What are type 1 and type 2 errors?

# Type 1 and Type 2 Errors Explained - Differences and Examples

Understanding type 1 and type 2 errors is essential. Knowing what and how to manage them can help improve your testing and minimize future mistakes.

## Types of errors in statistics

In product and web testing, we generally categorize statistical errors into two main types—type 1 and type 2 errors. These are closely related to the ideas of hypothesis testing and significance levels.

Researchers often develop a null (H0) and an alternate hypothesis (H1) when conducting experiments or analyzing data. The null hypothesis usually represents the status quo or the baseline assumption, while the alternative hypothesis represents the claim or effect being investigated.

The goal is to determine whether the observed data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

With this in mind, let’s explore each type and the main differences between type 1 errors vs type 2 errors.

### Type 1 Error

A type 1 error occurs when you reject the null hypothesis when it is actually true. In other words, you conclude there is a notable effect or difference when there isn’t one—such as a problem or bug that doesn’t exist.

This error is also known as a “false positive” because you’re falsely detecting something insignificant. Say your testing flags an issue with a feature that’s working correctly—this is a type 1 error.

The problem has not resulted from a bug in your code or product but has come about purely by chance or through unrelated factors. This doesn’t mean your testing was completely incorrect, but there isn’t enough weighting to confidently say the flag is genuine and significant enough to make changes.

Type 1 errors can lead to unnecessary reworks, wasted resources, and delays in your development cycle. You might alter something or add new features that don’t benefit the application.

### Type 2 Error

A type 2 error, or “false negative,” happens when you fail to reject the null hypothesis when the alternative hypothesis is actually true. In this case, you’re failing to detect an effect or difference (like a problem or bug) that does exist.

It’s called a “false negative,” as you’re falsely concluding there’s no effect when there is one. For example, if your test suite gives the green light to a broken feature or one not functioning as intended, it’s a type 2 error.

Type 2 errors don’t mean you fully accept the null hypothesis—the testing only indicates whether to reject it. In fact, your testing might not have enough statistical power to detect an effect.

A type 2 error can result in you launching faulty products or features. This can massively harm your user experience and damage your brand’s reputation, ultimately impacting sales and revenue.

## Probability in error types

Understanding and managing type 1 and type 2 errors means understanding some math, specifically probability and statistics.

Let’s unpack the probabilities associated with each type of error and how they relate to statistical significance and power.

### Type 1 Error Probability

The probability of getting a type 1 error is represented by alpha (α).

In testing, researchers typically set a desired significance level (α) to control the risk of type 1 errors. This is the statistical probability of getting those results (p value). You get the p value by doing a t-test, comparing the means of two groups.

Common significance levels (α) are 0.05 (5%) or 0.01 (1%)—this means there’s a 5% or 1% chance of incorrectly rejecting the null hypothesis when it’s true.

If the p value is lower than α, it suggests your results are unlikely to have occurred by chance alone. Therefore, you can reject the null hypothesis and conclude that the alternative hypothesis is supported by your data.

However, the results are not statistically significant if the p value is higher than α. As they could have occurred by chance, you fail to reject the null hypothesis, and there isn’t enough evidence to support the alternative hypothesis.

You can set a lower significance level to reduce the probability of a type 1 error. For example, reducing the level from 0.05 to 0.01 effectively means you’re willing to accept a 1% chance of a type 1 error instead of 5%.

### Type 2 Error Probability

The probability of having a type 2 error is denoted by beta (β). It’s inversely related to the statistical power of the test—this is the extent to which a test can correctly detect a real effect when there is one.

Statistical power is calculated as 1 - β. For example, if your risk of committing a type 2 error is 20%, your power level is 80% (1.0 - 0.02 = 0.8). A higher power indicates a lower probability of a type 2 error, meaning you’re less likely to have a false negative. Levels of 80% or more are generally considered acceptable.

Several factors can influence statistical power, including the sample size, effect size, and the chosen significance level. Increasing the sample size and significance level increases the test's power, indirectly reducing the probability of a type 2 error.

### Balancing Type 1 and Type 2 Errors

There’s often a trade-off between type 1 and type 2 errors. For instance, lowering the significance level (a) reduces the probability of a type 1 error but increases the likelihood of a Type 2 error (and vice versa).

Researchers and product teams must carefully consider the relative consequences of each type of error in their specific context.

Take medical testing—a type 1 error (false positive) in this field might lead to unnecessary treatment, while a type 2 error (false negative) could result in a missed diagnosis.

It all depends on your product and context. If the cost of a false positive is high, you might want to set a lower significance level (to lower the probability of type 1 error). However, if the impact of missing a genuine issue is more severe (type 2 error), you might choose a higher level to increase the statistical power of your tests.

Knowing the probabilities associated with type 1 and type 2 errors helps teams make better decisions about their testing processes, balance each type's risks, and ensure their products meet proper quality standards.

## Type 1 error examples

To help you better understand type 1 errors or false positives in product software and web testing, here are some examples.

In each case, the Type 1 error could lead to unnecessary actions or investigations based on inaccurate or false positive results despite the absence of an actual issue or effect.

### Mistaken A/B test result

Your team runs an A/B test to see if a new feature improves user engagement metrics, such as time spent on the platform or click-through rates.

The results show a statistically significant difference between the control and experiment groups, leading you to conclude the new feature is successful and should be rolled out to all users.

However, after further investigation and analysis, you realize the observed difference was not due to the feature itself but an unrelated factor, such as a marketing campaign or a seasonal trend.

