Transcript An experiment deliberately imposes a treatment on a group

Experiment
• An experiment deliberately imposes a treatment
on a group of objects or subjects in the interest
of observing the response.
• Differs from an observational study, which
involves collecting and analyzing data without
changing existing conditions
Experimental Controls
• The control group is practically identical to the
treatment group, except for the single variable of
interest whose effect is being tested, which is
only applied to the treatment group.
• An example would be a drug trial.
▫ The group receiving the drug would be the
treatment group and the one receiving the placebo
would be the control group.
Treatment Groups
• In experiments, a treatment is something that
researchers administer to experimental units .
• The treatment groups are the groups of subjects
that received a particular treatment
• For example, in a drug test, three different
groups of subjects received three different types
of drugs
• The treatment is the administration of a
particular drug type
Experimental Design
• The proper organization of the experiment
ensures that the right type of data, and enough
of it, is available to answer the questions of
interest as clearly and efficiently as possible.
• This process is called experimental design.
• Because the validity of a experiment is directly
affected by its construction and execution,
attention to experimental design is extremely
important
Factors
• In an experimental design, a factor in an
experiment is a controlled independent variable
▫ A variable whose levels are set by the
experimenter
• A factor consists of categories of treatments
▫ Remember: Factors are independent variables
• From a statistical standpoint, the researcher
looks for differences in the averages of the
dependent variable(s) across the groups of
independent variables
Experimental Bias
• When researchers fail to control for the effects of
the differences in subjects, it can lead to
experimental bias
• Experimental bias is the favoring of certain
outcomes over others
Randomization
• Because it is generally extremely difficult for
experimenters to eliminate bias using only their
expert judgment, the use of randomization in
experiments is common practice.
• In a randomized experimental design, objects or
individuals are randomly assigned (by chance)
to an experimental group.
Replication
• To improve the significance of an experimental
result, replication, the repetition of an experiment
on a large group of subjects, is required.
• If a treatment is truly effective, the long-term
averaging effect of replication will reflect its
experimental worth.
• If it is not effective, then the few members of the
experimental population who may have reacted to
the treatment will be negated by the large numbers
of subjects who were unaffected by it.
Formats
• Experimental Designs are defined by their
formats
• Examples of these formats include:
▫
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▫
Student t-test- two groups
One-way Analysis of Variance
Multivariate Analysis of Variance
Factorial Analysis of Variance
Split Plot Design
Latin Square Design
One-way Analysis of Variance
Production
3
4
2
4
5
6
4.00
Office
1
0
0
1
2
3
1.17
Maintenance
7
8
5
7
9
6
7.00
Multivariate Analysis of Variance
Split Plot Design
One-way Analysis of Variance Example
• A One-way Analysis of Variance identifies
significant differences between group averages
• In a One-way Analysis of Variance, the researcher
randomly selects subjects and assigns them to one of
three different forklift driving training programs.
• The three different programs are:
▫ Classroom based only
▫ Hands-on only
▫ Combination hands-on and classroom
• Our treatment variable (or factor) is “forklift
training program” and it has three levels (listed
above)
One-way Analysis of Variance Example
• The researcher randomly selects 11 subjects for
each of the different training program, formats
▫ If the subjects are not randomly selected, what
could occur?
• The researcher will compare the average number
of forklift accidents incurred by each group to
determine if there is a significant difference
between the averages
Classroom
Hands-on
Combination
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
1
0
1
0
1
2
0
0
1.0000
0.454545
0.090909
Average
Classroom Hands-on
2
1
0
0
1
0
0
0
0
0
2
0
1
1
0
2
2
1
1
0
2
0
Combination
0
0
0
0
0
0
0
0
0
1
0
Performing the Analysis
• The ANOVA utilizes the F-ratio to determine if
there is a significant difference between the
group averages
• The null hypothesis is:
▫ Ave Grp 1 = Ave Grp 2 = Ave Grp 3
• The alternative hypothesis is:
▫ Ave Grp 1 NE Ave Grp 2 NE Ave Grp 3
• A significant F-ratio indicates there is a
significant difference between the group
averages
ANOVA Results
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Class Training
11
11
1
0.8
Hand on only
11
5
0.454545
0.472727
Both
11
1
0.090909
0.090909
SS
df
MS
F
P-value
F crit
Between Groups
4.606061
2
2.30303
5.066667
0.012713
3.31583
Within Groups
13.63636
30
0.454545
Total
18.24242
32
ANOVA
Source of Variation
Interpretation
• The ANOVA procedure found the significance of the
F-ratio to be .0127.
• If an Alpha level of .05 is used, then because .012 is
less than .05, one can conclude there is a significant
difference between the group averages
• The odds of these results occurring totally due to
random chance is .0127.
• Another way of saying this is “The researcher has a
.0127 percent chance of rejecting the Null
Hypothesis when the Null Hypothesis is in fact true”
Post-Hoc Tests
• When the ANOVA test result is found to be
significant, the next step is to run a post-hoc test to
determine where the significance lies between
groups.
• There are a number of different post-hoc tests that
can be run (Scheffe’s, Tukey’s, etc.)
▫ For example, is Group 1 significantly different from
Groups 2 or 3
▫ Is Group 2 significantly different from Groups 1 or 3
▫ Etc.
Correlation