I lightly rewrite this already outstanding /r/eli5 comment, to simplify it further. I changed "New Yorker to "Utahn" as the latter's shorter. Show
Suppose you want to show that, say, Texans eat more than Utahns do. What you're really trying to prove is that Texans do not eat the same or less amount as Utahns do. This statement ("Texans and Utahns eat the same amount") is something called your "null hypothesis". Hypothesis testing has the goal of disproving the null hypothesis to prove what you're trying to show. The idea of statistical testing is to say "well, assuming that Texans and Utahns did eat the same amount, how likely would we get the data we did? The chance of getting the data you got if, in fact, they did eat the same amount is called a p-value. For instance, if we say that p = 0.05, we mean that if Texans and Utahns ate the same amount, there'd be a 1/20 chance to observe the kinds of results we did observe. The lower the p-value, the less likely your null hypothesis is true, and the more confidence you have that, in fact, Texans do eat more. Significance is the lowest p-value you'll accept as "strong enough" evidence. Lower significance thresholds decrease your chances of a false positive (i.e., finding that Texans eat more when in fact they don't), but increase your chances of a false negative (concluding that you don't know that Texans eat more, when in fact they do). Usually 5% is the weakest significance anyone takes seriously, but for situations where there's extreme cost to a false positive, you may choose a much lower number like 0.1%. In the common setup, you perform a test involving a test statistic, say $T$, and obtain a p-value, say $a$. Given that you have observed a value $t$ of the test statistic, the relation between $T$ and $a$ often is something like $$ a = P(T > t\ |\ H_0) \quad \text{or} \quad a = P(|T| > t\ |\ H_0) \quad \text{or} \quad a = P(T < t\ |\ H_0), $$ where $H_0$ is the null. The way of defining $a$ depends on the meaning of your statistic $T$, as it represents the probability of observing $T = t$ or worse given that the null hypothesis is true. It depends of what you judge to be a bad value of $T$ (evidence against $H_0$). In your case, $T$ could be the difference in drug effect (bigger is better), i.e. $T = E_B - E_A$ and your p-value could then be $a = P(T > t)$. Observing a big value of $T$ gives more evidence in favor of the alternative hypothesis, that is against $H_0$. That being said, if $a$ is the probability of observing what you have observed (or worse) during the experiment, obtaining a small value of $a$ means that what you have observed is unlikely to happen if $H_0$ is true, and so there is not much evidence for $H_0$. Thus, you usually reject $H_0$ in this case. The role of $a$ is to quantify how unlikely it is to observe $T=t$. Now fix $t$ to be the value of the test statistic computed on the original experiement and say it corresponds to a p-value of $a=0.01$. Assuming that $H_0$ is indeed true, what would happen if you were to repeat this experiment over and over again? If $a$ is the probability of observing $T>t$, then this means you would indeed observe $T>t$ on approximately $0.01\times 100 = 1\%$ of you experiments. So even if $H_0$ is true, there is still a slight chance that you observe a small p-value. This "slight chance" is exactly what you specify as your significance level: you specify what it means for a p-value to be small (less than $5\%$ for example). All this to say, it is intuitive to think of the significance level $\alpha$ as follows : if $H_0$ was true and you were to repeat the experiment many times, you would expect to (wrongly) reject the null hypothesis $(\alpha\times 100)\%$ of the times. If you want to understand why hypothesis testing works, you should first have an idea about the significance level and the reject region. We assume you already know what a hypothesis is, so let’s jump right into the action. What Is the Significance Level?First, we must define the term significance level. Normally, we aim to reject the null if it is false. However, as with any test, there is a small chance that we could get it wrong and reject a null hypothesis that is true.  How Is the Significance Level Denoted?The significance level is denoted by α and is the probability of rejecting the null hypothesis, if it is true. So, the probability of making this error. Typical values for α are 0.01, 0.05 and 0.1. It is a value that we select based on the certainty we need. In most cases, the choice of α is determined by the context we are operating in, but 0.05 is the most commonly used value. A Case in PointSay, we need to test if a machine is working properly. We would expect the test to make little or no mistakes. As we want to be very precise, we should pick a low significance level such as 0.01. The famous Coca Cola glass bottle is 12 ounces. If the machine pours 12.1 ounces, some of the liquid would be spilled, and the label would be damaged as well. So, in certain situations, we need to be as accurate as possible. Higher Degree of ErrorHowever, if we are analyzing humans or companies, we would expect more random or at least uncertain behavior. Hence, a higher degree of error. For instance, if we want to predict how much Coca Cola its consumers drink on average, the difference between 12 ounces and 12.1 ounces will not be that crucial. So, we can choose a higher significance level like 0.05 or 0.1. Hypothesis Testing: Performing a Z-TestNow that we have an idea about the significance level, let’s get