- Blog Categories
- Software Development Projects and Ideas
- 12 Computer Science Project Ideas
- 28 Beginner Software Projects
- Top 10 Engineering Project Ideas
- Top 10 Easy Final Year Projects
- Top 10 Mini Projects for Engineers
- 25 Best Django Project Ideas
- Top 20 MERN Stack Project Ideas
- Top 12 Real Time Projects
- Top 6 Major CSE Projects
- 12 Robotics Projects for All Levels
- Java Programming Concepts
- Abstract Class in Java and Methods
- Constructor Overloading in Java
- StringBuffer vs StringBuilder
- Java Identifiers: Syntax & Examples
- Types of Variables in Java Explained
- Composition in Java: Examples
- Append in Java: Implementation
- Loose Coupling vs Tight Coupling
- Integrity Constraints in DBMS
- Different Types of Operators Explained
- Career and Interview Preparation in IT
- Top 14 IT Courses for Jobs
- Top 20 Highest Paying Languages
- 23 Top CS Interview Q&A
- Best IT Jobs without Coding
- Software Engineer Salary in India
- 44 Agile Methodology Interview Q&A
- 10 Software Engineering Challenges
- Top 15 Tech's Daily Life Impact
- 10 Best Backends for React
- Cloud Computing Reference Models
- Web Development and Security
- Find Installed NPM Version
- Install Specific NPM Package Version
- Make API Calls in Angular
- Install Bootstrap in Angular
- Use Axios in React: Guide
- StrictMode in React: Usage
- 75 Cyber Security Research Topics
- Top 7 Languages for Ethical Hacking
- Top 20 Docker Commands
- Advantages of OOP
- Data Science Projects and Applications
- 42 Python Project Ideas for Beginners
- 13 Data Science Project Ideas
- 13 Data Structure Project Ideas
- 12 Real-World Python Applications
- Python Banking Project
- Data Science Course Eligibility
- Association Rule Mining Overview
- Cluster Analysis in Data Mining
- Classification in Data Mining
- KDD Process in Data Mining
- Data Structures and Algorithms
- Binary Tree Types Explained
- Binary Search Algorithm
- Sorting in Data Structure
- Binary Tree in Data Structure
- Binary Tree vs Binary Search Tree
- Recursion in Data Structure
- Data Structure Search Methods: Explained
- Binary Tree Interview Q&A
- Linear vs Binary Search
- Priority Queue Overview
- Python Programming and Tools
- Top 30 Python Pattern Programs
- List vs Tuple
- Python Free Online Course
- Method Overriding in Python
- Top 21 Python Developer Skills
- Reverse a Number in Python
- Switch Case Functions in Python
- Info Retrieval System Overview
- Reverse a Number in Python
- Real-World Python Applications
- Data Science Careers and Comparisons
- Data Analyst Salary in India
- Data Scientist Salary in India
- Free Excel Certification Course
- Actuary Salary in India
- Data Analyst Interview Guide
- Pandas Interview Guide
- Tableau Filters Explained
- Data Mining Techniques Overview
- Data Analytics Lifecycle Phases
- Data Science Vs Analytics Comparison
- Artificial Intelligence and Machine Learning Projects
- Exciting IoT Project Ideas
- 16 Exciting AI Project Ideas
- 45+ Interesting ML Project Ideas
- Exciting Deep Learning Projects
- 12 Intriguing Linear Regression Projects
- 13 Neural Network Projects
- 5 Exciting Image Processing Projects
- Top 8 Thrilling AWS Projects
- 12 Engaging AI Projects in Python
- NLP Projects for Beginners
- Concepts and Algorithms in AIML
- Basic CNN Architecture Explained
- 6 Types of Regression Models
- Data Preprocessing Steps
- Bagging vs Boosting in ML
- Multinomial Naive Bayes Overview
- Gini Index for Decision Trees
- Bayesian Network Example
- Bayes Theorem Guide
- Top 10 Dimensionality Reduction Techniques
- Neural Network Step-by-Step Guide
- Technical Guides and Comparisons
- Make a Chatbot in Python
- Compute Square Roots in Python
- Permutation vs Combination
- Image Segmentation Techniques
- Generative AI vs Traditional AI
- AI vs Human Intelligence
- Random Forest vs Decision Tree
