Class Notes (836,147)
Canada (509,656)
Psychology (2,710)
PSYC 2002 (84)
Lecture 9

Lecture 9.docx
Premium

6 Pages
66 Views
Unlock Document

Department
Psychology
Course
PSYC 2002
Professor
Steven Carroll
Semester
Winter

Description
Lecture 9 t-test Z-test assumptions - Random sampling - Anormal sampling distribution - Independent observations - Constant  - Two of these are actually pretty hard to justify in the real world. Which? • Normal sampling distribution and Z-test assumptions - Constant  • You often don’t know ² • In fact, you often run experiments specifically so that you can estimate the population parameters - Anormal sampling distribution • If you can get a large enough sample, that’s fine • But what if you can’t? • This problem prompted a pilgrimage which I undertook a few years ago Gosset’s revolutionary discovery - The mean of a small n sample, that produces an estimate of , can be compared to a theoretical distribution of sample means that is NOT normally distributed - The distribution would be relatively platykurtic for small n’s, but would still be symmetrical and unimodal - The distribution would approach the shape of a normal distribution as n increased The student’s t-test - Used instead of a z-test whenever you don’t know  - Used instead of a z-test whenever you have small samples and, as such, can’t be certain that the distribution of sample means is normally distributed “New” formulae S = S M √n SS Where: S = √ n−1 M−µ t= S M Let’s have a flashback… - Remember in Quiz #1 when I asked you to find the missing X value given a particular mean? - Many of you found unique formulae that let you do this • That’s great! You got full marks for that - The problem is: those unique formulae missed the point of the question… Find the missing X - If X = {1, 2, 3, ???} and M = 5 what is the missing value? - One of the values is NOT FREE TO VARY - This means that, although most of the scores are free to vary, the sample has lost one degree of freedom - For any t-test: df = n – 1 df = n – 1 - A t distribution will approach a normal distribution as df increases - So how do you increase df for a t-test? The t-table - The table is a list of critical values to be used in hypothesis testing - This one is a bit more complicated than the z-table. Fortunately, you’ll only have to deal with an abbreviated version: • Only a few  values are listed - What critical t score would be associated with the following: • I tested 10 people who I believe were made better by my treatment.  = .05 • Do men perform differently than women? I tested 15 men.  = .05 Let’s do a t-test!! - I suspect that students will do better on Test 2 than on Test 1 because they will have had more exposure to the subject matter - I get a sample of 5 test takers - The mean grade for test 1 was µ = 5 - My sample had the following scores: • 6, 8, 4, 9, 8 - Test my hypothesis, maintaining a Type I error rate of 2.5% Getting the necessary values X (X-M)2 6 1 s2 = 16/(5-1) = 4 8 1 s = 2 4 9 9 4 8 1 M = 7 SS = 16 Step 1 - State the hypothesis H µ - 0 = treatmen≤ 5 - H 1 = µtreatmen> 5 Step 2 - State your critical value - At  = .025 one-tailed, and with df = 4, tcritic= 2.776 Step 3 - Run the test - T = (7 – 5) / (2 / 5) - = 2 / .89 - 2.2361 - 2.24 Step 4 - Compare obtained and critical values - T- observed (2.24) is less extreme than
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