Difference Between Parametric And Non-Parametric Tests

Statistical tests help us make conclusions about a larger group based on a smaller sample. There are two main types of statistical tests: parametric and non-parametric. Knowing the difference between these tests is important to pick the right one for your data and research question.

Introduction:

Statistical analysis is used in many areas like psychology, sociology, biology, and finance. It involves checking ideas (hypotheses) and seeing how strong the evidence is for or against them. One important choice in this process is selecting the correct type of test. This choice is often between parametric and non-parametric tests.

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What are parametric and non-parametric tests?

Parametric tests are statistical tests that assume the data comes from a population with a normal (bell-shaped) distribution. These tests use the mean and standard deviation to make conclusions about the population. They are usually more powerful than non-parametric tests, meaning they can detect smaller differences between groups. However, they need the data to follow certain rules, like being normally distributed and having equal variances, to work properly.

Non-parametric tests do not make any assumptions about the population's distribution. They use the ranks of the data instead of the actual values to draw conclusions. These tests are often used when the data does not meet the requirements for parametric tests, such as normality and equal variances. While non-parametric tests are generally less powerful, they are more flexible and can handle data that doesn't fit the normal distribution pattern.

Difference Between Parametric and Non-Parametric Tests:

Assumptions: Parametric tests assume certain things about the population, like the distribution of data. Non-parametric tests don’t need these assumptions.

Normality: Parametric tests need the data to follow a normal (bell-shaped) distribution. Non-parametric tests don’t require this.

Equal Variances: Parametric tests assume that the populations being compared have equal variances. Non-parametric tests don’t need this assumption.

Power: Parametric tests are usually more powerful, meaning they can find smaller differences between groups. Non-parametric tests might not be as powerful.

Sensitivity: Parametric tests are more sensitive to changes from the assumptions of normality and equal variances. Non-parametric tests are less sensitive to these changes.

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Types of Parametric Tests:

1. t-Test: This test compares the means of two independent groups. There are two types: two-sample t-test and paired-sample t-test.

2. Analysis of Variance (ANOVA): ANOVA compares the means of more than two groups. There are two types: one-way ANOVA and two-way ANOVA.

3. Multiple Regression: This examines the relationship between multiple independent variables and one dependent variable.

     Types of Non-Parametric Tests:

Wilcoxon Signed-Rank Test: This test compares the medians of two related groups. It's a non-parametric alternative to the paired-sample t-test.

Mann-Whitney U Test: This test compares the medians of two independent groups. It's a non-parametric substitute for the two-sample t-test.

Kruskal-Wallis H Test: This test compares the medians of more than two independent groups. It's the non-parametric equivalent of a one-way ANOVA.

Application of Parametric Tests
Parametric tests assume that the population has a normal distribution. They use parameters like mean, variance, and standard deviation to describe the population. Common parametric tests include t-tests, ANOVA, and regression. These tests are usually used in natural and social sciences to test hypotheses about differences in means or relationships between variables.

Application of Non-Parametric Tests
Non-parametric tests do not assume the population has a normal distribution. They rely on the rank order of the data rather than the actual values. These tests are used when data doesn’t meet the assumptions of parametric tests, such as normality, equal variance, and independent observations. Common non-parametric tests include the Wilcoxon rank-sum test, the Kruskal-Wallis test, and the Friedman test. These tests are often used in fields like psychology and medical research.

Advantages & Disadvantages of Parametric Tests

Advantages:

1. More Powerful: Parametric tests can find smaller effects with fewer samples.
2. Precise Estimates: They give accurate estimates of the population parameters.
3. Easy to Interpret: The results are easier to understand.

Disadvantages:

1. Strong Assumptions: They assume the population follows a certain distribution, which might not always be true.
2. Misleading Results: If the assumptions are wrong, the test results can be incorrect.
3. Sensitive to Outliers: Extreme values in the data can affect the results.

Advantages & Disadvantages of Non-Parametric Tests

Advantages:

1. No Assumptions: They do not require the population to follow a specific distribution.
2. Less Sensitive to Outliers: Extreme values have less impact on the results.

Disadvantages:

1. Less Powerful: They may need more samples to detect the same effect as parametric tests.
2. Less Precise: They give less accurate estimates of the population parameters.
3. Harder to Interpret: The results can be more difficult to understand.