Parametric Test in Research

  

Definition:
Parametric tests are statistical tests that make certain assumptions about the parameters of the population distribution from which the sample is drawn—primarily that the data follows a normal distribution and that interval or ratio scale is used.

 Key Assumptions of Parametric Tests

To use a parametric test, the following assumptions must typically be met:

Assumption

Description

Normality

The data should be approximately normally distributed.

Homogeneity of variance

Variances in different groups should be equal (especially for t-tests and ANOVA).

Scale of measurement

Data should be on an interval or ratio scale (quantitative).

Independence

Observations should be independent of each other.

 Common Parametric Tests

Test Name

Purpose

Example

t-test (Independent Samples)

Compares means of two independent groups.

Comparing test scores of boys and girls.

Paired t-test

Compares means of the same group at two different times.

Before and after training scores of employees.

One-way ANOVA

Compares means among three or more independent groups.

Comparing performance of students across three teaching methods.

Two-way ANOVA

Tests effect of two independent variables on one dependent variable.

Studying effect of gender and study method on exam scores.

Z-test

Tests the population mean when sample size is large (n > 30).

Comparing sample mean to known population mean.

Pearson Correlation

Measures the strength and direction of a linear relationship.

Relationship between income and expenditure.

Regression Analysis

Predicts value of a dependent variable based on one or more independent variables.

Predicting sales based on advertising spend.

 Advantages of Parametric Tests

  • More powerful (less likely to make Type II errors) if assumptions are met.
  • Allow for more complex analysis (e.g., multiple predictors in regression).
  • Provide specific estimates (like confidence intervals and effect sizes).

 Disadvantages

  • Invalid if assumptions are violated.
  • Less flexible than non-parametric tests for small or skewed data.

 When to Use Non-Parametric Tests Instead

Use non-parametric tests if:

  • The sample size is small.
  • Data are ordinal or not normally distributed.
  • Variances are unequal between groups.

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