DDBA 8438: Introduction to Hypothesis Testing Video Podcast Transcript

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1 DDBA 8438: Introduction to Hypothesis Testing Video Podcast Transcript JENNIFER ANN MORROW: Welcome to "Introduction to Hypothesis Testing." My name is Dr. Jennifer Ann Morrow. In today's demonstration, I'll review with you what hypothesis testing is. We'll talk about the types of hypotheses. We'll go over the four steps to hypothesis testing. We'll discuss decisions in hypothesis testing. We'll go over the different errors in hypothesis testing. And we'll briefly go over power and effect size. All right, let's get started. Hypothesis Testing JENNIFER ANN MORROW: Hypothesis testing is a statistical method that uses sample data to evaluate a hypothesis about a population parameter. It is an inferential procedure that uses sample data to evaluate the credibility of a hypothesis about a population. What you're trying to do is infer your data from your sample to your population. Types of Hypotheses JENNIFER ANN MORROW: There are two types of hypotheses. The first one is the null hypothesis, and that is designated by H sub zero. This is the hypothesis that we test. It states that there is no effect, no change, no relationship, or no difference among the variables of interest. The other type of hypothesis is the alternative or research hypothesis. And this is designated as H sub A or H sub 1. This is the hypothesis that states that there is an effect or a change or a relationship or a difference among the variables of interest. This is what is expected to happen. And this is the one that is considered the research hypothesis. Steps to Hypothesis Testing JENNIFER ANN MORROW: There are four steps to hypothesis testing. Step 1 is where you state the hypothesis. Step 2 is where you set the criteria for a decision. In Step 3, you collect the data and compute your sample statistics. And lastly, in Step 4, you make a

2 decision. Now let's learn about these steps in more detail. In Step 1, you create your null and alternative hypotheses. Just remember that testing a hypothesis does not prove or disprove the statement. It can only confirm or disconfirm. You can never prove a hypothesis. You can only confirm or disconfirm your hypothesis. In Step 2, you choose your alpha level and determine the critical region for the analysis. You also need to choose whether or not to conduct a onetailed or a two-tailed test. Now let's go over alpha level and one- and two-tailed testing in more detail. An alpha level, or the level of significance, is a probability value that is used to define the very unlikely sample outcomes if the null hypothesis is true. And this is established a priori, which means before you begin your actual research project. And some common alphas that are used in psychological research are 0.05 and An alpha level of 0.05 is saying that only 5% of the time, this result would occur by chance alone. And an alpha level of 0.01 is saying that only 1% of the time, this result would occur by chance alone. Your critical region, also known as the rejection region, is composed of extreme sample values that are very unlikely to be obtained if the null hypothesis is true. This is determined by your alpha level. If sample data fall in the critical region, then you can reject your null hypothesis. There are two types of statistical tests that you can choose, no matter what type of specific statistical analysis that you're looking at. One is a one-tailed test. A one-tailed test, also known as a directional hypothesis, is when your rejection region is on only one side of the distribution. This is a much more liberal or powerful or sensitive test than a two-tailed test. When you use a one-tailed test, it's much easier for you to detect a difference. For a two-tailed test, this is when your rejection region is split on both sides of your distribution. This is a more conservative test, so it's less powerful, less sensitive than a onetailed test. However, it is the most frequently used test. In Step 3 of hypothesis testing, you collect the data for your study and then use statistics to conduct analyses on your sample data. And lastly, in Step 4 of hypothesis testing, now you make a decision about the null hypothesis, according to the criteria that you've established in Step 2. You decide whether or not to accept or reject the null hypothesis. Recap JENNIFER ANN MORROW: All right, let's recap. So far, we've gone over hypothesis testing. We've talked about the two types of hypotheses: null and alternative. And we've learned about the four

3 steps to hypothesis testing: stating the hypothesis, setting the criteria, collecting data and analyzing data, and lastly, making that decision. Now let's go over decision-making in hypothesis testing. Decisions in Hypothesis Testing JENNIFER ANN MORROW: In hypothesis testing, you can make one of four decisions. The first one is, a true hypothesis is rejected. This is also known as alpha or Type I error, and sometimes you'll see it referred to as a false alarm. And I have found in the past that my students tend to remember that one the most. The second decision that you could make is, a true hypothesis is not rejected. And this is known as 1 minus alpha or a correct decision. Another decision that you could possibly make in hypothesis testing is, a false hypothesis is rejected. And this is known as 1 minus beta, and this is also a correct decision. And lastly, you could also make the decision where a false hypothesis is not rejected. And this is known as beta or Type II error, and sometimes you see it referred to as a miss, and again, past experience with students has shown, they tend to remember that one the most. Now let me show you a chart that may make it easier for you to remember these four decisions in hypothesis testing. Here you see on the left, or where the rows are labeled, are your statistical decisions, whether you reject the null hypothesis or fail to reject the null hypothesis. At the top, the labels for the columns is what is found in reality, whether your null is true or your null hypothesis is false. As you can see, the top right and the bottom left are correct decisions. You reject a false null, or you fail to reject a true null. The other two decisions that you can make are known as errors in hypothesis testing. Errors in Hypothesis Testing JENNIFER ANN MORROW: There are two errors that you can make in hypothesis testing. The first one is Type I error, also known as alpha. This is when you reject a true null hypothesis. You are saying that there is a difference or a relationship when, in fact, none exists. And again, this is sometimes referred to as a false alarm. You're saying something is there when there isn't anything there. The second type of error that you can make is called a Type II error, also known as beta. This is when you fail to reject a false null hypothesis. You are saying that there is no difference or relationship when, in

4 fact, one does exist. And this is sometimes referred to as a miss. So you're saying that there is nothing there when, in fact, there really is. Power JENNIFER ANN MORROW: Power is how well you can detect a difference. This is known as the probability of rejecting a false hypothesis. And it's usually stated as 1 minus beta or 1 minus the probability of Type II error. If you increase your alpha, or your Type I error, you will increase power. For example, if you go from an alpha level of 0.05 to an alpha level of 0.10, you will have increased power for your statistical test, which means it'll be easier for you to achieve significance. If you decrease beta, or Type II error, you increase power. So the smaller the beta, the more power you have. The more likely you are to detect a difference or find a relationship. Type I and Type II error have an inverse relationship with each other. And what that means is, is when one goes up, the other goes down. So when you have more Type I error, you have less Type II error, and the reverse is also true. Effect Size JENNIFER ANN MORROW: It is not enough to just look at the statistical significance of a test, whether or not you've achieved a statistically significant result. You also have to look at the practical significance. Is your result meaningful? Effect size is one way to show if your result is meaningful. An effect size is a statistical measure of the strength of the relationship or the magnitude of the difference. It is a measure of how much variance in a dependent variable can be explained by an independent variable. And one popular measure of effect size is Cohen's D. This is the simplest way to measure effect size. All you have to do is divide the mean difference by the standard deviation. All right, let's recap. Recap JENNIFER ANN MORROW: We've gone over the decisions in hypothesis testing: true hypothesis is rejected or a true hypothesis is not rejected or a false hypothesis is rejected or a false hypothesis is not rejected. And we also went over the two errors in hypothesis

5 testing: Type I and Type II error. And we talked briefly about power and effect size. We have now come to the end of our demonstration. Don't forget to review the chapter on hypothesis testing in your textbook. Thank you, and have a great day.

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