Type 1 and Type 2 Error Calculator

Here’s a comprehensive table summarizing all you need to know about Type 1 and Type 2 Errors:

Aspect	Type 1 Error (α)	Type 2 Error (β)
Definition	Rejecting a true null hypothesis	Failing to reject a false null hypothesis
Also Known As	False Positive	False Negative
Symbol	α (alpha)	β (beta)
Probability	P(Type 1 Error) = α	P(Type 2 Error) = β
Relationship to Hypothesis	H₀ is true, but rejected	H₀ is false, but not rejected
Significance Level	α is the significance level	Not directly related
Power of the Test	Not directly related	Power = 1 – β
Typical Values	Often set at 0.05 or 0.01	Varies, but aim for low β (high power)
Control Method	Set by researcher	Reduced by increasing sample size
Trade-off	Decreasing α increases β	Decreasing β increases α
In Medical Testing	False alarm (diagnosing a healthy patient as sick)	Missing a real effect (failing to diagnose a sick patient)
In Criminal Justice	Convicting an innocent person	Acquitting a guilty person
In Quality Control	Rejecting a good batch of products	Accepting a defective batch of products
Consequence	Wasted resources, false alarms	Missed opportunities, undetected effects
Relationship to Sample Size	Unaffected by sample size	Decreases as sample size increases
Calculation	Set by researcher before the study	1 – Power (calculated or simulated)
Visualization	Area in the tail(s) of null distribution	Area under the alternative distribution overlapping with non-rejection region
Effect on Confidence Interval	Narrower CI (higher confidence level)	Wider CI (lower confidence level)
Relationship to p-value	p-value < α leads to rejecting H₀	Not directly related to p-value
Minimizing Strategy	Increase significance level	Increase sample size, effect size, or α

Key points to remember:

1. Type 1 and Type 2 errors are inversely related; reducing one typically increases the other.
2. The significance level (α) is set by the researcher and directly relates to Type 1 error.
3. Power (1 – β) is the probability of correctly rejecting a false null hypothesis.
4. Increasing sample size generally reduces Type 2 error without affecting Type 1 error.
5. In practice, researchers often focus on controlling Type 1 error (α) and then try to maximize power (minimize β) within practical constraints.
6. The choice of α and acceptable β depends on the field of study and the consequences of each type of error.
7. Understanding both types of errors is crucial for interpreting research results and making informed decisions based on statistical analyses.
8. In many fields, there’s a convention to use α = 0.05, but this is not a hard rule and should be considered in the context of the specific research question.
9. The balance between Type 1 and Type 2 errors is a key consideration in experimental design and statistical power analysis.