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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
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Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
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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
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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
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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
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What’s the Difference Between Type I and Type II Errors ?

Janvi Kumari
Janvi Kumari Last Updated : 25 Jul, 2024
6 min read

Introduction

Imagine you are conducting a study to determine whether a new drug effectively reduces blood pressure. You administer the drug to a group of patients and compare their results to a control group receiving a placebo. You analyze the data and conclude that the new drug significantly reduces blood pressure when, in reality, it does not. This incorrect rejection of the null hypothesis (that the drug has no effect) is a Type I error. On the other hand, suppose the drug actually does reduce blood pressure, but your study fails to detect this effect due to insufficient sample size or variability in the data. As a result, you conclude that the drug is ineffective, which is a failure to reject a false null hypothesis—a Type II error.

These scenarios highlight the importance of understanding Type I and Type II errors in statistical testing. Type I errors, also known as false positives, occur when we mistakenly reject a true null hypothesis. Type II errors, or false negatives, happen when we fail to reject a false null hypothesis. Much of statistical theory revolves around minimizing these errors, though completely eliminating both is statistically impossible. By understanding these concepts, we can make more informed decisions in various fields, from medical testing to quality control in manufacturing.

Type I and Type II Errors

Overview

  • Type I and Type II errors represent false positives and false negatives in hypothesis testing.
  • Hypothesis testing involves formulating null and alternative hypotheses, choosing a significance level, calculating test statistics, and making decisions based on critical values.
  • Type I errors occur when a true null hypothesis is mistakenly rejected, leading to unnecessary interventions.
  • Type II errors happen when a false null hypothesis is not rejected, causing missed diagnoses or overlooked effects.
  • Balancing Type I and Type II errors involves trade-offs in significance levels, sample sizes, and test power to minimize both errors effectively.

Table of contents

The Basics of Hypothesis Testing

Hypothesis testing is a method used to decide whether there is enough evidence to reject a null hypothesis (H₀) in favor of an alternative hypothesis (H₁). The process involves:

  1. Formulating Hypotheses
    • No effect or no difference: No effect or no difference.
    • Alternative Hypothesis (H₁): An effect or a difference exists.
  2. Choosing a Significance Level (α): The probability threshold for rejecting H₀, typically set at 0.05, 0.01, or 0.10.
  3. Calculating the Test Statistic: A value derived from sample data used to compare against a critical value.
  4. Making a Decision: If the test statistic exceeds the crucial value, reject H₀; otherwise, do not reject H₀.
Hypothesis Testing

Also read: End-to-End Statistics for Data Science

Type 1 Error( False Positive)

A Type I error occurs when an experiment’s null hypothesis(H0) is true but mistakenly rejected (the Graph is mentioned below).

This error represents identifying something that is not actually present, similar to a false positive. This can be explained in simple terms with an example: In a medical test for a disease, a Type I error would mean the test indicates a patient has the disease when they do not, essentially raising a false alarm. In this case, the null hypothesis(H0) would state: The patient does not have disease.

The likelihood of committing a Type I error is called the significance level or rate level. It’s denoted by the Greek letter α (alpha) and is known as the alpha level. Typically, this chance or probability is set at 0.05 or 5%. This way, researchers are usually inclined to accept a 5% chance of incorrectly rejecting the null hypothesis when it is sincerely actual.

Type I errors can lead to unnecessary treatments or interventions, causing stress and potential harm to individuals.

Let’s understand this with Graph:

  1. Null Hypothesis Distribution: The bell curve shows the range of possible outcomes if the null hypothesis is true. This means the results are due to random chance without any actual effect or difference.
  2. Type I Error Rate: The shaded area under the curve’s tail represents the significance level, α. It is the probability of rejecting the null hypothesis when it is actually true. Which results in a Type I error (false positive).
Type I

Type 2 Error ( False Negative)

A Type II error happens when a valid alternative hypothesis goes unrecognized. In simpler terms, it’s like failing to spot a bear that’s actually there, thus not raising an alarm when one is needed. In this scenario, the null hypothesis (H0) still states, “There is no bear.” The investigator commits a Type II error if a bear is present but undetected.

The key difficulty isn’t always whether the disease exists but whether it is effectively diagnosed. The error can arise in two ways: either by failing to discover the disease when it’s present or by claiming to discover the disease when it is not present.

