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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
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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
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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
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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

Introduction to Power Analysis and Statistical Power

V
Vidhi Last Updated : 09 Apr, 2024
6 min read

How much data is sufficient for statistical significance? What’s the ideal sample size? Often, it is not entirely feasible to perform the statistical experiment multiple times to ensure enough power. At the same time, our machine learning models might not be statistically conclusive if we do not have an adequate sample size. This is where power analysis steps in. It estimates the required sample size to gauge study effects at the desired significance level, effect size, and statistical power. In this article, we will explore the importance and uses of power analysis and sample size.

This article was published as a part of the Data Science Blogathon.

Table of contents

What is Statistical Power?

Let’s first discuss the statistical power in detail.

Statistical power in a hypothesis test signifies the probability of detecting an effect when a true effect exists, providing confidence in study results. It has an inverse relationship with type 2 error whic is the occurrence of a False Negative, where a false null hypothesis isn’t rejected.

Note that type 2 error is False Negative where we fail to reject the false null hypotheses.

What is Null Hypothesis?

At this point, it is important to understand what is the Null Hypothesis?

It is a statistical hypothesis test that assumes an outcome. For example, the null hypothesis in the KS statistic implies that the two populations belong to similar distribution.

power analysis hypothesis testing
Source: Wik

It is important to note from the above illustration that:

  • Higher test power corresponds to a lower type 2 error (β).
  • Lower statistical power in an experiment can lead to unreliable conclusions, necessitating a minimum power threshold, typically 80% or more.
  • A power of 80% indicates an 80% chance of detecting an existing effect, with a 20% chance of a Type 2 error.

What is Power Analysis?

Power analysis, also known as statistical power analysis, is used in statistics to determine the statistical power of a hypothesis test. It involves assessing the likelihood of detecting a relationship between variables, given a specific sample size, significance level, effect size, and statistical test.

Importance of Power Analysis

In hypothesis testing, researchers formulate null (H0) and alternative (H1) hypotheses to investigate relationships or differences between variables within a population. The statistical power of a test quantifies its ability to correctly reject the null hypothesis when the alternative hypothesis is true, essentially measuring a test’s capacity to detect genuine effects.

Power analysis precedes data collection and assists researchers in determining the optimal sample size required to achieve their desired level of statistical power. It helps in: 

  • Estimating the likelihood of obtaining statistically significant results.
  • Taking into account factors such as effect size.
  • Significance level (often denoted as α), and the desired power level (usually represented as 1-β, with β indicating the probability of a Type II error).

Why Power Analysis Matters?

  • Informs study design: Power analysis guides decisions about study design, including the appropriate sample size and choice of statistical tests.
  • Reduces Type II errors: A higher statistical power lowers the risk of failing to detect genuine effects, ensuring more reliable and meaningful results.
  • Cross-disciplinary utility: Power analysis is widely applicable in various research fields, from psychology and medicine to social sciences and engineering.
  • Resource allocation: Researchers can efficiently allocate resources by optimizing study designs through power analysis.
  • Enhanced effect detection: Increasing statistical power boosts the likelihood of uncovering significant relationships or effects within the collected data.

Power analysis, therefore, empowers researchers to conduct more robust studies and increase the chances of obtaining valuable insights.

Three Considerations for Power Analysis

Simple Sampling Population

The assumption used in most general sample size computations is a normal, bell-shaped (Gaussian) population distribution. But changes among subpopulations must be taken into account for more intricate investigations and designs, including stratified random sampling. Inaccurate estimates of demographic characteristics may result from neglecting to take these variabilities into consideration.

Appropriate Sample Size

Depending on the kind of statistical analysis being done, a certain sample size may be needed. While more sophisticated methods like multiple regression, ANOVA, or log-linear analysis frequently require a larger sample, descriptive statistics could be sufficient with a “reasonable” sample size. Additionally, a substantially larger sample size may be necessary to provide statistical power if comparison analysis among sub-groups of the testing groups is needed.

Compensation for error rate

Apart from fulfilling the fundamental prerequisites for sample size, investigators must guarantee that the sample size is adequate to include participants who might need to be excluded from the study. This could be the result of inadequate experiments, outliers, or inaccurate outcome recording. Many researchers take this worry into account when calculating sample sizes by adding a 25 percent buffer to account for possible exclusions.

Variables in Power Analysis

Let’s delve into the broader context of power analysis, which revolves around four interconnected variables:

  • Effect Size: The magnitude of the observed effect directly influences the degree of random error in the analysis. Larger effects tend to yield more accurate results.
  • Sample Size: Increasing the sample size enhances the ability to detect smaller effects, as it reduces the impact of random variability.
  • Level of Significance (α): The chosen significance level determines the threshold for statistical significance, often set at 0.05 or 5%.
  • Statistical Power: Statistical power (often denoted as 1-β) represents the likelihood of correctly identifying a true effect when it exists.

These variables are intricately linked, meaning that alterations in one variable can ripple through and affect the others. Understanding their relationships is essential for effective power analysis.

Also Read: Explore our Exclusive Course on Statistics & Exploratory Data Analysis.

Relation Between Variables and Sample Size

Power analysis involves estimating one of the four variables while having values for the other three. It is particularly useful for determining the minimum sample size required for an experiment.

As we increase the sample size, our ability to detect even small effects improves. However, this comes at the cost of conducting more statistical experiments. Eventually, there is a point of diminishing returns, where adding more data ceases to increase statistical power significantly.

It’s important to note that, in some cases, our sample may not capture an existing effect in the population. This discrepancy can often be attributed to sampling error, where the sample is not truly representative of the entire population.

Validating Experiment using Power Analysis

Power Analysis is also used to check and validate the results and findings from the experiment. For example, if we specify the effect size, sample size, and significance level, we can calculate the power of an experiment to check whether type 2 error probability is within an acceptable range.

As per documentation, we can solve any one of the 4 parameters in an independent 2 sample T-test:

power analysis t-test
Source: Author

We can also use plot power curves to check how varying the effect size and different sample size changes the power of the experiment at a given significance level.

power analysis graph
Source: Author

Conclusion

Understanding power analysis and sample size empowers data professionals to make informed decisions. They help strike a balance between collecting enough data to detect meaningful effects and avoiding unnecessary data collection. By grasping the interplay between variables, effect size, sample size, significance level, and statistical power, we navigate the complexities of data science more effectively.

For those seeking to delve deeper into statistics, here’s our tutorial on valuable resources and hands-on experiences to enhance your statistical expertise:

Frequently Asked Questions

Q1. What are the methods of power analysis?

A. Common methods of power analysis include the a priori, post hoc, and sensitivity analysis. A priori power analysis involves determining the sample size needed before conducting a study. Post hoc power analysis assesses the statistical power after data collection. Sensitivity analysis examines how varying assumptions affect the power of a study.

Q2. What is the principle of power analysis?

A. The principle of power analysis is to determine the statistical power of a study, which is the probability of detecting a true effect when it exists. It involves assessing factors such as sample size, effect size, and significance level to ensure that a study has a high likelihood of detecting real differences or effects.

Q3. What does a power analysis of 80% mean?

A. A power analysis of 80% means that the study has an 80% probability of detecting a true effect if it exists. In other words, there is an 80% chance that the study will correctly identify a significant difference or relationship between variables if one truly exists.

Q4. What is power analysis in SPSS?

A. In SPSS (Statistical Package for the Social Sciences), power analysis is a feature used to calculate the statistical power of a study. It allows researchers to estimate the required sample size for achieving a desired level of power, given specific parameters such as effect size, significance level, and desired power.

V
Vidhi

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