- Neural Network Overview
- Perceptron Learning Algorithm
- Selection Sort Algorithm
- Career and Practical Applications in AIML
- AI Salary in India Overview
- Biological Neural Network Basics
- Top 10 AI Challenges
- Production System in AI
- Top 8 Raspberry Pi Alternatives
- Top 8 Open Source Projects
- 14 Raspberry Pi Project Ideas
- 15 MATLAB Project Ideas
- Top 10 Python NLP Libraries
- Naive Bayes Explained
- Digital Marketing Projects and Strategies
- 10 Best Digital Marketing Projects
- 17 Fun Social Media Projects
- Top 6 SEO Project Ideas
- Digital Marketing Case Studies
- Coca-Cola Marketing Strategy
- Nestle Marketing Strategy Analysis
- Zomato Marketing Strategy
- Monetize Instagram Guide
- Become a Successful Instagram Influencer
- 8 Best Lead Generation Techniques
- Digital Marketing Careers and Salaries
- Digital Marketing Salary in India
- Top 10 Highest Paying Marketing Jobs
- Highest Paying Digital Marketing Jobs
- SEO Salary in India
- Brand Manager Salary in India
- Content Writer Salary Guide
- Digital Marketing Executive Roles
- Career in Digital Marketing Guide
- Future of Digital Marketing
- MBA in Digital Marketing Overview
- Digital Marketing Techniques and Channels
- 9 Types of Digital Marketing Channels
- Top 10 Benefits of Marketing Branding
- 100 Best YouTube Channel Ideas
- YouTube Earnings in India
- 7 Reasons to Study Digital Marketing
- Top 10 Digital Marketing Objectives
- 10 Best Digital Marketing Blogs
- Top 5 Industries Using Digital Marketing
- Growth of Digital Marketing in India
- Top Career Options in Marketing
- Interview Preparation and Skills
- 73 Google Analytics Interview Q&A
- 56 Social Media Marketing Q&A
- 78 Google AdWords Interview Q&A
- Top 133 SEO Interview Q&A
- 27+ Digital Marketing Q&A
- Digital Marketing Free Course
- Top 9 Skills for PPC Analysts
- Movies with Successful Social Media Campaigns
- Marketing Communication Steps
- Top 10 Reasons to Be an Affiliate Marketer
- Career Options and Paths
- Top 25 Highest Paying Jobs India
- Top 25 Highest Paying Jobs World
- Top 10 Highest Paid Commerce Job
- Career Options After 12th Arts
- Top 7 Commerce Courses Without Maths
- Top 7 Career Options After PCB
- Best Career Options for Commerce
- Career Options After 12th CS
- Top 10 Career Options After 10th
- 8 Best Career Options After BA
- Projects and Academic Pursuits
- 17 Exciting Final Year Projects
- Top 12 Commerce Project Topics
- Top 13 BCA Project Ideas
- Career Options After 12th Science
- Top 15 CS Jobs in India
- 12 Best Career Options After M.Com
- 9 Best Career Options After B.Sc
- 7 Best Career Options After BCA
- 22 Best Career Options After MCA
- 16 Top Career Options After CE
- Courses and Certifications
- 10 Best Job-Oriented Courses
- Best Online Computer Courses
- Top 15 Trending Online Courses
- Top 19 High Salary Certificate Courses
- 21 Best Programming Courses for Jobs
- What is SGPA? Convert to CGPA
- GPA to Percentage Calculator
- Highest Salary Engineering Stream
- 15 Top Career Options After Engineering
- 6 Top Career Options After BBA
- Job Market and Interview Preparation
- Why Should You Be Hired: 5 Answers
- Top 10 Future Career Options
- Top 15 Highest Paid IT Jobs India
- 5 Common Guesstimate Interview Q&A
- Average CEO Salary: Top Paid CEOs
- Career Options in Political Science
- Top 15 Highest Paying Non-IT Jobs
- Cover Letter Examples for Jobs
- Top 5 Highest Paying Freelance Jobs
- Top 10 Highest Paying Companies India
- Career Options and Paths After MBA
- 20 Best Careers After B.Com
- Career Options After MBA Marketing
- Top 14 Careers After MBA In HR
- Top 10 Highest Paying HR Jobs India
- How to Become an Investment Banker
- Career Options After MBA - High Paying
- Scope of MBA in Operations Management
- Best MBA for Working Professionals India
- MBA After BA - Is It Right For You?
