Interview Prep
Career
GenAI
Prompt Engg
ChatGPT
LLM
Langchain
RAG
AI Agents
Machine Learning
Deep Learning
GenAI Tools
LLMOps
Python
NLP
SQL
AIML Projects

Reading list

Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

Hypothesis Testing: A Way to Accept or Reject Your Hypothesis Using p-value

G
Guest Blog Last Updated : 19 Jul, 2020
7 min read

Introduction

Hypothesis Testing

One of the most basic concepts in statistics is hypothesis testing. Not just in Data Science, Hypothesis testing is important in every field. Want to know how??? Let us take an example. You must have heard about lifebuoy?? Suppose

lifebuoy claims that, it kills 99.9% of germs. So how can they say so? There has to be a testing technique to prove this claim right?? So hypothesis testing uses to prove a claim or any assumptions.

Table of Content

  1. Definition of Hypothesis Testing.
  2. Null and Alternative Hypothesis Testing
  3. Simple and composite Hypothesis Testing
  4. One-tailed and two-tailed testing
  5. Critical Region.
  6. Type I and Type II error.
  7. Statistically significant.
  8. Level of confidence
  9. Level of significance
  10. P-value.

This blog breaks these concepts down into small pieces so that you can understand their motivation and their uses. By the time you’re done with this blog, Hypothesis Testing basics will be clear!!!

Definition of Hypothesis Testing

The hypothesis is a statement, assumption or claim about the value of the parameter (mean, variance, median etc.).

A hypothesis is an educated guess about something in the world around you. It should be testable, either by experiment or observation.

Like, if we make a statement that “Dhoni is the best Indian Captain ever.” This is an assumption that we are making based on the average wins and losses team had under his captaincy. We can test this statement based on all the match data.

Null and Alternative Hypothesis Testing

The null hypothesis is the hypothesis to be tested for possible rejection under the assumption that it is true. The concept of the null is similar to innocent until proven guilty We assume innocence until we have enough evidence to prove that a suspect is guilty.

In simple language, we can understand the null hypothesis as already accepted statements, For example, Sky is blue. We already accept this statement.

The alternative hypothesis complements the Null hypothesis. It is the opposite of the null hypothesis such that both Alternate and null hypothesis together cover all the possible values of the population parameter.

Let’s understand this with an example:

A soap company claims that its product kills on an average of 99% of the germs. To test the claim of this company we will formulate the null and alternate hypothesis.

Null Hypothesis(H0): Average =99%

Alternate Hypothesis(H1): Average is not equal to 99%.

Note: When we test a hypothesis, we assume the null hypothesis to be true until there is sufficient evidence in the sample to prove it false. In that case, we reject the null hypothesis and support the alternate hypothesis. If the sample fails to provide sufficient evidence for us to reject the null hypothesis, we cannot say that the null hypothesis is true because it is based on just the sample data. For saying the null hypothesis is true we will have to study the whole population data.

Simple and Composite Hypothesis Testing

When a hypothesis specifies an exact value of the parameter, it is a simple hypothesis and if it specifies a range of values then it is called a composite hypothesis.

e.g. Motor cycle company claiming that a certain model gives an average mileage of 100Km per liter, this is a case of simple hypothesis.

The average age of students in a class is greater than 20. This statement is a composite hypothesis.

One-tailed and two-tailed Hypothesis Testing

If the alternate hypothesis gives the alternate in both directions (less than and greater than) of the value of the parameter specified in the null hypothesis, it is called a Two-tailed test.

If the alternate hypothesis gives the alternate in only one direction (either less than or greater than) of the value of the parameter specified in the null hypothesis, it is called a One-tailed test.

e.g. if H0: mean= 100 H1: mean not equal to 100

here according to H1, mean can be greater than or less than 100. This is an example of a Two-tailed test

Similarly, if H0: mean>=100 then H1: mean< 100

Here, the mean is less than 100. It is called a One-tailed test.

Critical Region

The critical region is that region in the sample space in which if the calculated value lies then we reject the null hypothesis.

Let’s understand this with an example:

Suppose you are looking to rent an apartment. You listed out all the available apartments from different real state websites. You have a budget of Rs. 15000/ month. You cannot spend more than that. The list of apartments you have made has a price ranging from 7000/month to 30,000/month.

You select a random apartment from the list and assume below hypothesis:

H0: You will rent the apartment.

H1: You won’t rent the apartment.

Now, since your budget is 15000, you have to reject all the apartments above that price.

Here all the Prices greater than 15000 become your critical region. If the random apartment’s price lies in this region, you have to reject your null hypothesis and if the random apartment’s price doesn’t lie in this region, you do not reject your null hypothesis.

The critical region lies in one tail or two tails on the probability distribution curve according to the alternative hypothesis. The critical region is a pre-defined area corresponding to a cut off value in the probability distribution curve. It is denoted by α.

Critical values are values separating the values that support or reject the null hypothesis and are calculated on the basis of alpha.

We will see more examples later on and it will be clear how do we choose α.

Based on the alternative hypothesis, three cases of critical region arise:

Case 1) This is a double-tailed test.

Two Tail Hypothesis Test

Case 2) This scenario is also called a Left-tailed test.

One Tail Hypothesis Testing

Case 3) This scenario is also called a Right-tailed test.

One Tail Hypothesis Testing

Type I and Type II Error

So Type I and type II error is one of the most important topics of hypothesis testing. Let’s simplify it by breaking down this topic into a smaller portion.

