Hypothesis testing (ALL YOU NEED TO KNOW!)

The video begins with an introduction to the concept of hypothesis testing in statistical inference by Justin Zeltser. The presenter outlines the structure of the video, which includes an intuitive look at hypothesis testing without delving into numbers initially. The aim is to provide a comprehensive understanding of the topic, starting with the basics and moving through various subtopics like the null hypothesis, alternate hypothesis, level of significance, test statistic, and p-value. The presenter also promises to cover confidence intervals, significance, power, and sample size, suggesting that these concepts are interconnected and crucial for a full grasp of hypothesis testing.

This paragraph delves into the intuition behind hypothesis testing using a coin bias example. The presenter explains the concept of a fair coin and how hypothesis testing can help determine if a coin is biased towards showing more tails than heads. The idea of a sample, critical value, and rejection region are introduced to illustrate the process of hypothesis testing. The paragraph emphasizes the importance of assessing how extreme a sample is in relation to the null hypothesis and deciding whether the evidence is sufficient to reject the assumption of fairness.

The presenter discusses the null hypothesis and the alternate hypothesis in the context of hypothesis testing. Using the example of surgical treatments for proximal humerus fractures, the video explains how to set up these hypotheses to test for a difference in outcomes between operative treatment and physiotherapy. The concept of level of significance (alpha) is introduced, highlighting its role in determining the likelihood of rejecting a true null hypothesis, which is a type 1 error.

The paragraph explains the concept of a test statistic in hypothesis testing, which is used to determine how extreme a sample is relative to the null hypothesis. The presenter uses the central limit theorem to justify the normal distribution of the test statistic, even when dealing with proportions from binomial distributions. The standard error of the test statistic is calculated, and the concept of critical values is introduced, which help in determining the rejection region for the hypothesis test.

The presenter applies the concepts of hypothesis testing to an example involving surgical and non-surgical treatments for ankle fractures in children. The video demonstrates how to calculate the test statistic and determine its position relative to the critical value, which helps in deciding whether to reject the null hypothesis. The significance of the chosen level of significance and its impact on the decision to reject or fail to reject the null hypothesis is emphasized.

This paragraph explores the concept of p-values in hypothesis testing. The p-value is defined as the probability of obtaining a test statistic as extreme or more extreme than the one calculated from the sample, assuming the null hypothesis is true. The relationship between p-values, the level of significance (alpha), and the decision to reject the null hypothesis is discussed. The paragraph also clarifies the difference between proving and inferring in statistical analysis.

The presenter introduces confidence intervals as a method to estimate population parameters based on sample statistics. The paragraph explains how to calculate the standard error of a sample statistic and use it to construct a confidence interval. The video illustrates how confidence intervals provide a range within which the true population parameter is likely to fall, with a certain level of confidence.

This paragraph compares hypothesis testing and confidence intervals as tools for statistical inference. The presenter discusses how confidence intervals can provide a more nuanced understanding of the population parameter by considering the sample's perspective, unlike hypothesis testing, which focuses on the null hypothesis. The video also touches on the concept of significant treatment difference and how confidence intervals can be used to assess whether a certain improvement threshold has been met.

The video discusses the concepts of power and sample size in the context of hypothesis testing. Power is defined as the probability of correctly rejecting a false null hypothesis, while sample size affects the precision of the estimates and the power of the test. The presenter explains how increasing the sample size or the effect size can increase the power of the test to detect a true effect. The paragraph also introduces the idea of type 1 and type 2 errors in relation to power and sample size.

The presenter provides an example to calculate the power of a hypothesis test to detect a 10% improvement in the operative cohort for ankle fractures in children. The video demonstrates the process of calculating the variances for the null and alternative hypotheses and using these to determine the power of the test. The example illustrates how the power of a test can be influenced by the specified difference and the sample size.

The final paragraph focuses on calculating the required sample size to achieve a specific power in a hypothesis test. The presenter outlines the steps to determine the sample size needed to provide a power of 90% for detecting a 10% improvement in the operative cohort. The video concludes with the algebraic process of solving for the sample size, emphasizing the importance of rounding up to ensure adequate power in the test.