- Best Online MBA Courses India
- MBA Project Ideas and Topics
- 11 Exciting MBA HR Project Ideas
- Top 15 MBA Project Ideas
- 18 Exciting MBA Marketing Projects
- MBA Project Ideas: Consumer Behavior
- What is Brand Management?
- What is Holistic Marketing?
- What is Green Marketing?
- Intro to Organizational Behavior Model
- Tech Skills Every MBA Should Learn
- Most Demanding Short Term Courses MBA
- MBA Salary, Resume, and Skills
- MBA Salary in India
- HR Salary in India
- Investment Banker Salary India
- MBA Resume Samples
- Sample SOP for MBA
- Sample SOP for Internship
- 7 Ways MBA Helps Your Career
- Must-have Skills in Sales Career
- 8 Skills MBA Helps You Improve
- Top 20+ SAP FICO Interview Q&A
- MBA Specializations and Comparative Guides
- Why MBA After B.Tech? 5 Reasons
- How to Answer 'Why MBA After Engineering?'
- Why MBA in Finance
- MBA After BSc: 10 Reasons
- Which MBA Specialization to choose?
- Top 10 MBA Specializations
- MBA vs Masters: Which to Choose?
- Benefits of MBA After CA
- 5 Steps to Management Consultant
- 37 Must-Read HR Interview Q&A
- Fundamentals and Theories of Management
- What is Management? Objectives & Functions
- Nature and Scope of Management
- Decision Making in Management
- Management Process: Definition & Functions
- Importance of Management
- What are Motivation Theories?
- Tools of Financial Statement Analysis
- Negotiation Skills: Definition & Benefits
- Career Development in HRM
- Top 20 Must-Have HRM Policies
- Project and Supply Chain Management
- Top 20 Project Management Case Studies
- 10 Innovative Supply Chain Projects
- Latest Management Project Topics
- 10 Project Management Project Ideas
- 6 Types of Supply Chain Models
- Top 10 Advantages of SCM
- Top 10 Supply Chain Books
- What is Project Description?
- Top 10 Project Management Companies
- Best Project Management Courses Online
- Salaries and Career Paths in Management
- Project Manager Salary in India
- Average Product Manager Salary India
- Supply Chain Management Salary India
- Salary After BBA in India
- PGDM Salary in India
- Top 7 Career Options in Management
- CSPO Certification Cost
- Why Choose Product Management?
- Product Management in Pharma
- Product Design in Operations Management
- Industry-Specific Management and Case Studies
- Amazon Business Case Study
- Service Delivery Manager Job
- Product Management Examples
- Product Management in Automobiles
- Product Management in Banking
- Sample SOP for Business Management
- Video Game Design Components
- Top 5 Business Courses India
- Free Management Online Course
- SCM Interview Q&A
- Fundamentals and Types of Law
- Acceptance in Contract Law
- Offer in Contract Law
- 9 Types of Evidence
- Types of Law in India
- Introduction to Contract Law
- Negotiable Instrument Act
- Corporate Tax Basics
- Intellectual Property Law
- Workmen Compensation Explained
- Lawyer vs Advocate Difference
- Law Education and Courses
- LLM Subjects & Syllabus
- Corporate Law Subjects
- LLM Course Duration
- Top 10 Online LLM Courses
- Online LLM Degree
- Step-by-Step Guide to Studying Law
- Top 5 Law Books to Read
- Why Legal Studies?
