Ch. 9 Analysis of Variance

Levels =

Labels

Observational Studies

a statistical study is observational when it is conducted using PRE-EXISTING data and or collected without any exact design

ex: using data from product registrations and warranty cards

observing consumer purchases in a store

Retrospective

studies an outcome in the present by examining historical records

retro= back then

Prospective

identifies subjects in advance and collects data as events unfold

collects as it goes

Elements of a design:

experiment, factors, treatment, response variable

Factors

the variables being manipulated by setting them to particular values called levels (labels)

Treatment

the combination of factor levels assigned to a subject

Principles of design

Control

Random assignment

Replication

Blocking

Control

one can control the sources of variation other than the factors being manipulated by making conditions as similar as possible for all treatment groups

Control Treatment

special treatment class designed to mark the baseline of stud y

Random assignment

no single group is represented more heavily than another

Replication

Repeated observations at each treatment is called replicates. If the number of replicates is the same for each treamtment combo, the experiment is said to be balanced

1 factor, completely randomized design

2nd kind of replication

repeat entire experiment for a different group of subjects, under different circumstances or at different times

Blocking

Group or block subjects together according to some factor that is uncontrollable but may affect the response

ex: sex, ethnicity, marital status

in a grid, treatment will be at the top (horizontal) and block will be on the side (vertical)

Volume

Information increased by: selecting factors, choosing treatments, determining sample size

RANDOM ASSIGNMENT REDUCES..

NOISE

Noise

ERROR reduced by: randomly assigning treatments to the experimental units

BLINDING KEEPS OUT..

bias

2 sources of unwanted bias

1. those who might influence the results (subjects, treatment admins, technicians)

2. Those who evaluate the results (judges, experimenters, stakeholder)

Single-Blind Experiment

either the subjects OR the analysts are blinded

Double-Blind Experiment

both groups are blinded

best- keeps bias out

Confounding is good or bad?

BAD

Confounded definition

when the levels of one fact are associated with the levels of another factor

& is..

bad. means tow things are confounded

Lurking Variables is good or bad

BAD

Lurking Variables

“drives” two other variables in such a way that a causal relationship is suggested between the two

ex: the economy may be a lurking variable in business experiments

ANOVA can be applied to observational data IF

The box plots show equal spreads and symmetric, outlier-free distributions

Cons of ANOVA on Observational Data

1. Observational studies are frequently unbalanced

2. Randomization is usually absent

3. There is no control over lurking variables or confounding

4. Cannot draw causal conclusions even when the F-stat is significant

3 Different types of designs

1. Completely Randomized

2. Randomized Block

   1. Factorial Design

Completely Randomized-

when each of the possible treatments is assigned to at least one subject at random

aka: one factor ANOVA

one factor with replication

Randomized Block-

two factors, but the experiment is not replicated

Factorial Design

has two factors with replication

Hypothesis for ANOVA

Ho: us=uw=unp

Ha: at least two means differ

Levels not connected by the same letter are

significantly different

Randomized Block

require randomizing the subject treatment within each block

Randomized Block has how many hypothesis

2

Factorial Designs

contains treatments that represent all possible combos of factors at different levels

2 factors with replication

1st step in factorial design

Test for Interaction first- the effect of changing the level of one factor depends upon the level of other factor

• look for interacted term in effect tests and look at f test

Pitfalls in ANOVA

• Watch out for changing variances

• Be wary of drawing causality conclusions from observational studies

• Be sure to fit an interaction term when it exists. If the interaction term is not significant, fit a simpler block design to test the main effects instead