Lecture 8

Instructor

Jeremy Jackson

| May 5, 2020

Location:

NW 3428

| New Westminster

Sir Ken Robinson: "Learning happens in the minds and souls, not in the databases of multiple-choice tests"

**Text Font Conventions**

- You will be responsible for knowing a number of definitions of key concepts. You may be asked to give an accurate definition and example of any of the key concepts. Key concepts are in italics, bolded and colored red throughout the notes.Key conceptsCritical points - There are some points that require extra emphasis because they are fundamental to the example or concept being discussed. Critical points are bolded, in italics and colored orange.

- These are the questions given in the learning objectives document.Course learning objective questions

**Lecture 8**

Let's begin this week by looking at the effect of changing the sample size and effect size on alpha, beta and power. To some degree, this is a repetition of many of the ideas we looked at in the last lecture but it does require a more refined and nuanced understanding of alpha, beta and power. Here goes...

1) The effect of sample size on alpha, beta and power....here

2) The effect of effect size on alpha, beta and power....here

Now, it turns out that we have been using something called test statistics for a few weeks now, but I have not mentioned the name explicitly. Now it's time to incorporate the idea of a test statistic in to what we have been doing and transition in to a type of test statistic that is useful in the real-world. This new test statistic makes reference to something called a t-distribution. This is the second kind of sampling distribution you will be exposed to in the course. The first was the standard normal distribution or we might say the "z" distribution. So, we have the "z" distribution (which is Normal and has a mean of 0 and SD of 1) and the t-distribution, which has a "t" shape, a mean of 0 and an SD of...you don't need to know this but it's a bit bigger than 1. So go ahead and watch the next video on test statistics and the t-distribution...

3) Test statistics and t....here

Now, one idea that we are required to touch on in this course is the idea that the t-distribution gets closer in shape to the Normal distribution as the sample size increases. The following video explains this admittedly tricky idea.

4) t gets closer to Normal as n increases...here

So far, the test statistics we have looked at are not at all common in the real-world because they deal with situations that are generally more simple than the situations in which most researchers are interested. The next test statistic we will look at is the simplest in which people tend to be interested and, in fact, very commonly used. It is called the independent groups t-test. The next video takes you through the use of that test statistic and the appropriate situation in which to use it. Here goes...

5) The independent groups t-test....here

The next video goes into an explanation of alpha, beta and power for the two-group case...the case in which the independent groups t-test is the appropriate test statistic. This video is an answer to learning objectives question 24 (not 25 as I say in the video), so watch carefully and ask if you have any questions. Here goes...

6) The population bag, 2 groups example....here

In the next video, I do the same thing as the previous video but I use a computer to do the simulation. You are not required to understand how to use a computer to do this, but you should know the logic. here goes...

7) Computer simulation of the 2 group case...here

That's it for this week. Next week we deal with the remaining learning objectives questions and the last new topic in the course...ANOVA.

Now on to lecture 9.