- Pursuing a Career in Law
- How to Become Lawyer in India
- Career Options and Salaries in Law
- Career Options in Law India
- Corporate Lawyer Salary India
- How To Become a Corporate Lawyer
- Career in Law: Starting, Salary
- Career Opportunities: Corporate Law
- Business Lawyer: Role & Salary Info
- Average Lawyer Salary India
- Top Career Options for Lawyers
- Types of Lawyers in India
- Steps to Become SC Lawyer in India
- Tutorials
- C Tutorials
- Recursion in C: Fibonacci Series
- Checking String Palindromes in C
- Prime Number Program in C
- Implementing Square Root in C
- Matrix Multiplication in C
- Understanding Double Data Type
- Factorial of a Number in C
- Structure of a C Program
- Building a Calculator Program in C
- Compiling C Programs on Linux
- Java Tutorials
- Handling String Input in Java
- Determining Even and Odd Numbers
- Prime Number Checker
- Sorting a String
- User-Defined Exceptions
- Understanding the Thread Life Cycle
- Swapping Two Numbers
- Using Final Classes
- Area of a Triangle
- Skills
- Software Engineering
- JavaScript
- Data Structure
- React.js
- Core Java
- Node.js
- Blockchain
- SQL
- Full stack development
- Devops
- NFT
- BigData
- Cyber Security
- Cloud Computing
- Database Design with MySQL
- Cryptocurrency
- Python
- Digital Marketings
- Advertising
- Influencer Marketing
- Search Engine Optimization
- Performance Marketing
- Search Engine Marketing
- Email Marketing
- Content Marketing
- Social Media Marketing
- Display Advertising
- Marketing Analytics
- Web Analytics
- Affiliate Marketing
- MBA
- MBA in Finance
- MBA in HR
- MBA in Marketing
- MBA in Business Analytics
- MBA in Operations Management
- MBA in International Business
- MBA in Information Technology
- MBA in Healthcare Management
- MBA In General Management
- MBA in Agriculture
- MBA in Supply Chain Management
- MBA in Entrepreneurship
- MBA in Project Management
- Management Program
- Consumer Behaviour
- Supply Chain Management
- Financial Analytics
- Introduction to Fintech
- Introduction to HR Analytics
- Fundamentals of Communication
- Art of Effective Communication
- Introduction to Research Methodology
- Mastering Sales Technique
- Business Communication
- Fundamentals of Journalism
- Economics Masterclass
- Free Courses
Power Analysis in Statistics: What is it & How to carry out?
Updated on 30 June, 2023
6.84K+ views
• 11 min read
Table of Contents
Hypothesis testing is a crucial aspect of any Statistical Analysis. However, there are a lot of things to be predefined so that the test we conduct can be as correct as possible. Here is where the concept of power comes into play and defines the heuristics of a Statistical Test.
By the end of this tutorial, you will know:
- Heuristics of Statistical Tests
- What is the Power of a test?
- What is the need for Power Analysis?
- How to carry out Power Analysis
Heuristics of Statistical Tests
Carrying out correct Statistical Tests upon several heuristics which need to be preset before conducting the test. It is highly important to set the right heuristics as these cannot be changed once the test is started. Let’s have a look at few of these.
1. Significance Level and Confidence Interval
Before starting any statistical test, a threshold of probability needs to be set. This threshold or significance level is called the Critical Value (alpha). The complete region under the probability curve beyond the alpha value is called the Critical Region.
The alpha value tells us how farther the sample data point (or the experimental point) must be from the null hypothesis(original mean point) before concluding that it is unusual enough to reject the null hypothesis. A common value of alpha that is used is 0.05 or 95% confidence interval.
2. P-Value
To evaluate whether the test results that we got are statistically significant or not, we compare the Critical Value (alpha) that we had set before the test with the P-Value of the test. The p-value is the probability of getting values as extreme or even more extreme as the value we are testing for.
Our learners also read: Learn Python Online for Free
3. Type 1 & Type 2 Errors
The Statistical Tests can never be 100% certain. There is always room for error and getting misled by the results. As discussed above, if we set an alpha value of 0.05, there is a confidence interval of 95%. Therefore, there is a 5% chance that the result you’ve got is incorrect and misleading. These incorrect results are what we call as errors. There are 2 types of error – Type 1 & Type 2.
The significance level value of 0.05 means that your statistical test will be 95% times correct. Which also means that there is a 5% chance of it being incorrect! That will be a case of you rejecting the null hypothesis when it was correct. This is an example of a Type 1 Error. And we can also say that alpha(α) is the probability of committing a Type 1 error.
It can also be a case when you conclude that the null hypothesis is true or accept it when it is false. Technically, we can never accept the null hypothesis. We can only fail to reject it. This is what we call a Type 2 Error. Similarly, the probability of you making a Type 2 error is given by Beta — β.
Read: Data Analysts: Top Skills & Tools to Master
upGrad’s Exclusive Data Science Webinar for you –
Explore our Popular Data Science Courses
What is the Power of a Statistical Test?
