# What is Parametric tests? Complete guide for 2024

Do you want to know more about parametric tests and how they can help you draw meaningful conclusions from your data? Then you are at the right place. These are statistical tests that assume, that the data being analyzed is normally distributed.

Understanding parametric tests is essential for anyone (Researcher, Data analyst, Lean Six Sigma practitioner, Statistics student) who wants to analyze data accurately and make informed decisions based on statistical evidence.

In this article, I will break down this complex concept into easy-to-understand terms so that you can confidently choose the right type of test for your data and make informed conclusions from your data.

Whether you are a researcher, data analyst, or Lean Six Sigma practitioner, this guide will provide you with a clear understanding of parametric tests, their types, and the applications of each type. So let’s get started…

## What is parametric testing?

Parametric testing is a powerful tool used in statistics and engineering to analyze and understand data. It’s all about identifying the characteristics of a population or sample, using numerical parameters such as mean, and standard deviation to make inferences and draw conclusions.

Why it is important for you to understand this? Let’s take an example, Imagine you are designing a new product like a fancy new phone. You want to make sure that the phone performs well under different conditions, so you test it in various environments like hot/cold temperatures.

Parametric testing allows you to analyze the data from these tests and determine how the phone will perform under various conditions, giving you valuable insights for improving the design and ensuring customer satisfaction.

The key concept behind parametric testing is that it assumes the data being analyzed follows a certain distribution, typically the normal distribution. This allows more accurate predictions and inferences about the population & provides a solid foundation for statistical analysis.

This statistical tool is widely used in different fields such as healthcare, engineering, finance, scientific research, quality management, manufacturing, etc, where it is important to accurately analyze large amounts of data and draw a meaningful conclusion from the data.

In Lean Six Sigma, parametric testing is often used to compare two or more groups of data and determine if they are significantly different from each other. This helps the team identify opportunities for improvement and make data-driven decisions.

Let’s imagine a scenario, suppose a company wants to improve the quality of its product, specifically the length of a particular component. They want to know if there is a significant difference between the length of components produced by two different machines.

To test this, they take samples of components produced by each machine and measure their length. They use parametric testing to determine if there is a significant difference in the mean length of components produced by each machine.

Here the first step is to define the parameters of the population. In this case, they assumed certain things which are common assumptions in parametric testing. See the assumptions below:

1. The length of components produced by each machine follows a normal distribution.
2. The variance of both the machine (length of component data) data groups is equal.
3. Length of component data collected from both machines is independent.

Next, the team calculates the sample mean and standard deviation of the length of components produced by each machine. As here there are 2 data groups (i.e. two machines) they go for 2 sample t-tests to determine if there is a significant difference in the means of the two samples.

After calculating all the statistical measures like a confidence interval, p-value, test statistic value, etc. As per their calculation, they got a p-value less than 0.05. They use standard criteria of hypothesis tests to reject/fail to reject the null hypothesis.

As per that criteria, when the p-value is less than 0.05 null hypothesis must be rejected. Hence the team concluded in this example that there is a significant difference between the mean length of components produced by each machine.

This information now the team can use to identify the root cause of the difference in the length and take corrective action to improve the quality of components produced by both machines.

That’s how parametric testing is used to make data-based decisions in process improvement projects. You can use this powerful statistical tool to make data-based decisions in any field.

There are different types of parametric tests that you can use depending on your type of data. We will see those different types along with when to use which type later in this article. Now let’s understand the applications of parametric tests.

### Applications of parametric testing

• One of the most common applications of parametric tests is to test for significant differences between the means of two or more groups. This can be done using tests like the t-test, ANOVA, and MANOVA.
• It can also be used to conduct regression analysis. Linear regression is a common example of a parametric test that is used to model the relationship between a dependent variable and one or more independent variables.
• It can also be used to test whether data is normally distributed. This is important because many parametric tests assume that the data is normally distributed. Tests like Anderson’s darling test or Shapiro wilk test can be used to test normality.
• It can also be used in quality control to determine whether a process is producing products that meet certain specifications. Tests like process capability analysis and control chart analysis are used in quality control.

