Difference Between Parametric and Nonparametric Test

# Difference Between Parametric and Nonparametric Test

Rashmi Karan
Manager - Content
Updated on Jul 10, 2024 15:56 IST

Parametric tests require data to follow a specific distribution, typically normal, and are ideal for large, numerical datasets that meet these criteria. They offer precision but are sensitive to outliers. Non-parametric tests, on the other hand, are more flexible, accommodating various data types, including ordinal and nominal, without needing a normal distribution. They are robust against outliers and suitable for smaller or non-standard datasets, making them a versatile tool in statistical analysis.

Have you ever wondered how statisticians make sense of complex data? The secret lies in choosing the right tool: parametric or non-parametric tests. But what sets these two apart? Parametric tests are like precise instruments, ideal for data that follows a familiar pattern. Non-parametric tests, however, are the versatile heroes, adaptable to more unpredictable data. This choice isn't just academic; it's a practical decision with real-world implications. So, how do you decide which test to use? Let's explore these statistical paths, each with its unique strengths, and uncover how they shape the story your data tells. This article will explain both types of tests and cover the difference between parametric and nonparametric test.

If you need to the single most important point of difference between parametric and non-parametric tests, it's this:

Parametric tests rely on specific assumptions about the underlying data distribution (like normality), while non-parametric tests make no such assumptions and are "distribution-free."

This means:

• Parametric tests can be more powerful and precise if their assumptions hold, but they're more sensitive to violations of those assumptions.
• Non-parametric tests are less powerful but more robust, meaning they work well even when the data doesn't perfectly follow any specific distribution.

Remember, both tests can be valuable tools, but choosing the right one depends on your data and research goals.

## Table of Content

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## What is a Parametric Test?

A parametric test in statistics is like using a standard measuring tape in a well-organised toolbox. It's ideal for situations where your data, like heights or test scores, neatly lines up with common patterns, such as the familiar bell-shaped curve. This test assumes that your data behaves in a predictable way, making it a reliable choice for drawing conclusions when these standard conditions are met. Think of it as the go-to tool for measuring things that fit the usual expectations.

### Parametric Tests - Key Pointers

• Scenario: You're a teacher comparing students' test scores before and after a new teaching method.
• Data Pattern: The test scores must follow a 'normal distribution', meaning most scores are around the average, creating a bell-shaped curve on a graph.
• Why Use It: To determine if the change in scores is due to the new teaching method or just by chance.
• Test Example: A 'T-test' is a type of parametric test used here to compare the average scores from two different years.
• Requirement: For the parametric test to be appropriate, the data (test scores) should be normally distributed (bell-shaped curve).
• Outcome: The test helps you understand if the new teaching method has significantly affected the students' performance.
• Data Distribution: The data should ideally be normally distributed, meaning most values cluster around a central point, creating a bell-shaped curve.
• Data Type: Best suited for numerical data (like heights, weights, test scores) that can be measured on a scale.
• Sample Size: Larger sample sizes are generally more effective, as this helps ensure the data distribution is normal.
• Sensitivity to Outliers: Parametric tests are sensitive to outliers (extreme values), which can skew the results.
• Common Examples: T-tests (for comparing two groups' means) and ANOVA (for comparing means across multiple groups).
• Assumptions: These tests often assume homogeneity of variance (all groups have similar variances) and linearity.
• Use Cases: Ideal for scenarios where you're comparing averages or means, like examining the effectiveness of a new teaching method by comparing average test scores before and after its implementation.
• Accuracy: They can provide more precise results when their assumptions are met.

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A non-parametric test in statistics is like using a flexible measuring tape that can adapt to any shape or size. It's useful when your data doesn't follow a standard pattern, like a bell-shaped curve. This type of test doesn't assume your data fits a specific, predictable model, making it versatile for analyzing a wide range of situations, especially when the data is unusual or doesn't meet typical standards. Think of it as the handy, all-purpose tool in your statistical toolkit, ready to measure things that don't conform to the usual norms.