Power of a test is the probability of correctly rejecting the Null Hypothesis when it is false. Or in other words, Power is inversely proportional to the probability of making a type 2 error. Therefore, Power = 1-β. For example, if we set the power to be 80%, then we mean that 80% of our statistical tests are correct and not the bogus ones. Therefore, the higher the power value, the lesser is the probability of committing a type 2 error.
But why can the results be bogus? This is because we are dealing with random samples here. And sometimes the sample that is taken is too far from the mean of the distribution and hence gives unrealistic results, forcing us to make incorrect decisions. The whole aim of Power Analysis is to prevent us from making these incorrect decisions.
Are we P-Hacking?
Let’s take up an example where we have made a vaccine for COVID-19 and we are very much sure that the vaccine will have significant results. We proceed to conduct a Statistical test to see if our belief holds true statistically as well. So set the alpha as 0.05 and carry out a test using 100 samples.
After the test, we get a P-value as 0.06. We see that it is so close to our alpha but not less than it so that we can safely reject the null hypothesis. It gets tempting to see what happens if we increase the samples and redo the test.
So we add 50 more samples and see that the P-Value now comes as 0.045. Did we just prove our vaccine to be statistically significant? NO! We just P-hacked as we increased the number of samples after we got the first result. Learn more about What is P-Hacking & How To Avoid It?
Top Data Science Skills to Learn
What is Power Analysis?
As we saw in the above example, we found that the sample size was small and we increased it later. This is wrong and should never be done. The sample size value should be preset before starting the test itself. But what value of sample size is right for us?
Let’s consider an example where we carry out multiple tests using sample size as just 1. Therefore, when we sample 1 data point randomly from the population, it can be either around the mean which correctly represents our data, or it can be also a lot far away from the mean and does not represent the data well.
The issue arises when we conduct statistical tests using these far off data points. The P-value that we will get will be incorrect. We now conduct another series of tests taking 2 as the sample size. Now even if one value is far off from the data mean, the other value which is on the other side of the distribution will pull the average of them to centre, hence reducing the effect of that far off value. Therefore, with a sample size of 2, our results will more true with correct P-Values.
Power Analysis is the technique used to find out the right amount of sample size that is needed to conduct tests as well as possible. Higher the Power that we need more is the amount of sample size that will be required. So you might think that why not just take a large sample size because a large sample size means better and more trustable results. This is not right as collecting data is costly and knowledge of the sample size required is essential.
Power Analysis In Statistics: Why Is It Needed?
Researchers can prevent both type I and type II errors by using the power of statistical test. If a doctor told a man he was pregnant, that would be a type I error since it would accept the null hypothesis when it is untrue. Telling a pregnant lady she is not pregnant is a type II error since it is a false negative. Both mistakes can be very troublesome.
For small impact sizes and 45% for medium impact sizes, respectively, type II errors are reported to be likely in business research. The unintended consequences may be disastrous for a streaming service or a cosmetics business. Saying a product is harmless when it actually causes skin damage is a type I error in the context of the cosmetics industry.
A type II error implies that the formulation is detrimental when it is not. Thus, releasing a dangerous substance that causes skin rashes constitutes a kind I error. Saying the formulation is harmful when it isn’t is a type II error that wastes all the resources, time, and funds invested in the study and formulation.
How to carry out Power Analysis?
The power of a test depends on some factors. The first step to carry out a power analysis is to set a Power Value. Consider that you set a common power of 0.8, meaning that you want to have at least an 80% chance of correctly rejecting the null hypothesis. If we are validating the effect of COVID-19 vaccine on a set of people, we want to prove that the distribution of data points of vaccinated people is different from that of people that were given a placebo.
1. Amount of overlap
We need to consider the amount of overlap between the two distributions we are comparing. More the overlap, more difficult it will be for us to safely reject the null and hence we’ll need more sample size. However, if the overlap is very less, then we can quite easily safely reject the null. And we’d require quite less sample size. Overlap depends on the distance between the means of the two distributions and their standard deviations.
2. Effect size
Effect size is a way to combine the effects of the difference between the means and the standard deviations of the populations. Effect size (d) is calculated as The estimated difference between the means divided by Pooled estimated standard deviations. One of the simplest ways to calculate Pooled estimated Standard Deviations is Square root of the squared sum of Standard deviations divided by 2.
