Class Notes (923,108)
CA (543,084)
McGill (33,293)
MGCR (644)
MGCR 271 (16)
Lecture 2

MGCR 271 Lecture 2: Inference for 2-Way Tables
Premium

5 Pages
62 Views

Department
Management Core
Course Code
MGCR 271
Professor
Glenn Zabowski

This preview shows pages 1-2. Sign up to view the full 5 pages of the document.
1
Inference for Two-Way Tables
Contingency Table Test for Independence:
H0: The two criteria are independent of each other.
H1: The two criteria are not independent of each other.
**OR**
H0: p1 = p2 = p3 = … = pi (The populations are homogeneous).
H1: Not all p’s are equal (The populations are not homogeneous).
Notation:
RTi = Row total for row i.
CTj = Column total for column j.
NR = Number of rows.
NC = Number of columns.
Oij = Observed frequency for (i, j) cell.
Eij = Expected frequency for (i, j) cell.
n = Sample size.
find more resources at oneclass.com
find more resources at oneclass.com
2
Smoking Example:
A teacher at McGill University claims that the amount of smoking done by undergraduate
students depends on the year of study. A random sample of 200 students registered in the BCom
program was surveyed with the following results:
YEAR
1 2 3
HEAVY
24
27
32
83
LIGHT
14
47
17
78
NON-SMOKER
7
22
10
39
45 96 59 200
Test the teacher’s claim at the 5% level of significance.
Procedure:
Assuming that the null hypothesis is true, calculate the expected frequencies:
Eij = P(an observation is found in i-j cell)*n = P(Joint)*n.
Recall that the following property of statistical independence should be true under H0:
P(A B) = P(A)*P(B).
From this property:
Eij = P(Row)*P(Column)*n = (RTi / n)*(CTj / n)*n =
.
TS:
(O E )
E
ij ij 2
ij
.
AL: 2(; df) where df = (NR - 1)(NC - 1).
DR: Conclude H0 if TS AL and Conclude H1 if TS > AL.
find more resources at oneclass.com
find more resources at oneclass.com

Loved by over 2.2 million students

Over 90% improved by at least one letter grade.

Leah — University of Toronto

OneClass has been such a huge help in my studies at UofT especially since I am a transfer student. OneClass is the study buddy I never had before and definitely gives me the extra push to get from a B to an A!

Leah — University of Toronto
Saarim — University of Michigan

Balancing social life With academics can be difficult, that is why I'm so glad that OneClass is out there where I can find the top notes for all of my classes. Now I can be the all-star student I want to be.

Saarim — University of Michigan
Jenna — University of Wisconsin

As a college student living on a college budget, I love how easy it is to earn gift cards just by submitting my notes.

Jenna — University of Wisconsin
Anne — University of California

OneClass has allowed me to catch up with my most difficult course! #lifesaver

Anne — University of California
Description
Inference for Two-Way Tables Contingency Table Test for Independence: H 0 The two criteria are independent of each other. H 1 The two criteria are not independent of each other. **OR** H 0 p =1p = 2 = 3= p (The pipulations are homogeneous). H 1 Not all ps are equal (The populations are not homogeneous). Notation: RT =iRow total for row i. CT =jColumn total for column j. NR = Number of rows. NC = Number of columns. O ijObserved frequency for (i, j) cell. E ijExpected frequency for (i, j) cell. n = Sample size. 1Smoking Example: A teacher at McGill University claims that the amount of smoking done by undergraduate students depends on the year of study. A random sample of 200 students registered in the BCom program was surveyed with the following results: YEAR 1 2 3 HEAVY 24 27 32 83 LIGHT 14 47 17 78 NON-SMOKER 7 22 10 39 45 96 59 200 Test the teachers claim at the 5% level of significance. Procedure: Assuming that the null hypothesis is true, calculate the expected frequencies:
More Less
Unlock Document


Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

Unlock Document
You're Reading a Preview

Unlock to view full version

Unlock Document

Log In


OR

Don't have an account?

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