8.1.2 Basics of Hypothesis Testing - Significance Level, Type I and Type II Error

This paragraph introduces the concept of hypothesis testing, focusing on the significance level and the concept of Type 1 and Type 2 errors. It explains the goal of the video is to help viewers understand and identify these errors by the end. The speaker contextualizes hypothesis testing as a formalized procedure used across various fields and reviews the basic procedure, which includes stating a null and alternative hypothesis, computing a sample statistic, and determining its significance. The paragraph emphasizes the importance of graphing the sampling distribution and using it to assess whether the sample statistic is significantly high or low, which would lead to the rejection of the null hypothesis.

The second paragraph delves deeper into the process of hypothesis testing, explaining the conversion of a sample statistic into a test statistic, which can be a z-score, t-score, or chi-squared value depending on the context. It discusses two methods for determining if the sample statistic is significantly high or low: the critical value method and the p-value method. The paragraph also touches on the concept of the critical region and how extreme values of test statistics correspond to small probabilities, which could lead to the rejection of the null hypothesis. Finally, it stresses the importance of stating conclusions in non-technical terms, relating back to the original claim.

This paragraph explores the meaning of 'significantly high' or 'significantly low' in the context of hypothesis testing, quantifying these terms using probabilities and introducing the significance level (alpha). It explains that the significance level is the probability of making a Type 1 error, which is the mistake of rejecting a true null hypothesis. The speaker uses the example of a sample proportion to illustrate how one might decide to reject the null hypothesis based on an unlikely but still possible event occurring. The paragraph also introduces the concept of a Type 2 error, which is the mistake of failing to reject a false null hypothesis, represented by the probability beta.

The fourth paragraph uses a visual approach to understand hypothesis testing outcomes and the potential for Type 1 and Type 2 errors. It presents a table that organizes the possible states of reality (null hypothesis being true or false) against the evidence's suggestions (suggesting the null is false or not). The paragraph explains the correct decisions of rejecting a false null or not rejecting a true null and contrasts them with the incorrect decisions that lead to Type 1 and Type 2 errors. It also provides hints to help keep track of these errors and emphasizes stating conclusions in terms of the original claim rather than the null hypothesis.

In this paragraph, the concept of hypothesis testing is analogized to the legal system's 'innocent until proven guilty' principle. It explains how Type 1 and Type 2 errors relate to finding an innocent person guilty or failing to find a guilty person not guilty, respectively. The speaker emphasizes minimizing Type 1 errors in the legal system and discusses the implications of prioritizing one type of error over the other. The paragraph also provides an example of a medical procedure's effectiveness to illustrate how Type 1 and Type 2 errors might be described in a practical scenario.

The final paragraph provides a detailed example of Type 1 and Type 2 errors in the context of a medical procedure claimed to increase the likelihood of having a baby girl. It outlines the null and alternative hypotheses and describes the errors in terms of the original claim: a Type 1 error would be concluding the procedure works when it does not, while a Type 2 error would be concluding there is no effect when the procedure actually increases the likelihood. The paragraph reinforces the significance level's role in determining these errors and the importance of evidence in making such conclusions.