-way ANOVA → effect of 2 independent variables on a dependent variable.
   • MANOVA → multiple dependent variables.

(B) Tests of Association

1. Pearson’s Product-Moment Correlation (r)
   • Measures the strength and direction of linear relationship between 2 variables.
   • Value ranges from –1 to +1.
2. Regression Analysis
   • Simple regression → predicts dependent variable from one independent variable.
   • Multiple regression → predicts dependent variable from multiple independent variables.

(C) Advanced Parametric Techniques

• ANCOVA → ANOVA + regression (adjusts for covariates).
• Factor Analysis → reduces data into fewer dimensions (used in social sciences to group related variables).
• Path Analysis / Structural Equation Modeling (SEM) → tests causal relationships among variables.

4. Advantages of Parametric Tests

• Powerful & Efficient – Use more information from data (mean, variance).
• Precise Estimates – Provide exact probabilities for hypothesis testing.
• Flexible – Can be extended to complex designs (e.g., MANOVA, regression).
• Generalizability – If assumptions are satisfied, results can be generalized to population.

5. Limitations

1. Require strict assumptions (normality, equal variance, interval data).
2. Not suitable for ordinal or nominal data.
3. Can give misleading results if assumptions are violated.
4. Sometimes require large samples.

6. Applications in Social Research

• Comparing farmers’ income before and after training (paired t-test).
• Testing differences in knowledge score of adopters and non-adopters of a technology (independent t-test).
• Checking whether extension methods (method demonstration, lecture, film) differ in effectiveness (ANOVA).
• Measuring correlation between education level and adoption of improved practices (Pearson’s r).
• Predicting income (Y) from education, age, and land size (regression).

7. Common Parametric Tests and Their Uses