Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Two-Way ANOVA: Comparing Means with Two Factor Effects, Study notes of Statistics

University of South Carolina (USC) - ColumbiaStatistics

An overview of two-way anova, a statistical method used to compare the mean of a response variable across different levels of two factor effects. The model equation, interpretation of coefficients, and the use of dummy coding, contrast coding, unweighted effect coding, and weighted effect coding. It also discusses the significance of interaction terms and the use of type i and type iii sums of squares.

Typology: Study notes

Pre 2010

Uploaded on 09/02/2009

koofers-user-d3j
koofers-user-d3j 🇺🇸

10 documents

1 / 3

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Two-Way ANOVA
1 Two-Way ANOVA (2 levels for each) with No Inter-
action
The main goal in two-way ANOVA is to compare the mean of a certain response variable
across different levels of two factor effects.
Taught BSE
No Yes
HISTORY No ¯
Y00 ¯
Y01
Yes ¯
Y10 ¯
Y11
The Model that we would like to fit is:
Yi=B0+B1HI STi+B2BSEi+i(1)
Where our variables for the ith individual:
Yi= Perceived benefit of mammography. And ¯
Yij = the average perceived benefit of mam-
mography for history i and BSE j.
Historyi=(0, No History
1, History
BSEi=(0, Not Taught BSE
1, T aug ht BS E
What does our model look like when Disease = 0?
What does our model look like when Disease = 1?
What does our B0estimate?
What does our B1estimate?
What does our B2estimate?
What is the overall F-test testing in terms of our means?
What will the individual H0:Bi= 0 test in terms of our means?
When is it appropriate to use dummy coding, contrast coding, unweighted effect coding,
and weighted effect coding?
1
pf3

Partial preview of the text

Download Two-Way ANOVA: Comparing Means with Two Factor Effects and more Study notes Statistics in PDF only on Docsity!

Two-Way ANOVA

1 Two-Way ANOVA (2 levels for each) with No Inter-

action

The main goal in two-way ANOVA is to compare the mean of a certain response variable across different levels of two factor effects.

Taught BSE

No Yes

HISTORY YesNo^ YY¯¯^0010 YY¯¯^0111

The Model that we would like to fit is: Yi = B 0 + B 1 HISTi + B 2 BSEi + i (1) Where our variables for the ith^ individual: Yi = Perceived benefit of mammography. And Y¯ij = the average perceived benefit of mam- mography for history i and BSE j. Historyi =

{ 0 , N o History 1 , History BSEi =

{ 0 , N ot T aught BSE 1 , T aught BSE What does our model look like when Disease = 0? What does our model look like when Disease = 1? What does our B 0 estimate? What does our B 1 estimate? What does our B 2 estimate? What is the overall F-test testing in terms of our means? What will the individual H 0 : Bi = 0 test in terms of our means? When is it appropriate to use dummy coding, contrast coding, unweighted effect coding, and weighted effect coding?

2 Two-Way ANOVA Full Model w/ Dummy Coding Above we assumed that there was no interaction in the different effects. However as we sawin our first example that might not be a good assumption. Lets try refitting that model with an interaction term. We will be fitting the model: P Bi = B 0 + B 1 HISTi + B 2 BSEi + B 3 HISTi ∗ BSEi i (2) Using Dummy coding what will our: What does our B 0 estimate? What does our B 1 estimate? What does our B 2 estimate? What does our B 3 estimate? What will the individual H 0 : B 3 = 0 test? Lets try this in SAS: proc means;by HIST BSE; VAR PB; PROC GLM DATA=MAMMO;MODEL PB = HIST BSE HISTBSE/SOLUTION; OUTPUT OUT=OUT1 R=RY P=PY; PROC PLOT DATA=OUT1; PLOT RYPY;RUN; QUIT; Since our interaction term is insignificant I would refit this model as an additive model (nointeraction) and interpret the means separately.

How could we use the Type I and Type III sums of squares, for testing the significanceof two different research factors A (with four groups), B (with three groups) and A × B?

When would be the appropriate time to use Type I? Type III?