Class Notes (836,135)
Canada (509,645)
Psychology (2,710)
PSYC 2002 (84)
Lecture 5

Lecture 5.docx
Premium

7 Pages
45 Views
Unlock Document

Department
Psychology
Course
PSYC 2002
Professor
Steven Carroll
Semester
Winter

Description
Lecture 5: Z test/score Where we are going... - Z-scores requires a knowledge of standard deviation - Probability theory requires a knowledge of frequency distributions, proportions - The distribution of sample means requires an understanding of the mean and of the standard deviation - Hypothesis testing requires an understanding of z-scores, probability theory, and the distribution of sample means Consider the following... - Imagine you wrote two different tests TEST 1 TEST 2 X = 60 X = 60 µ = 50 µ = 50 - Are you happier with your mark on the first test, or with your mark on the second test? - What if I included this information? TEST 1 TEST 2 X = 60 X = 60 µ = 50 µ = 50  = 20  = 5 - Are you happier with your mark on the first test, or with your mark on the second test? Why? Calculate X−µ Z= ❑ - Calculate z when X= 60, µ= 50, and = 20 - Calculate z when X= 60, µ= 50, and = 5 What is a z-score? - It describes the exact location of a score in a distribution - Az-score of +.5 indicates X was exactly one-half standard deviations above the mean of the distribution of scores - Az-score of +2 indicates X was exactly two standard deviations above the mean of the distribution of scores Calculate X−µ Z= ❑ - Calculate z when X= 50, µ= 60, and = 20 - Calculate z when X= 50, µ= 60, and = 5 What is a z-score? - Az-score of -.5 indicates X was exactly one-half standard deviations below the mean of the distribution of scores - Az-score of -2 indicates X was exactly two standard deviations below the mean of the distribution of scores Imagine the test scores were normally distributed - Az-score of “1” indicates that the raw score X is one standard deviation above the mean of the distribution of scores - Since the height of this distribution indicates the likelihood of a score occurring, it should be noted that more extreme z-scores are comparatively rare - So you should be quite happy with a z-score of +2.0! Why? 50 If =. 5 60 If =.2 60 Try it! X 1 1 1 2 5 - Transform this distribution of raw scores into a distribution of z-scores Consider the following distribution of scores X X – µ (X – µ)2 z 1 1 1 2 5 - What is µ? - What is ? X X – µ (X – µ)2 z 1 -1 1 -.65 1 -1 1 -.65 1 -1 1 -.65 2 0 0 0 5 3 9 1.94 - What is µ? (2) - What is ? (1.55) Let’s do some more math! z -.65 -.65 -.65 0 1.94 - What is the mean of the distribution of z-scores? 0 - What is the standard deviation of the distribution of z-scores? 1 z z – µ (z – z µz )² -.65 -.65 .42 -.65 -.65 .42 -.65 -.65 .42 0 0 0 1.94 1.94 3.76 Always true!! - The mean of a distribution of z-scores is ALWAYS 0 • All positive z-scores are above the mean, and all the negative z-scores are below the mean - The standard deviation of a distribution of z-scores is ALWAYS 1 Let’s draw graphs! - First draw a frequency distribution of the raw scores 1, 1, 1, 2, 5 - Then, draw a
More Less

Related notes for PSYC 2002

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit