We use cookies essential for this site to function well. Please click to help us improve its usefulness with additional cookies. Learn about our use of cookies in our Privacy Policy & Cookies Policy.
Show details
Powered By
Cookies
This site uses cookies to ensure that you get the best experience possible. To learn more about how we use cookies, please refer to our Privacy Policy & Cookies Policy.
brahmaid
It is needed for personalizing the website.
csrftoken
This cookie is used to prevent Cross-site request forgery (often abbreviated as CSRF) attacks of the website
Identityid
Preserves the login/logout state of users across the whole site.
sessionid
Preserves users' states across page requests.
g_state
Google One-Tap login adds this g_state cookie to set the user status on how they interact with the One-Tap modal.
MUID
Used by Microsoft Clarity, to store and track visits across websites.
_clck
Used by Microsoft Clarity, Persists the Clarity User ID and preferences, unique to that site, on the browser. This ensures that behavior in subsequent visits to the same site will be attributed to the same user ID.
_clsk
Used by Microsoft Clarity, Connects multiple page views by a user into a single Clarity session recording.
SRM_I
Collects user data is specifically adapted to the user or device. The user can also be followed outside of the loaded website, creating a picture of the visitor's behavior.
SM
Use to measure the use of the website for internal analytics
CLID
The cookie is set by embedded Microsoft Clarity scripts. The purpose of this cookie is for heatmap and session recording.
SRM_B
Collected user data is specifically adapted to the user or device. The user can also be followed outside of the loaded website, creating a picture of the visitor's behavior.
_gid
This cookie is installed by Google Analytics. The cookie is used to store information of how visitors use a website and helps in creating an analytics report of how the website is doing. The data collected includes the number of visitors, the source where they have come from, and the pages visited in an anonymous form.
_ga_#
Used by Google Analytics, to store and count pageviews.
_gat_#
Used by Google Analytics to collect data on the number of times a user has visited the website as well as dates for the first and most recent visit.
collect
Used to send data to Google Analytics about the visitor's device and behavior. Tracks the visitor across devices and marketing channels.
AEC
cookies ensure that requests within a browsing session are made by the user, and not by other sites.
G_ENABLED_IDPS
use the cookie when customers want to make a referral from their gmail contacts; it helps auth the gmail account.
test_cookie
This cookie is set by DoubleClick (which is owned by Google) to determine if the website visitor's browser supports cookies.
_we_us
this is used to send push notification using webengage.
WebKlipperAuth
used by webenage to track auth of webenagage.
ln_or
Linkedin sets this cookie to registers statistical data on users' behavior on the website for internal analytics.
JSESSIONID
Use to maintain an anonymous user session by the server.
li_rm
Used as part of the LinkedIn Remember Me feature and is set when a user clicks Remember Me on the device to make it easier for him or her to sign in to that device.
AnalyticsSyncHistory
Used to store information about the time a sync with the lms_analytics cookie took place for users in the Designated Countries.
lms_analytics
Used to store information about the time a sync with the AnalyticsSyncHistory cookie took place for users in the Designated Countries.
liap
Cookie used for Sign-in with Linkedin and/or to allow for the Linkedin follow feature.
visit
allow for the Linkedin follow feature.
li_at
often used to identify you, including your name, interests, and previous activity.
s_plt
Tracks the time that the previous page took to load
lang
Used to remember a user's language setting to ensure LinkedIn.com displays in the language selected by the user in their settings
s_tp
Tracks percent of page viewed
AMCV_14215E3D5995C57C0A495C55%40AdobeOrg
Indicates the start of a session for Adobe Experience Cloud
s_pltp
Provides page name value (URL) for use by Adobe Analytics
s_tslv
Used to retain and fetch time since last visit in Adobe Analytics
li_theme
Remembers a user's display preference/theme setting
li_theme_set
Remembers which users have updated their display / theme preferences
We do not use cookies of this type.
_gcl_au
Used by Google Adsense, to store and track conversions.
SID
Save certain preferences, for example the number of search results per page or activation of the SafeSearch Filter. Adjusts the ads that appear in Google Search.
SAPISID
Save certain preferences, for example the number of search results per page or activation of the SafeSearch Filter. Adjusts the ads that appear in Google Search.
__Secure-#
Save certain preferences, for example the number of search results per page or activation of the SafeSearch Filter. Adjusts the ads that appear in Google Search.
APISID
Save certain preferences, for example the number of search results per page or activation of the SafeSearch Filter. Adjusts the ads that appear in Google Search.
SSID
Save certain preferences, for example the number of search results per page or activation of the SafeSearch Filter. Adjusts the ads that appear in Google Search.
HSID
Save certain preferences, for example the number of search results per page or activation of the SafeSearch Filter. Adjusts the ads that appear in Google Search.
DV
These cookies are used for the purpose of targeted advertising.
NID
These cookies are used for the purpose of targeted advertising.
1P_JAR
These cookies are used to gather website statistics, and track conversion rates.
OTZ
Aggregate analysis of website visitors
_fbp
This cookie is set by Facebook to deliver advertisements when they are on Facebook or a digital platform powered by Facebook advertising after visiting this website.
fr
Contains a unique browser and user ID, used for targeted advertising.
bscookie
Used by LinkedIn to track the use of embedded services.
lidc
Used by LinkedIn for tracking the use of embedded services.
bcookie
Used by LinkedIn to track the use of embedded services.
aam_uuid
Use these cookies to assign a unique ID when users visit a website.