## Difference between Parametric Vs Non-parametric testing

This comparison is based on 6 essential factors that you need to understand i.e. its basic definition, Measurement level data, Measure of central tendency, powerful results, outliers, and applicability. Let’s understand each factor one by one:

Meaning –

Parametric tests are the statistical tests in which specific assumptions are made about the population parameter means tests like the Z test, T-test, and ANOVA in which we assume that the sample data we collected is from the normally distributed population.

On the other hand, NPT tests are statistical tests in which no assumptions are made about the population from which the sample has been drawn. It means these tests do not assume anything about population hence it is distribution-free tests.

Measurement level data –

Parametric tests can handle interval as well as ratio-level data. Interval data means the data that can be arranged in an ordering scheme and differences between the data values can be interpreted. Eg- temperature in degrees Celcius.

Rato-level data means the data that can be ranked where all the arithmetic operations including division can be performed on the data set. Ratio-level data has an absolute zero value. Eg – weight, length, breadth, etc.

On the other hand, NPT tests handle all types of data i.e. nominal, ordinal, interval as well as ratio level data, and rank data.

Here nominal data means the data that can not be arranged in an ordering form and no arithmetic operations are performed on this data. Eg- Blood groups A, AB, O.

Ordinal data means the data that can be arranged in ordering form but no arithmetic operations are performed on this data. (Check out – NPT test complete guide)

Eg- product ratings like good, bad, worst, and excellent. Rank data means just assigning ranks to data values from lowest to highest (Large data value – High rank, Small data value – Low rank)

Measure of central tendency –

Parametric tests are applicable when the mean better represents the center of the distribution. In parametric tests, we compare the mean of the sample group with each other. Eg – In the 1 sample Z-test and T-test we compare mean of the sample group with the target mean value.

On the other hand, NPT tests are applicable when the median better represents the center of a distribution. NPT compares the median of the sample group with each other. Eg – in 1 sample sign test, we compare the median of the sample group with the target median value.

Powerful results –

NPT tests provide statistically less powerful results than the parametric tests and this happens because NPT tests have fewer assumptions so these tests may not provide the ideal results which we want.

On the other hand, parametric tests provide statistically more powerful results, that’s why preferred in most applications but when normality assumptions fail then we need to think about NPT tests.

Outliers –

Parametric tests are significantly affected by outliers. In the case of extreme values or outliers in the data, parametric tests do not provide accurate results. That’s why we need to apply NPT tests in such cases because these tests do not seriously affect by outliers.

Applicability –

Parametric tests are applicable in the case of continuous or variable data sets like length, mass, time, etc. On the other hand, NPT tests are applicable in the case of variable as well as attribute data sets (like pass/fail, yes/no).

• Parametric tests are statistically more powerful than non-parametric tests, especially when the sample size is large and the data is normally distributed.
• It can provide a more precise estimation of population parameters such as means, and standard deviation, compared to non-parametric tests.
• These tests are often easier to interpret and communicate, as their results are based on familiar statistical concepts such as means, standard deviations, and p-values.
• These tests have well developed theoretical foundation making them more robust to violations of assumptions and more widely accepted by statistics experts.
• There are many types of parametric tests available for different types of data that allow a greater range of statistical analysis and also provide more information about data.

• Parametric tests are sensitive to outliers, which can greatly impact the results of the test. If outliers are present in the data, the results of the test may be inaccurate.
• These tests require a larger sample size. If the sample size is too small, the results of the test may be inaccurate.
• Parametric tests are useful in the case of normal data but not suitable for other types of data like ordinal, or categorical data.

## Types of Parametric tests

Let’s understand the 4 important types of parametric tests along with their application and hypothetical conditions.

T-test:

1) 1 sample T-test-

1 sample t-test is a type of hypothesis test used to determine whether the mean of a single sample of data differs significantly from a known or hypothesized population mean. It is commonly used when the population standard deviation is unknown and the sample size is small (n < 25)

Example – Quality analysts use 1 sample t-test to determine whether the average thread length of bolts differs from the target of 30 mm. Here hypothesis target mean is 30 mm and only one 1 sample group is there i.e. thread length of bolts.

