What are Type I and Type II Errors

Oops! at 2:47, the "power of the test" is represented by "1-beta".

So, what are type I and type II errors? Type I error is the rejection of a true null hypothesis also known as a false positive finding. Features are: Rejecting the true null hypothesis when it is true; represented by alpha called the size of the statistical test; the probability of rejecting the true null hypothesis; a false-positive scenario; classical statistics generally concentrates on a Type I error. Example of a Type I Error: When a person who has committed a crime is given a not guilty verdict based on the facts presented before the court of law. Not guilty is not the same as saying you are free. The former statement is due to insufficient evidence to convict the accused. The Judge in this case has committed a Type I error by letting a criminal off the hook! Type II error is failure to reject a false null hypothesis also known as a false negative finding. Features are: Failure to reject the null hypothesis when it is false; represented by 1-alpha called the power of the test; the probability of accepting the false hypothesis; a false-negative scenario. Examples of a Type II Error: When an innocent man is convicted of a crime when he is in fact innocent. The Judge in this case has committed a Type II error by sending an innocent man to jail! In Medicine, telling patients that Drug B is no more harmful than Drug A when it actually is can have serious consequences. Basic Steps to Hypothesis Testing: State the null and alternative hypotheses; Decide on the type of test (one-sided, two-sided); Set the sample size (preferably more than 30 observations); Decide on the level of alpha (statistical significance): alpha = 0.01 or 0.05 or 0.10; and interpret your findings. Causes: Type I Error: occurs when the outcome of the analysis lead to the rejection of a true null hypothesis. If the p-value is lower than 0.05, then the true null hypothesis is rejected in favour of the alternative hypothesis. Happens mostly when results are statistically significant. Type II Error: occurs when the outcome of the analysis lead to the failure to reject a false null hypothesis. If the p-value is higher than 0.05, then the false null hypothesis is accepted. Happens mostly when results are not statistically significant. Choosing alpha: Whether we reject or do not reject the null hypothesis depends critically on alpha, the level of significance or the probability of committing a Type I error—the probability of rejecting the true hypothesis. But, why is α commonly fixed at the 1, 5, or at the most 10 percent levels? As a matter of fact, there is nothing sacrosanct about these values; any other values will do just as well depending on the nature of your research. Features of the t-statistic: If the null hypothesis (H0) is rejected, the result of the test is statistically significant. On the other hand, if H0 is not rejected, then it is not statistically significant. A large t-statistic will be sufficient evidence against H0, ceteris paribus. In the language of significance tests, a statistic is said to be statistically significant if the value of the test statistic lies in the critical region. In this case the null hypothesis is rejected. By the same token, a test is said to be statistically insignificant if the value of the test statistic lies in the acceptance region. Features of the p-value: The probability value also known as the observed or exact level of significance or the exact probability of committing a Type I error. More technically, the p-value is defined as the lowest significance level at which a null hypothesis can be rejected. It gives statistical relevance to the t-statistic. What are the decision consequences? This is quite important for research involving medical and life sciences! Type I Error: Rejecting the true null hypothesis may have grave consequences. Type II Error: Failing to reject the null hypothesis when it is indeed false will have dire consequences, In my opinion, this is worse!. References used for this video tutorial are from: 1 Gujarati and Porter, 2009, Basic Econometrics, 5ed and 2. Wooldridge, JM, 2009, Introductory Econometrics: A Modern Approach, 4ed.

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