Statistics

1. INTRODUCTION TO
STATISTICS & PROBABILITY
Chapter 3: Producing Data
(Part 1)
Dr. Nahid Sultana
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2. Chapter 3: Producing Data
Introduction
3.1 Design of Experiments
3.2 Sampling Design
3.3 Toward Statistical Inference
3.4 Ethics
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3. Introduction
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 Available Data,
 Anecdotal Data
 Sample Surveys and Experiments
Observation vs. Experiment

4. 4
Obtaining Data
 Available data are data that were produced in the past for some
other purpose but that may help answer a present question
inexpensively.
The library and the Internet are sources of available data.
 Beware of drawing conclusions from our own experience or
hearsay or from anecdotal evidence --- data from anecdotes (a short
amusing or interesting story about a real incident or person,
especially a biographical one)…. They may not be a representative
of any larger group of cases.
 Some research questions require data produced specifically to
answer them. This leads to designing observational or experimental
studies.

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Observational vs. Experimental Studies
Observational study: A study where researcher observed
individuals and record information about variable of interest. No
treatment is imposed.
 The purpose is to describe some group or situation.
 Sample surveys are observational studies
Experimental study: A study where researcher intentionally
imposes treatments on individuals and measure their responses to
the treatments.
Experiments allow researchers to establish “cause and
effect” relationship.
The purpose is to study whether the treatment causes a
change in the response.

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Observational vs. Experimental Studies
(Cont…)
Lurking variable: A variable that affects the relationship between
the response variable and the explanatory variable but is not
included among the variables studied.
Confounding: Two variables (explanatory variables or lurking
variables) are confounded when their effects on a response variable
cannot be distinguished.
studying
intelligence
Good grade on test
CAUSE?
Confounding?
Well designed experiments take steps to defeat confounding.

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Population versus sample
Population: The entire group of
individuals in which we are interested
but can’t usually assess directly.
Example: All humans, all
working-age people in
California, all crickets
Sample: The part of the population
we actually examine and for which
we do have data.
How well the sample represents
the population depends on the
sample design.
A parameter is a number describing a
characteristic of the population.
A statistic is a number describing a
characteristic of a sample.

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3.1 Design of Experiments
 Experimental terminology
 Comparative Experiments
 Bias
 Principles of Experimental Design
 Statistical Significance
 Matched Pairs Design
 Block Design

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Terminology
 The individuals in an experiment are the experimental units. If
they are human, we call them subjects.
 In an experiment, we do something to the subject and measure
the response. The “something” we do is a called a treatment, or
factor.
 If the experiment involves giving two different doses of a drug,
we say that we are testing two levels of the factor.
 One group of people may be placed on a diet/exercise program
for 6 months (treatment), and their blood pressure (response variable)
would be compared with that of people who did not diet or exercise.

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Terminology (Cont..)
Example:

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Comparative Experiments
Experimental Units
In the laboratory environment, simple designs often work well.
Outside the laboratory, badly designed experiments often yield
worthless results and we can’t tell whether the response was due to
the treatment or to lurking variables.
Many laboratory experiments use a simple design :

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Comparative Experiments (Cont…)
We compare the response to a treatment versus to :
 Another treatment,
 No treatment (a control),
 A placebo
 Or any combination of the above
A control is a situation where no treatment is administered.
A placebo is a fake/dummy treatment, such as a sugar pill.
 Many patients respond favorably to any treatment, even a
placebo.
 The response to a dummy treatment is the placebo effect.
 Perhaps the most famous placebo is the kiss, blow, hug, band
aid—whatever your technique—that parents use (quite
effectively) for minor injuries in kids.

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Randomized Comparative Experiments
 The design of a study is biased if it systematically favors certain
outcomes.
 A double-blind experiment is one in which neither the subjects
nor the experimenter(s) know which individuals received which
treatment until the experiment is completed.
However, subjects must be informed that they will get one of a
number of treatments, and must consent to that condition (it
would be unethical otherwise).

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Randomized Comparative Experiments
(Cont…)
The best way to exclude biases from an experiment is to randomize
the design. Both the individuals and treatments are assigned
randomly.
Experimental
Units
Random
Assignment
Group 1
Group 2

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Principles of Experimental Design
Control: Compare two or more treatments. This will control the
effects of lurking variables on the response.
1. Randomize: Use neutral chance to assign experimental units to
treatments.
Replication: Repeat each treatment on many units to reduce
chance of variation in the results.
Principles of Experimental Design
 An observed effect so large that it would rarely occur by
chance is called statistically significant.
 It tells you that the investigators found good evidence for the
effect they were seeking.

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How to Randomize
 The idea of randomization is to assign subjects to treatments by
drawing names from a hat.
 To randomize an experiment we can use a table of random digits
(like Table B) or a statistical software.
The digits appear in groups of five and in numbered rows.
The groups and rows have no meaning

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Using Table B
Suppose we need to select five students from a class of 20 students.
Step 1 (Label): Since the class is of 20 students, list and number them as
01, 02 , 03, ….., 20
Step 2 (Table): Start anywhere in the table and read two digit groups.
Each of these two-digit groups is a label. The labels 00 and 21 to 99 are
not used in this example, so we ignore them. Continue to the next line.
45 46 71 17 09 77 55 80 00 95 32 86 32 94 85 82 22 69 00 56
52 71 13 88 89 93 07 46 02 ……

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Completely randomized designs
In a completely randomized experimental design,
individuals are randomly assigned to groups, then
the groups are randomly assigned to treatments.
Look at the
response!!!

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Blocked Designs
In a block or stratified design, subjects are divided into groups, or
blocks, prior to the experiment to test hypotheses about differences
between the groups.
The blocking, or stratification, here is by gender

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Matched Pairs Designs
 A common type of randomized block design for comparing two
treatments is a matched pairs design.
 Matched pairs:
 Choose pairs of subjects that are closely matched—e.g., same
sex, height, weight, age, and income.
 Within each pair, randomly assign who will receive which
treatment.
 The idea is that matched subjects are more similar than unmatched
subjects, so that comparing responses within a number of pairs is more
efficient than comparing the responses of groups of randomly
assigned subjects.

21. Is there a significant difference in resting pulse rates for men and
for women? A random sample of 28 men and 24 women had their
pulse rate measured at rest in the lab.
Many dairy cows now receive injections of BST, a hormone
intended to spur greater milk production. The milk production
of 60 dairy cows was recorded before and after they received
a first injection of BST.
What experimental design?
In a study of sickle cell anemia, 150 patients were given the
drug hydroxyurea, and 150 were given a placebo (dummy pill).
The researchers counted the episodes of pain in each subject
at the end of the study.
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