Lecture 3

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 3**

If we were teaching this course in-person, I would walk in to class on week 3 and go back to the concept of distance and how we represent it in statistics. We would circle back to the deviation scores, total distance, and average distance because the concept are so important that it's important to ensure they are firmly understood before we go on. So that's what we are going to do here. Watch the video on deviation scores again.

1) Deviation Score technical video....here

Now watch the video on the AAD. This introduces us to the ideas of total distance and average distance (as opposed to total score and average score...the mean).

2) The AAD technical video....here

Now watch the representational video on the AAD. Take careful notes and then teach this to someone. It is absolutely crucial you understand the concepts of individual distance form the mean (absolute deviation score), total distance from the mean (the sum of the absolute deviation scores - the numerator of the AAD) and average distance from the mean (the AAD).

3) The AAD representational video....here

Now watch the technical video on the standard deviation. First, make sure to recognize the similarity between the variance and the AAD. The AAD is the average distance scores are from the mean, the variance is the average SQUARED distance scores are from the mean. Make sure you can see this in the formula. Make sure you can see that the variance is the total squared distance scores are from the mean divided by the number of squared distances. Make sure you know that the sum of squares (SS) IS the total squared distance scores are from the mean.

Now, recognize that the standard deviation is just the square root of the variance. That's it...there is nothing more to it than that.

4) The standard deviation technical video....here

Now, watch the video on measuring variability or spread again. Put this all together so you have a clear picture of the the AAD, variance and SD.

5) Measures of variability technical video....here

On the multiple choice for quiz 1, I will ask you to calculate, in your head, the AAD, VAR and SD. Here are some exercises on how to do this.

6) Exercises on calculating the AAD, VAR and SD....here

Finally, watch this video on what measures of spread represent about the world.

7) What measures of spread represent....here

Now, you should be able to answer learning objectives questions: 1-6 and 10. Ask away if you have any questions. Make sure you now fully understand the difference between what measures of spread represent and what measures of location represent. Watch the following video for some help on this.

8) The difference between location and spread....here

Now, It's time to look at COvariability. This is not how one variable varies, but how two variables vary together. How they covary. There are a number of videos to watch. As usual, take notes and ask if you have questions. After watching these videos, you should be able to answer learning objectives questions 7-9. The first thing you need to understand before going on to the covariance and Pearson r as measures of covariability is the concept of conditional distributions.

9) Conditional distributions....here

10) The covariance....here

11) The Pearson r technical video....here

12) The Pearson r representational video....here

Now, finally, watch this video on outliers. It explains why we need to be very careful about outliers in the correlation context.

13) Outliers video....here

By the time you have watched and taken notes on the videos above and worked to understand them and commit to memory the names, definitions and symbols associated with each concept, you should understand what variance and covariance are, how they differ from measures of location and be able to do simple calculations in your head for the AAD, VAR and SD.

Also, if you have not done so yet, remember to write the two quizzes on Blackboard about how to do well in a statistics course and the rules for the semester in this course. You can do the quizzes as many times as you like until you get 10/10. You must complete the quizzes with a score of 10/10 in order to be eligible to write the remaining tests in the course.

Now, remember to create cue cards for the major concepts we are covering at the moment. DO NOT RELY on cheat sheets or your notes on tests for this information. If you do not know what concepts mean and can not define them, you will not do well on the tests in this course!

That's it for this week. Feel free to ask questions on the "Course Questions" discussion board in Blackboard. I will answer questions on Tuesdays and Thursdays of each week.

Now on to lecture 4.