How do you know when to reject the alternative hypothesis?
What Is a Type II Error?A type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one fails to reject a null hypothesis that is actually false.A type II error produces a false negative, also known as an error of omission. For example, a test for a disease may report a negative result when the patient is infected. This is a type II error because we accept the conclusion of the test as negative, even though it is incorrect. Show
A Type II error can be contrasted with a type I error is the rejection of a true null hypothesis, whereas a type II error describes the error that occurs when one fails to reject a null hypothesis that is actually false. The error rejects the alternative hypothesis, even though it does not occur due to chance. Key Takeaways
Understanding a Type II ErrorA type II error, also known as an error of the second kind or a beta error, confirms an idea that should have been rejected, such as, for instance, claiming that two observances are the same, despite them being different. A type II error does not reject the null hypothesis, even though the alternative hypothesis is the true state of nature. In other words, a false finding is accepted as true. A type II error can be reduced by making more stringent criteria for rejecting a null hypothesis (H0). For example, if an analyst is considering anything that falls within the +/- bounds of a 95% confidence interval as statistically insignificant (a negative result), then by decreasing that tolerance to +/- 90%, and subsequently narrowing the bounds, you will get fewer negative results, and thus reduce the chances of a false negative. Taking these steps, however, tends to increase the chances of encountering a type I error—a false-positive result. When conducting a hypothesis test, the probability or risk of making a type I error or type II error should be considered. The steps taken to reduce the chances of encountering a type II error tend to increase the probability of a type I error. Type I Errors vs. Type II ErrorsThe difference between a type II error and a type I error is that a type I error rejects the null hypothesis when it is true (i.e., a false positive). The probability of committing a type I error is equal to the level of significance that was set for the hypothesis test. Therefore, if the level of significance is 0.05, there is a 5% chance a type I error may occur. The probability of committing a type II error is equal to one minus the power of the test, also known as beta. The power of the test could be increased by increasing the sample size, which decreases the risk of committing a type II error. Some statistical literature will include overall significance level and type II error risk as part of the report's analysis. For example, a 2021 meta-analysis of exosome in the treatment of spinal cord injury recorded an overall significance level of 0.05 and a type II error risk of 0.1. Example of a Type II ErrorAssume a biotechnology company wants to compare how effective two of its drugs are for treating diabetes. The null hypothesis states the two medications are equally effective. A null hypothesis, H0,is the claim that the company hopes to reject using the one-tailed test. The alternative hypothesis, Ha, states the two drugs are not equally effective. The alternative hypothesis, Ha, is the state of nature that is supported by rejecting the null hypothesis. The biotech company implements a large clinical trial of 3,000 patients with diabetes to compare the treatments. The company randomly divides the 3,000 patients into two equally sized groups, giving one group one of the treatments and the other group the other treatment. It selects a significance level of 0.05, which indicates it is willing to accept a 5% chance it may reject the null hypothesis when it is true or a 5% chance of committing a type I error. Assume the beta is calculated to be 0.025, or 2.5%. Therefore, the probability of committing a type II error is 97.5%. If the two medications are not equal, the null hypothesis should be rejected. However, if the biotech company does not reject the null hypothesis when the drugs are not equally effective, a type II error occurs. What Is the Difference Between Type I and Type II Errors?A type I error occurs if a null hypothesis is rejected that is actually true in the population. This type of error is representative of a false positive. Alternatively, a type II error occurs if a null hypothesis is not rejected that is actually false in the population. This type of error is representative of a false negative. What Causes Type II Errors?A type II error is commonly caused if the statistical power of a test is too low. The highest the statistical power, the greater the chance of avoiding an error. It's often recommended that the statistical power should be set to at least 80% prior to conducting any testing. What Factors Influence the Magnitude of Risk for Type II Errors?As the sample size of the research increases, the magnitude of risk for type II errors should decrease. As the true population effect size increases, the type II error should also decrease. Last, the pre-set alpha level set by the research influences the magnitude of risk. As the alpha level set decreases, the risk of a type II error increases. How Can a Type II Error Be Minimized?It is not possible to fully prevent committing a Type II error; but, the risk can be minimized by increasing the sample size. However, doing so will also increase the risk of committing a Type I error instead. The Bottom LineIn statistics, a Type II error results in a false negative - meaning that there is a finding but it has been missed in the analysis (or that the null hypothesis is not rejected when it ought to have been). A Type II error can occur if there is not enough power in statistical tests, often resulting from sample sizes that are too small. Increasing the sample size can help reduce the chances of committing a Type II error. Type II errors can be contrasted with Type I errors, which are false positives. When should a hypothesis be rejected?If there is less than a 5% chance of a result as extreme as the sample result if the null hypothesis were true, then the null hypothesis is rejected. When this happens, the result is said to be statistically significant .
How do you know if you should reject the null hypothesis?Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go!
What does it mean to fail to reject the alternative hypothesis?However, if the data does not support the alternative hypothesis, this does not mean that the null hypothesis is true. All it means is that the null hypothesis has not been disproven—hence the term "failure to reject." A "failure to reject" a hypothesis should not be confused with acceptance.
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