to the mechanics of hypothesis testing. Imagine you are consulting a university and want to carry out an analysis on how students are performing on average. The university dean believes that on average students have a GPA of 70%. Being the data-driven researcher that you are, you can’t simply agree with his opinion, so you start testing. The null hypothesis is: The population mean grade is 70%. This is a hypothesized value. The alternative hypothesis is: The population mean grade is not 70%. You can see how both of them are denoted, below. Visualizing the GradesAssuming that the population of grades is normally distributed, all grades received by students should look in the following way. That is the true population mean. Performing a Z-testNow, a test we would normally perform is the Z-test. The formula is: Z equals the sample mean, minus the hypothesized mean, divided by the standard error. The idea is the following. We are standardizing or scaling the sample mean we got. If the sample mean is close enough to the hypothesized mean, then Z will be close to 0. Otherwise, it will be far away from it. Naturally, if the sample mean is exactly equal to the hypothesized mean, Z will be 0. In all these cases, we would accept the null hypothesis. What Is the Rejection Region?The question here is the following: How big should Z be for us to reject the null hypothesis? Well, there is a cut-off line. Since we are conducting a two-sided or a two-tailed test, there are two cut-off lines, one on each side. When we calculate Z, we will get a value. If this value falls into the middle part, then we cannot reject the null. If it falls outside, in the shaded region, then we reject the null hypothesis. That is why the shaded part is called: rejection region, as you can see below. What Does the Rejection Region Depend on?The area that is cut-off actually depends on the significance level. Say the level of significance, α, is 0.05. Then we have α divided by 2, or 0.025 on the left side and 0.025 on the right side. Now these are values we can check from the z-table. When α is 0.025, Z is 1.96. So, 1.96 on the right side and minus 1.96 on the left side. Therefore, if the value we get for Z from the test is lower than minus 1.96, or higher than 1.96, we will reject the null hypothesis. Otherwise, we will accept it. That’s more or less how hypothesis testing works. We scale the sample mean with respect to the hypothesized value. If Z is close to 0, then we cannot reject the null. If it is far away from 0, then we reject the null hypothesis. Example of One Tailed TestWhat about one-sided tests? We have those too! Let’s consider the following situation. Paul says data scientists earn more than $125,000. So, H0 is: μ0 is bigger than $125,000. The alternative is that μ0 is lower or equal to 125,000. Using the same significance level, this time, the whole rejection region is on the left. So, the rejection region has an area of α. Looking at the z-table, that corresponds to a Z-score of 1.645. Since it is on the left, it is with a minus sign. Accept or RejectNow, when calculating our test statistic Z, if we get a value lower than -1.645, we would reject the null hypothesis. We do that because we have statistical evidence that the data scientist salary is less than $125,000. Otherwise, we would accept it. Another One-Tailed TestTo exhaust all possibilities, let’s explore another one-tailed test. Say the university dean told you that the average GPA students get is lower than 70%. In that case, the null hypothesis is: μ0 is lower than 70%. While the alternative is: μ0` is bigger or equal to 70%. In this situation, the rejection region is on the right side. So, if the test statistic is bigger than the cut-off z-score, we would reject the null, otherwise, we wouldn’t. Importance of the Significance Level and the Rejection RegionTo sum up, the significance level and the reject region are quite crucial in the process of hypothesis testing. The level of significance conducts the accuracy of prediction. We (the researchers) choose it depending on how big of a difference a possible error could make. On the other hand, the reject region helps us decide whether or not to reject the null hypothesis. After reading this and putting both of them into use, you will realize how convenient they make your work. *** Interested in taking your skills from good to great? Try statistics course for free! Next Tutorial: Providing a Few Linear Regression Examples What does level of significance mean in hypothesis testing?The researcher determines the significance level before conducting the experiment. The significance level is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.
What is the meaning of level of significance in the context of hypothesis testing multiple choice question?The level of significance is the measurement of the statistical significance. It defines whether the null hypothesis is assumed to be accepted or rejected. It is expected to identify if the result is statistically significant for the null hypothesis to be false or rejected.
What defines the significance level of a test?In statistical tests, statistical significance is determined by citing an alpha level, or the probability of rejecting the null hypothesis when the null hypothesis is true. For this example, alpha, or significance level, is set to 0.05 (5%).
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What is the meaning of level of significance in the context of hypothesis testing?
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