So once we have Power value, alpha value and the effect size, we can plug these values into a Statistics Power Calculator and get the sample size value. Such a Statistics Power Calculator is easily available on the internet.
Get data science certification from the World’s top Universities. Learn Executive PG Programs, Advanced Certificate Programs, or Masters Programs to fast-track your career.
Advantages of Power Analysis In Statistics
Statistical Prominence
Power analysis in statistics provides the apparent advantage of verifying that the research or study’s findings have statistical significance—that is, the conclusion reached is accurate and cannot be explained by chance.
Minimal Harm or Risk
Recognizing that a study’s findings are probably accurate reduces the potential of harm to users, particularly if the findings concern actual people. A large amount of power ensures that no type I error will be returned from the study’s findings.
Accountability For Error Inside a Sample Population
If a business intends to launch a new feature, it can do testing and reasonably be certain that the outcome is accurate. For businesses to gain more control over the outcome, power analysis considers populations and subgroups within the larger groups.
An expensive error could be made by the company, for example, if a section of the population is not included, the quantity of surveys is insufficient, or the variety of questions is too narrow.
Factors To Consider For Power Analysis In Statistics
Before beginning any kind of inquiry, it is necessary to evaluate the following three factors that power analysis considers:
Sampling Population
Typically, statistical power calculations of the sample size necessitate a normal Gaussian (bell-curve-shaped) population distribution. Consider subpopulation differences in intricate evaluations and designs like stratified random sampling. Otherwise, it is impossible to anticipate that populations will vary.
Sample Size
The required power analysis for sample size depends on the statistical analysis type. Only a “reasonable” sample size is needed for descriptive statistics. However, a higher sample size becomes essential for multiple regression or log-linear analysis.
Error-Rate Compensation
Yes, the sample size has no choice but to satisfy the criteria. Besides that, it also must be large enough to account for individuals eliminated from the sample by researchers. It happens when:
- The outcomes’ recording had mistakes
- The experiment wasn’t conducted with proper caution and attention
- The samples are extreme outliers.
Read our popular Data Science Articles
Before you go
We calculated the sample size by carrying out Power Analysis using Power, alpha and effect size. So if we got a sample size value of 7, it will mean that we need a sample size of 7 to have an 80% chance of correctly rejecting the Null Hypothesis. Having the right amount of domain expertise is also crucial to estimate the population means and their overlaps and the power required.
If you are curious to learn about data science, check out IIIT-B & upGrad’s PG Diploma in Data Science which is created for working professionals and offers 10+ case studies & projects, practical hands-on workshops, mentorship with industry experts, 1-on-1 with industry mentors, 400+ hours of learning and job assistance with top firms.
Frequently Asked Questions (FAQs)
1. What is Power Analysis?
The power of a test or Power analysis is the probability of correctly rejecting the Null Hypothesis when it is false. Or in other words, Power is inversely proportional to the probability of making a type 2 error. Therefore, Power = 1-β. For example, if we set the power to be 80%, then we mean that 80% of our statistical tests are correct and not bogus ones. Therefore, the higher the power value, the lesser is the probability of committing a type 2 error. Power Analysis is all about preventing the wrong decisions as we are handling various random samples and there is a high chance that their mean would give an unrealistic mean and lead us to make incorrect decisions.
2. What factors are considered while carrying our Power Analysis?
There are certain factors that affect the test for power analysis. The very first step is to set the power value. Suppose we have a power of 0.7 value which implies that you have a 70% chance of rejecting the null hypothesis. Below are the affecting factors of Power analysis. The amount of overlap is the overlap between the two distributions that are being compared. The overlap should be as small as possible since the amount of overlap is directly proportionate to the difficulty to calculate null. Effect size is a method to club the difference between the mean and the standard deviation of the populations. It is denoted by “d” and is calculated as the estimated difference between the means divided by Pooled estimated standard deviations. Since now we have the power value, alpha value(amount of overlap), and the effect size, we can easily carry out the Power Analysis.
3. What is P-Hacking?
P-Hacking or Data dredging is a method to misuse the data analysis techniques to find patterns in data that appear significant but are not. This method affects the study negatively as it gives false promises to provide significant data patterns which can, in turn, lead to a drastic increase in the number of false positives. P-hacking can not be prevented completely but there are some methods that can surely reduce it and help avoid the trap.