INTRODUCTION TO STATISTICS

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INTRODUCTION TO STATISTICS
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Overview
There are three kinds of lies lies, damned
lies, and statistics. Benjamin Disraeli
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What is Statistics?

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Why do we need statistics?

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Who uses statistics?

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Reasons to Study Statistics

• Being an Informed Information Consumer
• Understanding and Making Decisions
• Evaluating Decisions That Affect Your Life

Statistics The Exploration and analysis of Data,
4th ed. Devore/Peck
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To Make Decisions, you must be able to do the
following

• Decide whether existing information is adequate
  or whether additional information is required.
• If necessary, collect more information in a
  reasonable and thoughtful way.
• Summarize the available data in a useful and
  informative manner.
• Analyze the available data.
• Draw conclusions, make decisions, and assess the
  risk of an incorrect decision.

Statistics The Exploration and analysis of Data,
4th ed. Devore/Peck
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The Official Definition

• Statistics is a collection of methods for
  planning studies and experiments, obtaining data,
  and then organizing, summarizing, presenting,
  analyzing, interpreting, and drawing conclusions
  based on the data.

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Types of Data
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Some Definitions

• Data are observations (such as measurements,
  genders, survey responses) that have been
  collected.
• A population is the complete collection of all
  elements to be studied. The collection is
  complete in the sense that it includes all
  subjects to be studied.
• A sample is a subcollection of members selected
  from a population.
• A census is the collection of data from every
  member of the population.

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More Definitions

• A parameter is a numerical measurement describing
  some characteristic of a population.
• A statistic is a numerical measurement describing
  some characteristic of a sample.

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Still More Definitions

• Quantitative data consists of numbers
  representing counts or measurements.
• Qualitative (or categorical or attribute) data
  can be separated into different categories that
  are distinguished by some nonnumeric
  characteristic.

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Even More Definitions

• Discrete data result when the number of possible
  values is either a finite number or a countable
  number.
• Continuous (numerical) data result from
  infinitely many possible values that correspond
  to some continuous scale that covers a range of
  values without gaps, interruptions or jumps.

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Levels of Measurement

• The nominal level of measurement is characterized
  by data that consist of names, labels, or
  categories only. The data cannot be arranged in
  an ordering scheme.
• Data are at the ordinal level of measurement if
  they can be arranged in some order, but
  differences between data values either cannot be
  determined or are meaningless.

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Levels of Measurement

• The interval level of measurement is like the
  ordinal level, with the additional property that
  the difference between any two data values is
  meaningful. However, data at this level do not
  have a natural zero starting point (where none of
  the quantity is present).

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Levels of Measurement

• The ratio level of measurement is the interval
  level with the additional property that there is
  also a natural zero starting point (where zero
  indicates that none of the quantity is present).
  For values at this level, differences and ratios
  are both meaningful.

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Example

• For the study, identify the following
• What is the population? Sample?
• Is the data quantitative or qualitative?
• Is the data discrete or continuous?
• Identify the level of measurement.

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Critical Thinking
Statistical thinking will one day be as
necessary for efficient citizenship as the
ability to read and write. H. G. Wells
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Statistical Thinking

• Data beats anecdotes
• Beware the lurking variable
• Where the data come from is important
• Variation is everywhere
• Conclusions are not certain

The Basic Practice of Statistics, 3rd ed. Moore
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Sampling

• Sample data must be collected in an appropriate
  way, such as through a process of random
  selection.
• If sample data are not collected in an
  appropriate way, the data may be so completely
  useless that no amount of statistical torturing
  can salvage them.

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Non-response

• How many people are actually called in order to
  get a sample of 1000 people? The Pew Research
  Center of the People and Press conducted a study
  on non-response and found
• 938 Households never screened (no answer, busy,
  answering machine, not available, callback)
• 678 Households that refused
• 221 Households with no eligible person
  (Language barrier, health problem, no person 18
  or older)
• 42 Households with eligible person (Incomplete
  interviews)
• 1000 Households with eligible person (Complete
  interview)
• So, Pew had to call 2879 residential phone
  numbers to get a sample of 1000 people.

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Another Definition

• A voluntary response sample (or self-selected
  sample) is one in which the respondents
  themselves decide whether to be included.

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Watch out for . . .

• Small Samples
• Graphs
• Pictographs
• Percentages
• Loaded Questions
• Order of Questions
• Nonresponse

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Watch out for . . .

• Missing Data
• Correlation and Causality
• Self-Interest Study
• Precise Numbers
• Partial Pictures
• Deliberate Distortions

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Evaluating a Research Study

• What were the researchers trying to learn? What
  questions motivated their research?
• Was relevant information collected? Were the
  right things measured?
• Was the data collected in a sensible way?
• Was the data summarized in an appropriate way?
• Was an appropriate method of analysis selected,
  given the type of data and how the data was
  collected?
• Are the conclusions drawn by the researchers
  supported by the data analysis?

