ANOVA Part 2

1
ANOVA Part 2

• Completely Randomized Design CRD
• Randomized Block Design RBD
• Factorial Design

2
CRD

• Testing for differences in means of multiple
  groups
• One Factor Being Analyzed
• Subjects are randomly in each treatment group
• 5-Step Hypothesis Testing Process
• F-Distribution

3
CRD
SSTR
SST
SSE
SST SSTR SSE
4
CRD
MSTR SSTR / (c-1)
MSE SSE / (n c)
Ftest MSTR/MSE
5
CRD (Excel Output)
6
RBD

• Used to isolate or Block a possible bias in the
  subject groupings.

SSTR
SST
SSBL
SSE
7
RBD (Example)
Example We are the owner of 4 Chillis
restaurants (A, B, C, and D). We want to
determine if there is a difference in service
between the 4 restaurants. Six raters are hired
to dine at each restaurant and to rate their
service on a scale of 0 (low) to 100 (high). Is
there a difference in service? What are the null
and alternative hypothesis? Test at a .05 level
of significance. Is there a rater bias? What
are the null and alternative hypothesis? Test at
a .05 level of significance.
8
RBD (Hypothesis)
Service H0 HA Rater Bias/Blocking
Effect H0 HA
9
RBD (Line Graphs)
Service Means
Rater Means
10
RBD (Excel Analysis)
11
Factorial Design

• Analyzing two primary factors at the same time to
  determine
• Is there a Factor A effect?
• H0 Factor A means equal, row means equal
• HA Factor A means are not all equal
• Is there a Factor B effect?
• H0 Factor B means equal, column means equal
• HA Factor B means are not all equal
• Is there an Interaction (AB) effect?
• H0 No Interaction
• HA There is Interaction

12
Factorial Design

• Terms
• Treatment Group - A group of subjects receiving
  the same treatment.
• Replicates Number of subjects in a treatment
  group.
• Interaction The measurement for Factor B in a
  treatment group is significantly different
  depending on a Factor A group. Example The
  number of students in one section of Statistics
  has significantly more As than another section.
  You could say, the number of students getting an
  A depends on the Section (there is interaction
  between Grade and Section).

13
Factorial Design (Example)
14
Factorial Design (Interaction)
Observe the means for each treatment group.
15
Factorial Design (Excel ANOVA Analysis)
There is a Temperature effect.
Rows, Temp
There is a Brand effect.
Columns, Brands
There is an Interaction effect.