Hypothesis Testing Explained with Simple Animations

Let's explore how scientists test whether a new medicine is effective.We start by dividing patients into two groups: one receiving the new medicine, and one receiving a placebo.In hypothesis testing, we start with two competing claims. The null hypothesis represents the status quo - that the medicine has no effect.The alternative hypothesis represents our new claim - that the medicine is effective.To test these hypotheses, we need to collect data. We start by assuming the null hypothesis is true.We collect data from multiple trials, looking for evidence against the null hypothesis.Remember, we need strong evidence against the null hypothesis before we can reject it. This is the foundation of hypothesis testing.In the next section, we'll learn exactly how to measure this evidence using p-values.To understand p-values, let's look at a standard normal distribution curve.The p-value represents how unlikely our observed results would be if the null hypothesis were true.We typically use a significance level of 5 percent, with 2.5 percent in each tail for a two-sided test.Let's look at a practical example. Suppose we flip a coin 8 times and get 7 heads.If the coin is fair, the probability of getting 7 or more heads out of 8 flips is only 0.035, or 3.5 percent.Since our p-value of 0.035 is less than our significance level of 0.05, this result falls in the critical region.The p-value represents the area beyond our observed value in the tail of the distribution.This small p-value suggests strong evidence against the null hypothesis of a fair coin.Now that we understand p-values, let's walk through the decision-making process.After calculating our p-value, we compare it to our significance level, typically 0.05.When making our decision, we need to be aware of two types of errors.Type I error occurs when we reject a true null hypothesis. This happens with probability alpha, our significance level.Type II error occurs when we fail to reject a false null hypothesis. This is represented by the beta region under the alternative distribution.Let's apply this to a practical example testing a new drug's effectiveness.We start with our hypotheses: the null hypothesis assumes no effect, while the alternative suggests a positive effect.After collecting data from 100 patients, we find a sample mean of 2.1 and calculate a p-value of 0.023.Since our p-value is less than 0.05, we reject the null hypothesis and conclude the drug has a significant positive effect.Let's review the key points about making decisions in hypothesis testing.Thanks for learning about hypothesis testing with Spark.E!