### Non-Parametric Tests - Key Pointers

1. Useful in Various Situations: Great for exploratory analysis or when data doesn't fit typical patterns.
2. Flexibility with Data Types: Non-parametric tests can handle various data types, including ordinal (like rankings), nominal (like categories), and numerical data that doesn't fit a normal distribution.

3. No Need for Normal Distribution: Unlike parametric tests, they don't require your data to follow a specific distribution pattern, such as the normal (bell-shaped) distribution.

4. Good for Small Samples: Works well even with a small amount of data.
5. Robust Against Outliers: Handles extreme or unusual data points better than parametric tests.
6. Focuses on Medians or Distributions: Often looks at the middle value (median) or overall pattern, not just the average.
7. Examples: Mann-Whitney U test (comparing two groups) and Kruskal-Wallis test (comparing more than two groups).
8. Less Assumption-Dependent: Doesn't rely heavily on data distribution assumptions.
9. Versatility: Ideal for exploratory analysis or when you're unsure about the underlying distribution of your data.

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## Difference Between Parametric and Nonparametric Test

Aspect Parametric Tests Non-Parametric Tests
What They Are Tests requiring data to follow a specific distribution are usually normal. Tests that do not need the data to follow a specific distribution.
Data Type Need numerical data (like height and weight) that ideally forms a bell curve. Can handle various data types, including rankings or categories (like survey responses).
When to Use Best for large samples that meet the test's requirements. Useful for smaller samples or when data doesn't meet strict requirements.
Examples

- T-test: Comparing average test scores between two classes.

- ANOVA: Examining salary differences across different industries.

- Mann-Whitney U test: Comparing customer satisfaction rankings between two stores.

- Kruskal-Wallis test: Assessing patient pain levels across different treatment groups.

Sensitivity to Outliers More likely to be affected by unusual or extreme values. More robust against outliers or unusual data.
Typical Use Cases

- Measuring the average growth of plants in different fertilizers.

- Comparing average blood pressure levels between different age groups.

- Ranking preferences for different brands.

- Comparing ordinal data like satisfaction levels (e.g., happy, neutral, unhappy.

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## Difference Between Parametric and Nonparametric Test - Examples

Parameter Parametric Test Example Non-Parametric Test Example
Data Type Comparing the average heights (numerical data) of male and female athletes. Ranking favourite flavours of ice cream from a survey (ordinal data).
Sample Size & Distribution Testing if the average scores on a maths test differ between two large classes with normally distributed results. Assessing whether two small groups have different levels of satisfaction with a service, without assuming normal distribution.
Outliers Examining the impact of a new teaching method on student grades, where a few students have exceptionally high scores. Comparing the effectiveness of two medications where some patients have extreme reactions.
Hypothesis Testing Checking if the mean monthly expenditure of families in two cities is different. Determining if the median response time of two emergency services differs.
Assumptions Assuming that the annual salaries of employees in a sector are normally distributed for comparison. Comparing customer preferences for two brands without assuming any specific distribution pattern.
Typical Use Case Measuring the average increase in blood pressure due to a specific diet in a large, normally distributed sample. Ranking the effectiveness of different teaching methods in small, non-standardised groups.

This table uses examples to highlight how parametric and non-parametric tests differ in terms of data type, sample size and distribution, handling of outliers, hypothesis testing, underlying assumptions, and typical use cases. Parametric tests are generally used for precise, numerical data under specific conditions, while non-parametric tests are more versatile, handling various data types and conditions, especially when standard assumptions of normality and scale are not met.

## Summarizing Key Difference Between Parametric and Nonparametric Test

The key difference between parametric and non-parametric tests lies in their assumptions about the data:

• Parametric Tests: Assume that the data follows a specific distribution, typically a normal (bell-shaped) distribution. They require numerical data and are best suited for large samples that adhere to these assumptions. Parametric tests are more precise under these conditions but can be sensitive to outliers.