Statistics The Exploration and analysis of Data,
4th ed. Devore/Peck
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Design of Experiments
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Planning and Conducting a Study

• Understand the Nature of the Problem
• Decide What to Measure and How to Measure It
• Data Collection
• Data Summarization and Preliminary Analysis
• Formal Data Analysis
• Interpretation of Results

Statistics The Exploration and analysis of Data,
4th ed. Devore/Peck
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Types of Studies

• In an observational study, we observe and measure
  specific characteristics, but we dont attempt to
  modify the subjects being studied.
• In an experiment, we apply some treatment and
  then proceed to observe its effects on the
  subjects. (Subjects in experiments are called
  experimental units.)

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Types of Observational Studies

• In a cross-sectional study, data are observed,
  measured, and collected at one point in time.
• In a retrospective (or case-control) study, data
  are collected from the past by going back in time
  (through examination of records, interviews, and
  so on).
• In a prospective (or longitudinal or cohort)
  study, data are collected in the future from
  groups sharing common factors (called cohorts).

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One More Definition

• Confounding occurs in an experiment when you are
  not able to distinguish among the effects of
  different factors.

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Example

• Some studies have suggested that drinking wine
  rather than beer or other alcohol has added
  health benefits.
• Wine drinkers eat less fried food, more
  vegetables and fruit.
• They are less likely to smoke.
• As a group, they are better educated and
  wealthier than the groups that consume beer or
  other alcohol.
• These results may be the result of confounding
  by dietary habits and other lifestyle factors.

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Important Factors to Consider in Designing an
Experiment

• Control the effects of variables.
• Use replication.
• Use randomization.

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Controlling Effects of Variables

• Blinding is a technique in which the subject
  doesnt know whether he or she is receiving a
  treatment or a placebo. An experiment is
  double-blind if both the subjects and the
  administers of the treatment dont know whether a
  subject has received a treatment or a placebo.
• The placebo effect occurs when an untreated
  subject reports an improvement in symptoms.

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Controlling Effects of Variables

• A block is a group of subjects that are similar,
  but blocks are different in the ways that might
  affect the outcome of the experiment.
• Randomized Block design If conducting an
  experiment of testing one or more different
  treatments, and there are different groups of
  similar subjects, but the groups are different in
  ways that are likely to affect the response to
  treatments, use this experimental design
• Form blocks (or groups) of subjects with similar
  characteristics.
• Randomly assign treatments to the subjects within
  each block.

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Controlling Effects of Variables

• With a completely randomized experimental design,
  subjects are assigned to different treatment
  groups through a process of random selection.
• With rigorously controlled design, subjects are
  very carefully chosen so that those given each
  treatment are similar in the ways that that are
  important to the experiment.

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Replication and Sample Size

• Repetition of an experiment on sufficiently large
  groups of subjects is called replication.
• Use a sample size that is large enough so that we
  can see the true nature of any effects and obtain
  the sample using an appropriate method, such as
  one based on randomness.

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Randomization and Other Sampling Strategies

• In a random sample members from the population
  are selected in such a way that each individual
  member has an equal chance of being selected.
• A simple random sample of n subjects is selected
  in such a way that every possible sample of the
  same size n has the same chance of being chosen.
• A probability sample involves selecting members
  from a population in such a way that each member
  has a known (but not necessarily the same) chance
  of being selected.

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Randomization and Other Sampling Strategies

• With convenience sampling, we simply use results
  that are very easy to get.
• In systematic sampling, we select some starting
  point and then select every kth element in the
  population.

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Randomization and Other Sampling Strategies

• With stratified sampling, we subdivide the
  population into at least two different subgroups
  (or strata) so that subjects within the same
  subgroup share the same characteristics, then we
  draw a sample from each subgroup (or stratum).
• In cluster sampling, we first divide the
  population area into sections (or clusters), then
  randomly select some of those clusters, and then
  choose all the members from those selected
  clusters.

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Randomization and Other Sampling Strategies

• A multistage sample design involves the selection
  of a sample in different stages that might use
  different methods of sampling.

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Sampling Errors

• A sampling error is the difference between a
  sample result and the true population result
  such an error results from chance sample
  fluctuations.
• A nonsampling error occurs when the sample data
  are incorrectly collected, recorded, or analyzed.

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Should Polls Be Banned?

• What is your interest in polls about campaigns
  and elections?
• Very interested,
• Somewhat interested
• Little interest
• No interest
• What is your interest in polls which measure how
  Americans feel about the major political issues
  of the day, including those on which Congress is
  debating and voting.
• Very interested
• Somewhat interested
• Little interest
• No interest
• Do you favor banning the publication of the
  polling results prior to an election?
• Yes
• No

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Should Polls Be Banned? Results
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Our Interest in Polls

• 76 of Americans were interested in polls about
  campaigns and elections.
• 23 said they had little or no interest in polls
  about campaigns and elections.
• 77 of Americans were interested in the results
  of polls which measure how Americans feel about
  the major political issues of the day, including
  those on which Congress is debating and voting.
• 22 said they had little or no interest in polls
  about political issues of the day.

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Compare Results

• How do our results compare?
• What can account for any differences?