Chapter 3
Obtaining Useful Evidence
Statistical Process
1.
2.
3.
4.
5.
6.
7.
Ask a specific question
Make a hypothesis
Design an experiment
Collect data
Use graphs and statistics to explore the evidence (data)
Determine if the evidence supports the theory
Make an evidence-based decision
Research design is that portion of the statistical process in
which planning is done so that the conclusions are drawn with
confidence and can be supported under scrutiny.
To learn how to design research, each table will send a
representative to a different conference (part of the room) to learn
about one type of research. The choices are:
Fallacies
Marijuana
Wealth gap and crime
Math anxiety medication
After learning about it, you will regroup, try all the problems
yourself, and then check answers for each problem with the expert.
Clarifications
Cause and Effect
Showing causation (a cause and effect relationship) is a
highly desirable outcome for many research questions.
In a causal relationship, a treatment produces a particular
outcome while not providing the treatment means that particular
outcome is not produced. Thus, simply showing that a certain
response occurred when a treatment was provided does not prove
the treatment caused the response.
A cause and effect relationship implies the existence of two
variables. One of those variables must happen before the other.
independent or explanatory variable
dependent or response variable
There are three types of research design that will be considered,
observational study, observational experiment, and manipulative
experiment.
Observational studies are investigations about characteristics of
one or more populations.
Examples of one population include: people, trees, mice, etc.
Examples of two or more populations include:
Democrat/Republican, Gender, Age
In general, there may be differences between two groups but the
groups do not cause these differences.
Observational study
The goal is to understand the population or differences
between the populations.
Units are randomly selected.
Cannot show causation
Experiments are investigations about the effect of an intervention
(treatment) that someone can make to cause a change in the
response variable. There must always be at least two levels of the
explanatory variable.
Manipulative Experiment: The researcher randomly decides
which subjects receive the treatment.
Manipulative experiment
The goal is to determine the effect of an interaction
Random assignment of units to groups facilitates showing
causation
Observational experiment: The decision for the treatment is
beyond the researcher’s control. Someone else (some governments
or mother nature) makes the decision.
Examples: Governments legalize drugs, governments institute a
method of taxation or a program, Mother Nature has storms or
earthquakes, etc
Observational experiment
The goal is to determine the effect of an interaction
No random assignment is possible.
Might be able to show causation
Latent Variables – potential explanatory variables that are
not used.
Example: Suppose the research question is “What affects
success in a statistics class?”
List possibilities:
Any of these possibility could be the explanatory variable in
a research project.
Approval for research: Institutional Review Board (IRB).
Complete the Research Design Assessment.
Recommendation – do it yourself and compare answers afterwards.
Complete In-class Activity– Design Tables –Page 275
Sampling
Observational studies and some observational experiments
require random sampling from a population. The next step in the
research design process is to determine how a sample will be taken
from the population so that it is representative of the population.
The objective is to avoid bias.
Bias can result from who is asked, who can’t be asked and
how they are asked.
Another source of bias comes from using data that is not
independent. Data that are independent means the knowledge of
one datum does not give any indication of the value of another.
Time series data is a special concern in this regard.
Using time series data for a BACI design or for a correlation
study must be done by sampling data from years that are far
enough apart that the data do not have serial dependence.
Probability Sampling Methods
Simple random – sample random selection from all units.
Complete In-class Activities – SRS on Calculator –Page 277
Stratified: Define strata then simple random from each stratum
separately.
Systematic: randomly select 1 value from 1 to k, then add k
repeatedly.
Cluster: Define the clusters then do a simple random sample of the
clusters and use all the units from the cluster.
Demonstrate on the book example.
Cluster 1
1 Yes
2 Yes
3 No
4 Yes
5 No
6 Yes
7 No
8 Yes
9 No
10 No
11 No
12 Yes
13 Yes
14 Yes
15 No
16 No
17 Yes
18 Yes
19 No
20 No
West Side of Harbor
Cluster 2
Cluster 3
21 No
41 Yes
22 No
42 No
23 No
43 No
24 No
44 Yes
25 No
45 No
26 Yes
46 Yes
27 No
47 No
28 No
48 No
29 No
49 No
30 No
50 No
31 No
51 Yes
32 No
52 Yes
33 No
53 Yes
34 No
54 Yes
35 Yes
55 No
36 Yes
56 No
37 Yes
57 No
38 Yes
58 No
39 No
59 Yes
40 No
60 No
Cluster 4
61 No
62 No
63 No
64 No
65 No
66 No
67 Yes
68 No
69 No
70 Yes
71 No
72 Yes
73 Yes
74 Yes
75 Yes
76 Yes
77 No
78 Yes
79 No
80 No
Cluster 5
81 No
82 Yes
83 No
84 No
85 Yes
86 Yes
87 No
88 No
89 Yes
90 No
91 No
92 Yes
93 No
94 Yes
95 No
96 No
97 Yes
98 No
99 No
100 No
East Side of Harbor
Cluster 6
101 No
102 No
103 Yes
104 Yes
105 Yes
106 No
107 No
108 Yes
109 No
110 No
111 No
112 Yes
113 No
114 No
115 No
116 No
117 Yes
118 Yes
119 Yes
120 Yes
Cluster 7
121 No
122 Yes
123 No
124 No
125 Yes
126 No
127 Yes
128 No
129 Yes
130 No
131 No
132 Yes
133 No
134 Yes
135 No
136 No
137 Yes
138 No
139 Yes
140 Yes
Complete and submit In-class Activities – Compare and Contrast
Sampling Methods - Page 279