You committed a Type 1 error by incorrectly rejecting the null hypothesis (no difference between the groups) when the new feature had no real effect.

### Usability testing false positive

Imagine you’re testing that same new feature for usability. Your testing finds that people are struggling to use it—your team puts this down to a design flaw and decides to redesign the element.

However, after getting the same results, you realize that the users’ difficulty using the feature isn’t due to its design but rather their unfamiliarity with it.

After more exposure, they’re able to navigate the feature more easily. Your misattribution led to unnecessary design efforts and a prolonged launch.

This is a classic example of a Type 1 error, where the usability test incorrectly rejected the null hypothesis (the feature is usable).

### Inaccurate performance issue detection

Your team uses performance testing to spot your app’s bottlenecks, slowdowns, or other performance issues.

A routine test reports a performance issue with a specific component, such as slow response times or high resource utilization. You allocate resources and efforts to investigate and confront the problem.

However, after in-depth profiling, load testing, and analysis, you find the issue was a false positive, and the component is working normally.

This is another example of a Type 1 error: testing incorrectly flagged a non-existent performance problem, leading to pointless troubleshooting efforts and potential resource waste.

## Type 2 error examples

In these examples, the type 2 error resulted in missed opportunities for improvement, the sending out of faulty products or features, or the failure to tackle existing issues or problems.

### Missed bug detection

Your team has implemented a new feature in your web application, and you have designed test cases to catch each bug.

However, one of the tests fails to detect a critical bug, leading to the release of a faulty feature with unexpected behavior and functionality issues.

This is a type 2 error—your testing failed to reject the null hypothesis (no bug) when the alternative (bug present) was true.

### Overlooked performance issues

Your product relies on a third-party API for data retrieval, and you regularly conduct performance testing to ensure optimal response times.

However, during a particular testing cycle, your team didn’t identify a significant slowdown in the API response times. This results in performance issues and a poor user experience for your customers, with slow page loads or delayed data updates.

As your performance testing failed to spot an existing performance problem, this is a type 2 error.

### Undetected security vulnerability

Your security team carries out frequent penetration testing, code reviews, and security audits to highlight potential vulnerabilities in your web application.

However, a critical cross-site scripting (XSS) vulnerability goes undetected, enabling malicious actors to inject client-side scripts and potentially gain access to sensitive data or perform unauthorized actions. This puts your users’ data and security at risk.

It’s also another type 2 error, as your testing didn’t reject the null hypothesis (no vulnerability) when the alternative hypothesis (vulnerability present) was true.

## How to manage and minimize type 1 and 2 errors

Although it’s impossible to eliminate type 1 and type 2 errors, there are several strategies your product teams can apply to manage and minimize their risks.

Implementing these can improve the accuracy and reliability of your testing process, ultimately leading to you delivering better products and user experiences.

We’ve already discussed adjusting significance levels—this is one of the most straightforward strategies.

Suppose the consequences of getting a false positive (type 1 error) are more severe. In that case, you may wish to set a lower significance level to reduce the probability of rejecting a true null hypothesis.

On the other hand, if overlooking an actual effect (type 2 error) is more costly, you can increase the significance level to improve the statistical power of your tests.

### Increase sample size

Increasing the sample size of your tests can help minimize the probability of both type 1 and type 2 errors.

A larger sample size gives you more statistical power, making it easier to spot genuine effects and reducing the likelihood of false positives or negatives.

### Implement more thorough testing methodologies

Adopting more thorough and accurate testing methods, such as comprehensive test case design, code coverage analysis, and exploratory testing, can help minimize the risk of missed issues or bugs (type 2 errors).

Regularly reviewing and updating your testing suite to meet changing product requirements can also make it more effective.

### Use multiple testing techniques

Combining different testing techniques, including unit, integration, performance, and usability tests, can give you a more complete view of your product’s quality. This reduces the chances of overlooking important issues, which could later affect your bottom line.

### Continuously monitor and feedback

Continuous monitoring and feedback loops enable you to identify and deal with any issues missed during the initial testing phases.

This might include monitoring your production systems, gathering user feedback, and conducting post-release testing.

### Conduct root cause analysis

When errors are flagged, you must do a root cause analysis to find the underlying reasons for this false positive or negative.

This can help you refine your testing process, improve test case design, and prevent similar errors from occurring in the future.

### Foster a culture of quality

Promoting a culture of quality within your organization can help ensure that everyone is invested in minimizing errors and delivering high-quality products.

To achieve this, ask your company to offer more training, encourage collaboration, and foster an environment where team members feel empowered to raise concerns or suggest improvements.

## Using Amplitude to reduce errors

Encountering type 1 and type 2 errors can be disheartening for product teams. Here’s where Ampltide Experiment can help.

The A/B testing platform features help compensate for and correct the presence of type 1 and type 2 errors. By managing and minimizing their risk, you’re able to run more confident product experiments and tests.

Some of Amplitude’s main experimental features include its:

• Sample size calculator: This helps you determine the minimum sample size needed to detect significant effects.
• Experiment duration estimator: The platform’s estimator gives you an idea of how long your experiment needs to run to reach statistical significance.
• Bonferroni correction application: Amplitude uses the Bonferroni correction to adjust the finance level when testing multiple hypotheses.
• Minimum sample size threshold: The platform sets a minimum threshold that experiments must meet before declaring significance.

Use Amplitude to help you design more robust testing, ensure sufficient statistical power, control for multiple tests, and oversee your results. Get increased confidence in your experiment results and make more informed decisions about product changes and feature releases.