UserMatchHistory
These cookies are set by LinkedIn for advertising purposes, including: tracking visitors so that more relevant ads can be presented, allowing users to use the 'Apply with LinkedIn' or the 'Sign-in with LinkedIn' functions, collecting information about how visitors use the site, etc.
li_sugr
Used to make a probabilistic match of a user's identity outside the Designated Countries
MR
Used to collect information for analytics purposes.
ANONCHK
Used to store session ID for a users session to ensure that clicks from adverts on the Bing search engine are verified for reporting purposes and for personalisation
We do not use cookies of this type.
Cookie declaration last updated on 24/03/2023 by Analytics Vidhya.
Cookies are small text files that can be used by websites to make a user's experience more efficient. The law states that we can store cookies on your device if they are strictly necessary for the operation of this site. For all other types of cookies, we need your permission. This site uses different types of cookies. Some cookies are placed by third-party services that appear on our pages. Learn more about who we are, how you can contact us, and how we process personal data in our Privacy Policy.
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.
Learning Outcomes
Differentiate between parametric analysis and non-parametric methods, understanding their applications in data analysis.
Apply regression techniques to analyze relationships between variables in data science.
Conduct parametric analysis on both small and large sample sizes, ensuring accurate interpretations.
Utilize non-parametric tests such as the Wilcoxon Signed Rank Test, Spearman correlation, and Chi-Square for data sets with ordinal data and non-normally distributed data.
Analyze blood pressure data and other health metrics using appropriate statistical methods.
Evaluate the differences in independent groups using both parametric and non-parametric methods.
Understand the significance of the distribution of the data in choosing the right statistical test.
Integrate statistical tests into broader data science projects for robust analysis and insights.
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:
Mean
Standard Deviation
Why Do We Need a Parametric Test?
Eventually, the classification of a test to be parametricis completely dependent on the population assumptions. There are many parametric tests available from which some of them are as follows:
To find the confidence interval for the population means with the help of known standard deviation.
To determine the confidence interval for population means along with the unknown standard deviation.
To find the confidence interval for the population variance.
To find the confidence interval for the difference of two means, with an unknown value of standard deviation.
What is a Non-parametric Test?
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.
Why Do we Need Non-parametric Test?
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 –
The main reason is that there is no need to be mannered while using parametric tests.
The second reason is that we do not require to make assumptions about the population given (or taken) on which we are doing the analysis.
Most of the nonparametric tests available are very easy to apply and to understand also i.e. the complexity is very low.
Differences Between Parametric and Non-parametric Test
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
Types of Parametric Tests for Hypothesis Testing
Let us explore types of parametric tests for hypothesis testing.
T-Test
It is a parametric test of hypothesis testing based on Student’s T distribution.
It is essentially, testing the significance of the difference of the mean values when the sample size is small (i.e, less than 30) and when the population standard deviation is not available.
Assumptions of this test:
Population distribution is normal, and
Samples are random and independent
The sample size is small.
Population standard deviation is not known.
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,
x̄ is the sample mean
s is the sample standard deviation
n is the sample size
μ is the population mean
Two-Sample T-test: To compare the means of two different samples.
where,
x̄1 is the sample mean of the first group
x̄2 is the sample mean of the second group
S1 is the sample-1 standard deviation
S2is the sample-2 standard deviation
n is the sample size
Note:
If the value of the test statistic is greater than the table value -> Rejects the null hypothesis.
If the value of the test statistic is less than the table value -> Do not reject the null hypothesis.
It is a non-parametric test of hypothesis testing.
It helps in assessing the goodness of fit between a set of observed and those expected theoretically.
It makes a comparison between the expected frequencies and the observed frequencies.
Greater the difference, the greater is the value of chi-square.
If there is no difference between the expected and observed frequencies, then the value of chi-square is equal to zero. It is also known as the “Goodness of fit test” which determines whether a particular distribution fits the observed data or not.
As a non-parametric test, chi-square can be used:
test of goodness of fit.
as a test of independence of two variables.
Chi-square is also used to test the independence of two variables.
Conditions for chi-square test:
Randomly collect and record the Observations.
In the sample, all the entities must be independent.
No one of the groups should contain very few items, say less than 10.
The reasonably large overall number of items. Normally, it should be at least 50, however small the number of groups may be.
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:
Mann-Whitney U-Test
It is a non-parametric test of hypothesis testing.
This test investigates whether two independent samples were selected from a population having the same distribution.
It serves as a true non-parametric counterpart of the T-test and provides the most accurate estimates of significance, especially when sample sizes are small and the population is not normally distributed.
It is based on the comparison of every observation in the first sample with every observation in the other sample.
The test statistic used here is “U”.
Maximum value of “U” is ‘n1*n2‘ and the minimum value is zero.
It is also known as:
Mann-Whitney Wilcoxon Test.
Mann-Whitney Wilcoxon Rank Test.
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,
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.
Frequently Asked Questions
Q1. Is chi-square a non-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.
Q2. What are the 4 parametric tests?
A. The 4 parametric tests are t-test, ANOVA (Analysis of Variance), pearson correlation coefficient and linear regression.
Q3. What are the 4 non-parametric tests?
A. The four non-parametric tests include the Wilcoxon signed-rank test, Mann-Whitney U test, Kruskal-Wallis test, and Spearman correlation coefficient.
Q4. What is an example of a parametric test?
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.
The media shown in this article is not owned by Analytics Vidhya and is used at the Author’s discretion.
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.
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
Ana Carol
25 May, 2023
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!
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!