Types of Errors

A false positive (type I error) — when you reject a true null hypothesis.

A false negative (type II error) — when you accept a false null hypothesis.

The probability of committing Type I error (False positive) is equal to the significance level or size of critical region α.

α= P [rejecting H0 when H0 is true]

The probability of committing Type II error (False negative) is equal to the beta β. It is called the ‘power of the test’.

β = P [not rejecting H0 when h1 is true]

Example:

The person is arrested on the charge of being guilty of burglary. A jury of judges has to decide guilty or not guilty.

H0: Person is innocent

H1: Person is guilty

Type I error will be if the Jury convicts the person [rejects H0] although the person was innocent [H0 is true].

Type II error will be the case when Jury released the person [Do not reject H0] although the person is guilty [H1 is true].

Statistically significant

To understand this topic let us consider an example: Suppose there is a candy bar factory which makes 500gm of candy bar every day. One day after the maintenance of the factory, one worker claims that they no more make 500gm of candy, it may be less or more. So on what basis did the worker claim this error??? So where do we draw a line to make a decision about the variation in the weight of candy bars? This decision/boundary is Statistically significant.

 

Level of confidence

As the name suggests a level of confidence: how confident are we in taking out decisions. LOC(Level of confidence) should be more than 95%. Less than 95% of confidence will not be accepted.

Level of significance(α)

The significance level, in the simplest of terms, is the threshold probability of incorrectly rejecting the null hypothesis when it is in fact true. This is also known as the type I error rate.

It is the probability of a type 1 error. It is also the size of the critical region.

Generally, strong control of α is desired and in tests, it is prefixed at very low levels like 0.05(5%) or 01(1%).

If H0 is not rejected at a significance level of 5%, then one can say that our null hypothesis is true with 95% assurance.

P-value

Let’s suppose we are conducting a hypothesis test at a significance level of 1%.

Where, H0: mean<X (we are just assuming a scenario of 1 tail test.)

We obtain our critical value (based on the type of test we are using) and find that our test statistic is greater than the critical value. So, we have to reject the null hypothesis here since it lies in the rejection region. Now if the null hypothesis is getting rejected at 1%, then for sure it will get rejected at the higher values of significance level, say 5% or 10%.

What if we take significance level lower than 1%, would we have to reject our hypothesis then also?

Yes, there might be a chance that the above scenario can happen, and here comes “p-value” in play.

the p-value is the smallest level of significance at which a null hypothesis can be rejected.

That’s why many tests nowadays give p-value and it is more preferred since it gives out more information than the critical value.

For right tailed test:

p-value = P[Test statistics >= observed value of the test statistic]

For left tailed test:

p-value = P[Test statistics <= observed value of the test statistic]

For two tailed test:

p-value = 2 * P[Test statistics >= |observed value of the test statistic|]

Decision making with p-value

We compare p-value to significance level(alpha) for taking a decision on Null Hypothesis.

If p-value is greater than alpha, we do not reject the null hypothesis.

If p-value is smaller than alpha, we reject the null hypothesis.

I hope this article clears some basic terms used in Hypothesis testing. But this is not the end. I will come up with Hypothesis testing techniques soon. Thank you so much for studying this blog. 🙂

About the Author

Ritika Singh – Data Scientist

I am a Data scientist by profession and a Blogger by passion. I have been working on machine learning projects for more than 2 years. Here you will find articles on “Machine Learning, Statistics, Deep Learning, NLP and Artificial Intelligence”.

confidence intervalconfidence levelHypothesis Testingone tailed testp-value statisticsstatisticstwo tailed test
G
Guest Blog

Free Courses

Generative AI 4.7

Generative AI - A Way of Life

Explore Generative AI for beginners: create text and images, use top AI tools, learn practical skills, and ethics.
Large Language Models 4.5

Getting Started with Large Language Models

Master Large Language Models (LLMs) with this course, offering clear guidance in NLP and model training made simple.
Prompt Engineering 4.6

Building LLM Applications using Prompt Engineering

This free course guides you on building LLM apps, mastering prompt engineering, and developing chatbots with enterprise data.
LlamaIndex 4.8

Improving Real World RAG Systems: Key Challenges & Practical Solutions

Explore practical solutions, advanced retrieval strategies, and agentic RAG systems to improve context, relevance, and accuracy in AI-driven applications.
RAG systems using LlamaIndex 4.7

Microsoft Excel: Formulas & Functions

Master MS Excel for data analysis with key formulas, functions, and LookUp tools in this comprehensive course.

Recommended Articles

Responses From Readers

Clear

vlad
vlad

Hi, Thanks for the article. Can you give examples from the text in R? vlad

123

Shahroz Khan
Shahroz Khan

Dear, What if P value is equal to alpha?? Which hypothesis will be accepted null or alterative?? Regards, Shahroz Khan

123

SheshNath Chaturvedi
SheshNath Chaturvedi

Systematically Explained. #A great thanks to you Mm.

123

Write for us

Write, captivate, and earn accolades and rewards for your work
  • Reach a Global Audience
  • Get Expert Feedback
  • Build Your Brand & Audience
  • Cash In on Your Knowledge
  • Join a Thriving Community
  • Level Up Your Data Science Game
imag
Congratulations, You Did It!
Well Done on Completing Your Learning Journey. Stay curious and keep exploring!
Understanding The Concept Of Hypothesis In Data Science!
Understanding The Concept Of Hypothesis In Data Science!
An Introduction to Hypothesis Testing
An Introduction to Hypothesis Testing

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