Chapter 3 Section 1

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Chapter 3 Section 1

• Producing Data First Steps

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Introduction

• Exploratory data analysis asks what the data tell
  us about the variables and their relations to
  each other. The conclusions of an exploratory
  analysis may not generalize beyond the specific
  data studied.
• Formal statistical inference produces answers to
  specific questions, along with a statement of how
  confident we can be that the answer is correct.
  The conclusions of statistical inference are
  usually intended to apply beyond the individuals
  actually studied.

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First Steps

• Designs are the arrangements or patterns for
  producing data.
• -- How many individuals to collect data from
• -- How to select the individuals
• -- How to form the groups if several groups are
  to receive different treatments
• If there is no design, then there is incomplete
  data or haphazard data.

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Where to find data the library and the Internet

• Anecdotal evidence is based on haphazardly
  selected individual cases, which often come to
  our attention because they are striking in some
  way. These cases need not be representative of
  any larger group of cases.
• Statistical Abstract of the United States,
  www.fedstats.gov, www.statcan.ca,
  www.inegi.gob.mx (US, Canada, Mexico)
• Ex. 3.1 General Social Survey (GSS)
• Available data are data that were produced in the
  past for some other purpose but that may help
  answer a present question.

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Sampling

• Sampling selects a part of a population of
  interest to represent the whole.
• A census is an attempt to contact every
  individual in the entire population.

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Experiments

• Observation vs Experiment
• An observational study observes individuals and
  measures variables of interest but does not
  attempt to influence the responses.
• An experiment deliberately imposes some treatment
  on individuals in order to observe their
  responses.
• Example 3.2

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Chapter 3 Section 2

• Design of Experiments

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Experimental Units, Subjects, Treatment

• The individuals on which the experiment is done
  are the experimental units.
• Subjects are human beings
• A specific experimental condition applied to the
  units is called a treatment
• The explanatory variables in an experiment are
  called factors
• A specific value is called a level.

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• Example 3.3
• A placebo is an item that does nothing. It is
  used in experiments to test the effectiveness of
  a drug. (A dummy treatment)
• Example 3.4
• In principle, experiments can give good evidence
  for causation.

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Comparative experiments

• Treatment ? Observe response
• A laboratory experiment is usually done this way.
• Example 3.5
• Gastric freezing ? Observe pain relief
• confounded with the placebo effect
• A control group are the subjects that receive the
  experiment without including the thing being
  studied.
• Control is a basic principle on statistical
  design.
• The design of a study is biased if it
  systematically favors certain outcomes.

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Randomization

• The design of an experiment first describes the
  response variable or variables, the factors
  (explanatory variables), and the layout of the
  treatments, with comparison as the leading
  principle.
• The second aspect is that of randomization the
  use of chance to divide experimental units .
• Example 3.6 figure 3.2
• This combines comparison with randomization

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Randomized comparative experiments

• Logic
• Randomization produces groups of rats that should
  be similar in all respects before the treatments
  are applied
• Comparative design ensures that influences other
  than the diets operate equally on both groups
• Therefore, differences in average weight gain
  must be due either to the diets or to the play of
  chance in the random assignment of rats to the
  two diets.

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Principles of Experimental Design

• The basic principles of statistical design of
  experiments are
• Control of the effects of lurking variables on
  the response, most simply by comparing several
  treatments
• Randomization
• Replication of the experiment on many units to
  reduce chance variation in the results.

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Statistical Significance

• An observed effect so large that it would rarely
  occur by chance is called statistically
  significant.

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How to randomize

• Table B is in the back of the book.
• A table of random digits (0-9) have the following
  qualities
• 1. The digit in any position in the list has the
  same chance of being any one of 0-9
• 2. The digits in different positions are
  independent in the sense that the value of one
  has no influence on the value of any other

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• 3. Any pair of random digits has the same chance
  of being any of the 100 possible pairs 00, 01,
  02, , 98, 99
• 4. Any triple of random digits has the same
  chance of being any of the 1000 possible triples
  000, 001, 002,,998,999.
• 5. and so on.
• Example 3.7
• Example 3.8 figure 3.3
• When all experimental units are allocated at
  random among all treatments, the experimental
  design is completely randomized.

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Cautions about experimentation

• Double-blind means neither the subjects nor the
  medical personnel knew which treatment any
  subject had received.
• Lack of realism
• Example 3.9

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Matched pairs designs

• Example 3.10
• Matched pairs are a common form of blocking for
  comparing just two treatments. In some matched
  pairs designs, each subject receives both
  treatments in a random order. In others, the
  subjects are matched in pairs as closely as
  possible, and one subject in each pair receives
  each treatment.

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Block designs

• Matched pairs are an example of blocking
• A block is a group of experimental units or
  subjects that are known before the experiment to
  be similar in some way that is expected to affect
  the response to the treatments.
• In a block design, the random assignment of units
  to treatments is carried out separately within
  each block.
• Example 3.11, 3.12

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Daily Work

• Pg 250-255
• 12, 14, 18, 22
• 26