Two-Factor ANOVA Equations•Mean square factor A:•Mean square factor B:•Mean square interaction:•Mean square error:

Two-Way ANOVA: The F-Test Statistic•Factor A main effect:•Factor B main effect:•Interaction effect:

Two-Factor ANOVA - Example
Airline company is concerned
because many of its frequent
flier program members have
accumulated large quantities of
free miles. They conducted an
experiment in which
each of three methods for
redeeming frequent flier miles
was offered to a sample of 16
customers divided in four age
groups. Factor A is the
redemption offer type with three
levels. Factor B is the
age group of each customer with
four levels.

Two-Factor ANOVA - Example Summary in Excel1. Open file.2. Select Data > Data Analysis.3. Select ANOVA: Two FactorWith Replication.4. Define data range(include factor A and B labels).5. Specify the numberof rows per sample: 46. Specify Alpha7. Indicate output range.
.
8. Click
OK
.

Two-Factor ANOVA Table – Example
Results

Interaction
No Interaction
Interaction is
present

Interaction
•
Test for interaction
•
If present, conduct a one-way ANOVA to
test the levels of one of the other factors
using only one level of the other factor
•
If NO interaction, test Factor A
and
Factor
B

Chapter 13
Review

Section 13.1
Goodness of Fit

Goodness of Fit Tests
•
In most of the analyses that we’ve done in this class and the Stats I
class, we made assumptions about the shape and distribution of the
data.
•
For instance, we assumed that the populations were normally
distributed in all of our ANOVA calculations.
•
In these and other cases, we can use what is called a goodness of fit
test to verify that the assumptions are being met.

Examples
•
Examples might include:
•
Is demand constant across each day of the week? (i.e. does it follow a uniform distribution?). Should we
staff the same number of people on the weekends as the weekdays?
•
Is our manufacturing process normally distributed?
•
Do the data follow a binomial distribution?
•
1:
The number of observations n is fixed.
•
2:
Each observation is independent.
•
3:
Each observation represents one of two outcomes ("success" or "failure").
•
4:
The probability of "success" p is the same for each outcome.

Example from Our Book•Checker Cab Company is interested in matching the number of cabs in service with customer demand throughout the week. Currently, the company runs the same number of taxis Monday through Friday, with 25% reduced staffing on the weekends. The manager wants to find out if the assumed demand pattern still applies.•Data collected over 140 days •Use a .05 level of significance.DayCustomer CountSun4502Mon6623Tue8308Wed10420Thu11032Fri10754Sat4361

Problem--Visualized
•
Here’s a look at the observed vs. the expected
demand (we’ll look at how to calculate expected
demand in a minute).
•
Since the curves do not match, can we stop now and
reject the null hypothesis?
•
No. We have to find out if the demand is
STATISTICALLY different. They might just be different
because drawing samples results in sampling error.