Hypothesis testing is a cornerstone of statistics, vital for statisticians, machine learning engineers, and data scientists. It involves using statistical tests to determine whether to reject the null hypothesis, which assumes no relationship or difference between groups. These tests, whether parametric or non-parametric, are essential for analyzing data sets, handling outliers, and understanding p-values and statistical power. This article explores various statistical tests, including parametric tests like T-test and Z-test, and non-parametric tests, which do not assume a specific data distribution. Through these tests, we can draw meaningful conclusions from our data.Also,in this article we explain about the parametric and non parametric test , and types of parametric and Non Parametric test etc.
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The basic principle behind the parametric tests is that we have a fixed set of parameters that are used to determine a probabilistic model that may be used in Machine Learning as well.
Parametric tests are those tests for which we have prior knowledge of the population distribution (i.e, normal), or if not then we can easily approximate it to a normal distribution which is possible with the help of the Central Limit Theorem.
Parameters for using the normal distribution is:
Eventually, the classification of a test to be parametric is completely dependent on the population assumptions. There are many parametric tests available from which some of them are as follows:
In Non-Parametric tests, we don’t make any assumption about the parameters for the given population or the population we are studying. In fact, these tests don’t depend on the population.
Hence, there is no fixed set of parameters is available, and also there is no distribution (normal distribution, etc.) of any kind is available for use.
This is also the reason that non-parametric tests are also referred to as distribution-free tests.
In modern days, Non-parametric tests are gaining popularity and an impact of influence some reasons behind this fame is –
| Parameter | Parametric Test | Nonparametric Test |
|---|---|---|
| Assumptions | Assume normal distribution and equal variance | No assumptions about distribution or variance |
| Data Types | Suitable for continuous data | Suitable for both continuous and categorical data |
| Test Statistics | Based on population parameters | Based on ranks or frequencies |
| Power | Generally more powerful when assumptions are met | More robust to violations of assumptions |
| Sample Size | Requires larger sample size, especially when distributions are non-normal | Requires smaller sample size |
| Interpretation of Results | Straightforward interpretation of results | Results are based on ranks or frequencies and may require additional interpretation |
Let us explore types of parametric tests for hypothesis testing.
Assumptions of this test:
Mann-Whitney ‘U’ test is a non-parametric counterpart of the T-test.
A T-test can be a:
One Sample T-test: To compare a sample mean with that of the population mean.
where,
Two-Sample T-test: To compare the means of two different samples.
where,
Note:
Assumptions of this test:
A Z-test can be:
One Sample Z-test: To compare a sample mean with that of the population mean.
Two Sample Z-test: To compare the means of two different samples.
where,
F-statistic is simply a ratio of two variances.
F = s12/s22
By changing the variance in the ratio, F-test has become a very flexible test. It can then be used to:
Assumptions of this test:
Assumptions of this test:
One-way ANOVA and Two-way ANOVA are is types.
F-statistic = variance between the sample means/variance within the sample
Learn more about the difference between Z-test and T-test
Let us now explore types of non-parametric tests.
As a non-parametric test, chi-square can be used:
Chi-square is also used to test the independence of two variables.
Conditions for chi-square test:
Chi-square as a parametric test is used as a test for population variance based on sample variance. If we take each one of a collection of sample variances, divide them by the known population variance and multiply these quotients by (n-1), where n means the number of items in the sample, we get the values of chi-square.
It is calculated as:
It is also known as:
Mathematically, U is given by:
U1 = R1 – n1(n1+1)/2
where n1 is the sample size for sample 1, and R1 is the sum of ranks in Sample 1.
U2 = R2 – n2(n2+1)/2
When you consult the significance tables, use the smaller values of U1 and U2. The sum of the two values is given by,
U1 + U2 = { R1 – n1(n1+1)/2 } + { R2 – n2(n2+1)/2 }
Knowing that R1+R2 = N(N+1)/2 and N=n1+n2, and doing some algebra, we find that the sum is:
U1 + U2 = n1*n2
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Understanding the distinctions and applications of parametric and non-parametric methods is crucial in quantitative data analysis. The choice between these methods depends on factors such as sample size, data distribution, and the presence of outliers. Techniques like the permutation test and the sign test provide robust alternatives when traditional assumptions are not met. Knowledge of standard deviation and other statistical measures enhances the reliability of your findings. For further reading and deeper insights into these topics, consult reputable sources such as Wiley publications.
Hope you like the article and get understanding of parametric and non-parametric tests it will help you for the get better understanding and also about the all about the parametric test.
Chi-square is a non-parametric test for analyzing categorical data, often used to see if two variables are related or if observed data matches expectations.
A. The 4 parametric tests are t-test, ANOVA (Analysis of Variance), pearson correlation coefficient
and linear regression.
A. The four non-parametric tests include the Wilcoxon signed-rank test, Mann-Whitney U test, Kruskal-Wallis test, and Spearman correlation coefficient.
An Example is t-test is a parametric test used to compare the means of two groups, assuming normal distribution. Types include independent samples t-test, paired samples t-test, and one-sample t-test.
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Currently, I am pursuing my Bachelor of Technology (B.Tech) in Electronics and Communication Engineering from Guru Jambheshwar University(GJU), Hisar. I am very enthusiastic about Statistics, Machine Learning and Deep Learning.
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Thanks for the wonderful lecture.
I liked your article Can you provide atleast one example of each parametric test and non parametric test to understand application of each statistical tools
Great article, Aashi Goyal! Thank you for providing a comprehensive overview of parametric and non-parametric tests in statistics. The importance of understanding these tests cannot be overstated, as they play a crucial role in hypothesis testing. Your article effectively explains the key differences between the two types of tests, highlighting the assumptions, data types, and test statistics involved. It's a valuable resource for statisticians, data scientists, and machine learning engineers. Keep up the excellent work!