The probability of Type II error is denoted by the Greek letter β (beta). This value is related to a test’s statistical power, which is calculated as 1 minus β (1−β).

Type II errors can result in missed diagnoses or overlooked effects, leading to inadequate treatment or interventions.

Let’s understand this with Graph:

  1. Alternative Hypothesis Distribution: The bell curve represents the range of possible outcomes if the alternative hypothesis is true. This means there is an actual effect or difference, contrary to the null hypothesis.
  2. Type II Error Rate (β): The shaded area under the left tail of the distribution represents the probability of a Type II error.
  3. Statistical Power (1 – β): The unshaded area under the curve to the right of the shaded area represents the test’s statistical power. Statistical power is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. Higher power means a lower chance of making a Type II error.
Type II

Also read: Learn all About Hypothesis Testing!

Comparison of Type I and Type II Errors

Here is the detailed comparison:

AspectType I ErrorType II Error
Definition and TerminologyRejecting a true null hypothesis (false positive)Accepting a false null hypothesis (false negative)
Symbolic Representationα (alpha)β (beta)
Probability and SignificanceEqual to the level of significance set for the testCalculated as 1 minus the power of the test (1 – power)
Error Reduction StrategiesDecrease the level of significance (increases Type II errors)Increase the level of significance (raises Type I errors)
Causal FactorsChance or luckSmaller sample sizes or less powerful statistical tests
Analogies“False hit” in a detection system“Miss” in a detection system
Hypothesis AssociationIncorrectly rejecting the null hypothesisFailing to reject a false null hypothesis
Occurrence ConditionsOccurs when acceptance levels are too lenientOccurs when acceptance criteria are overly stringent
ImplicationsPrioritized in fields where avoiding false positives is crucial (e.g., clinical testing)Prioritized in fields where avoiding false negatives is crucial (e.g., screening for severe diseases)

Also read: Hypothesis Testing Made Easy for Data Science Beginners

Trade-off Between Type I and Type II Errors

There is mostly a trade-off among Type I and Type II errors. Reducing the likelihood of one type of error generally increases the opportunity for the opposite.

  1. Significance Level (α): Lowering α reduces the chance of a Type I error but increases the risk of a Type II error. Increasing α has the opposite effect.
  2. Sample Size: Increasing the sample size can reduce both Type I and Type II errors, as larger samples provide more accurate estimates.
  3. Test Power: Enhancing the test’s power by increasing the sample size or using more sensitive tests can reduce the probability of Type II errors.

Conclusion

Type I and Type II errors are fundamental ideas in statistics and research techniques. By knowing the difference between these errors and their implications, we can interpret research findings better, conduct more powerful research, and make more informed decisions in diverse fields. Remember, the goal isn’t to eliminate errors (which is impossible) but to manage them successfully based on the particular context and potential outcomes.

Frequently Asked Questions

Q1. Can you completely avoid both Type I and Type II errors?

Ans. It’s challenging to eliminate both types of errors because reducing one often increases the other. However, by increasing the sample size and carefully designing the study, researchers can decrease both errors to applicable levels.

Q2. What are some common misconceptions about Type I and Type II errors?

Ans. Here are the common misconceptions about Type I and Type II errors:
Misconception: A lower α always means a better test.
Reality: While a lower α reduces Type I errors, it can increase Type II errors, leading to missed detections of true effects.
Misconception: Large sample sizes eliminate the need to worry about these errors.
Reality: Large sample sizes reduce errors but do not eliminate them. Good study design is still essential.
Misconception: A significant result (p-value < α) means the null hypothesis is false.
Reality: A significant result suggests evidence against H₀, but it does not prove H₀ is false. Other factors like study design and context must be considered.

Q3. How can I increase the power of my statistical test?

Ans. Increasing the power of your test makes it more likely to detect a true effect. You can do this by:
A. Increasing your sample size.
B. Using more precise measurements.
C. Reducing variability in your data.
D. Increasing the effect size, if possible.

Q4. What role do pilot studies play in managing these errors?

Ans. Pilot studies help you estimate the parameters needed to design a larger, more definitive study. They provide initial data on effect sizes and variability, which inform your sample size calculations and help balance Type I and Type II errors in the main study.

Janvi Kumari
Janvi Kumari

Hi, I am Janvi, a passionate data science enthusiast currently working at Analytics Vidhya. My journey into the world of data began with a deep curiosity about how we can extract meaningful insights from complex datasets.

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