Hypothetical statement

Null hypothesis (Ho):  Mean of thread length = Target mean (30mm)

Alternate hypothesis (Ha):  Mean of thread length ≠ Target mean (30mm)

2) 2 sample T-test-

A 2 sample t-test is a type of hypothesis test used to determine if two sets of data have different means. It is used when comparing the means of two groups of samples. It assumes that the data in each group are normally distributed and have equal variances.

Example – A healthcare consultant wants to compare the patient satisfaction ratings of two hospitals and he collects ratings from 15 patients for each of the hospitals. Here the two sample groups are hospital A and hospital B.

Hypothetical statement

Null hypothesis (Ho):  Mean of patient ratings of A = Mean of patient ratings of B

Alternate hypothesis (Ha):  Mean of patient ratings of A ≠ Mean of patient ratings of B

3) Paired T-test

Paired t-test is a type of test used to determine if there is a significant difference between two sets of paired observations. It is used when the data for the two groups come from the same group or the same sample is measured twice. (Before and after treatment)

Example – The manager of the fitness gym uses a paired t-test to determine whether the group of 20 participants improved their fitness after a 5-week program.

Here sample groups come from the same participants, manager measured their fitness data before the program and after the program.

Hypothetical statement

Null hypothesis (Ho):  Mean of fitness data before the program = Mean of fitness data after the program

Alternate hypothesis (Ha):  Mean of fitness data before the program ≠ Mean of fitness data after the program

Z-test:

1) 1 sample T-test –

1 sample Z test is a type of hypothesis test used to determine whether the sample mean is significantly different from a known population mean when the standard deviation is known.

It is nearly same as the 1 sample t-test only difference is, to perform the 1 sample Z test the standard deviation must be known. You can refer the

Example – A teacher claims that the mean score of students in his class is greater than 85 with a standard deviation of 20. Here student score is one sample group and SD is 20.

Hypothetical statement

Null hypothesis (Ho):  Mean score of students = Target mean 85

Alternate hypothesis (Ha):  Mean score of students > Target mean 85

2) 2 sample Z-test –

2 sample Z-test is a type of hypothesis test used to compare the means of two independent populations when the sample size is greater than 30 and the standard deviation is known.

This test assumes that the two samples are randomly selected from normal populations and that the variances of the two populations are equal. (You can apply this for the same example of 2 sample t-tests with n>30)

Example – A healthcare consultant wants to compare the patient satisfaction ratings of two hospitals and he collects ratings from 35 patients for each of the hospitals. Here the two sample groups are hospital A and hospital B. (Standard deviation is 12)

Hypothetical statement

Null hypothesis (Ho):  Mean of patient ratings of A = Mean of patient ratings of B

Alternate hypothesis (Ha):  Mean of patient ratings of A ≠ Mean of patient ratings of B

One-way ANOVA:

One-way ANOVA is used to compare means across two or more groups. It is called ‘one way’ because it considers only one factor or independent variable that divides the group. The factor can be a categorical variable or a continuous variable that is split into categories.

In simple terms, use ANOVA when you have a categorical factor and a continuous response and want to determine whether the population means of two or more groups differ.

Example – A carpet manufacturer wants to determine whether there are differences in durability among 3 types of carpet. Here carpets C1, C2, and C3 are categorical factors, and durability data for each carpet is a continuous response.

Hypothetical statement

Null hypothesis (Ho):  Mean of C1 = Mean of C2 = Mean of C3

Alternate hypothesis (Ha):  Mean of C1 ≠ Mean of C2 ≠ Mean of C3

These are the important types of parametric tests you need to be aware of and if you want to learn more about hypothesis testing then check out these 2 articles.

1st article will help you understand the basic concepts of hypothesis testing and 2nd will help you understand how to perform hypothesis tests step by step.

## Conclusion

Parametric tests play a crucial role in the field of statistics and data analysis. As we have seen throughout this complete guide, these powerful tests allow us to draw meaningful conclusions about a population based on the sample.

By understanding the types of parametric tests, advantages & disadvantages, and differences between parametric vs NPT tests, we can make informed decisions about which test to use and how to interpret its results.

Whether you are a researcher, data analyst, or lean six sigma practitioner, mastering the concept and types of parametric tests can help you make sense of the complex patterns and relationships that lie hidden in the data.