• Non-Parametric Tests: Do not assume a specific distribution of the data. They are more flexible, able to handle various types of data including ordinal, nominal, and non-normally distributed numerical data. Non-parametric tests are particularly useful for smaller samples and are more robust against outliers.

In summary, parametric tests require data to fit a specific pattern and are used when these conditions are met, offering precision. Non-parametric tests are more versatile and suitable for a wider range of data types and conditions, especially when standard assumptions are unmet.

Related – Difference Between Independent and Dependent Variables

For a researcher doing statistical analysis, choosing between parametric and non-parametric testing takes work. To perform hypotheses, if the information about the population is wholly known, using parameters, then the test is a parametric test. At the same time, if there is no knowledge about the population and it is necessary to test the hypothesis about the population, then the test can be non-parametric. Before applying nonparametric or parametric tests, it is important to know the research’s objective, the population’s size, and the scale used to measure the data.

We hope this article helped you understand the difference between parametric and nonparametric tests.

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## FAQs

What Exactly Are Parametric Tests?

Parametric tests are statistical tests that assume the data follows a specific distribution, typically a normal distribution. This is akin to following a specific recipe in cooking, where certain ingredients are essential. The 'normal distribution' is a statistical term for data that clusters around a central value in a specific, predictable pattern.

Do parametric tests require larger sample sizes compared to nonparametric tests?

In general, parametric tests may require larger sample sizes to ensure that the assumptions of normality and homogeneity of variance hold. Nonparametric tests can handle smaller sample sizes effectively.

Can I convert my nonparametric data into parametric data to use parametric tests?

Converting data from nonparametric to parametric is generally not advisable, as it may lead to biased results. If the assumptions of parametric tests are not met, it is best to use appropriate nonparametric tests.

When Should I Use a Parametric Test?

A parametric test is the right choice when your data meets certain conditions: it should be numerical and ideally follow a normal distribution. These tests are particularly powerful when dealing with large datasets that adhere to these requirements.

What Are Some Examples of Parametric Tests?

Common examples include the T-test, used for comparing the means of two groups, and ANOVA, used for comparing means across multiple groups. For instance, a T-test might be used to compare the average heights of male and female athletes.

What Are Non-Parametric Tests?

Non-parametric tests do not require data to follow a specific distribution. They are more flexible, like improvising a dish with whatever ingredients you have. These tests are suitable for various data types, including ordinal data (like survey responses) and numerical data that does not fit a normal distribution.

When Is It Appropriate to Use a Non-Parametric Test?

These tests are ideal for smaller samples or when your data doesn’t meet the strict requirements of parametric tests. They are also more robust against outliers or unusual data points.

Can You Provide Examples of Non-Parametric Tests?

The Mann-Whitney U test, used for comparing two independent groups, and the Kruskal-Wallis test, used for comparing more than two groups, are common non-parametric tests. For example, the Mann-Whitney U test could be used to compare customer satisfaction rankings between two stores.

How Do I Choose Between Parametric and Non-Parametric Tests?

The choice depends on the nature of your data and the specific requirements of your analysis. Consider factors like data type, distribution, sample size, and the presence of outliers. Neither type of test is universally better; it all depends on the situation.

What Are the Limitations of Each Type of Test?

Parametric tests can be less reliable if the data does not meet their assumptions (like normal distribution). Non-parametric tests, while more flexible, might be less powerful in detecting a true effect when the data actually meets the assumptions for a parametric test.

How Do Outliers Affect Parametric and Non-Parametric Tests?

Parametric tests are more sensitive to outliers, which can skew the results. Non-parametric tests are generally more resistant to the impact of outliers.

Can I Use These Tests for Small Data Sets?

Parametric tests typically require larger sample sizes to be effective. Non-parametric tests, on the other hand, can be a better choice for smaller data sets.