Introduction to Statistics

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Chapter 1

• Introduction to Statistics

• 1.1 An Overview of Statistics
• 1.2 Data Classification
• 1.3 Experimental Design

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Section 1.1 and 1.2

• An Overview of Statistics
• Classifying Data
• Critical Thinking

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What is Statistics?

• Statistics
• The science of collecting, organizing, analyzing,
  and interpreting data in order to make decisions.

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Definitions
Population The collection of all outcomes,
responses, measurements, or counts that are of
interest.
Sample The collection of data from a subset of
the population.
Census The collection of data from every member
of the population.
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Example Identify the population, and whether a
census or sample would be done.

• 1. HCC is doing a study on how many credit hours
  a HCC student is taking.
• 2. HCC is doing a study on many hours a week a
  HCC student is working.
• A fashion magazine gathers data on the price of
  womens jeans.

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What is Data?

• Data
• The responses, counts, measurements, or
  observations that have been collected.
• Data can be classified as one of 2 types

1. Qualitative Data 2. Quantitative Data
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Qualitative Data

• Qualitative Data Consists of non-numeric,
  categorical attributes or labels

Major
Place of birth
Eye color
Common statistic calculated percentages
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Quantitative Data

• Quantitative data Numerical measurements or
  counts.

Temperature
Weight of a letter
Age
Common statistic calculated averages
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Quantitative DataDiscrete vs. Continuous

• Discrete data finite number of possible data
  values 0, 1, 2, 3, 4.
• ex Number of classes a student is taking

Continuous data infinite number of possible data
values on a continuous scale ex Weight of a
baby
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Parameters and Statistics

• Parameter
• A number that describes some characteristic of an
  entire population.
• Average age of all people in the United States

Statistic A number that describes some
characteristic from a sample. Average age of
people from a sample of three states
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• Ex Parameters vs. Statistics

Decide whether the numerical value describes a
population parameter or a sample statistic.

1. The average credit load of all HCC full-time
   students is 14.2 credit hours.
2. From a sample of 300 HCC full-time students
   showed the average work hours a week is 18.3
   hours.
3. A gallup poll of 1012 adults nationwide showed
   34 owned a handgun.

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White House 2008 Republican Nomination        

Pew Research Center for the People the Press survey conducted by Princeton Survey Research Associates International. Dec. 19-30, 2007. N471 registered voters nationwide who are Republicans or lean Republican. MoE 5.
"I'm going to read you the names of some Republican presidential candidates. Which one of the following Republican candidates would be your first choice for president see below?" If unsure "Just as of today, would you say you lean toward see below?" (Names were rotated)
Candidate Percent
John McCain 22
Rudy Giuliani 20
Mike Huckabee 17
Mitt Romney 12
Fred Thompson 9
Ron Paul 4
Duncan Hunter 1
Other (vol) 1
None (vol.) 2
Unsure 12
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Branches of Statistics
Descriptive Statistics Involves organizing,
summarizing, and displaying data. Describes the
important characteristics of the data. e.g.
Tables, charts, averages, percentages
Inferential Statistics Involves using sample
data to draw conclusions or make inferences about
an entire population.
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Example Descriptive and Inferential Statistics

• Decide which part of the study represents the
  descriptive branch of statistics. What
  conclusions might be drawn from the study using
  inferential statistics?

A sample of Illinois adults showed that 22.7 of
those with a high school diploma were obese, and
16.7 of college graduates were obese. (Source
Illinois BRFSS, 2004)
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Example Descriptive and Inferential Statistics

• Decide which part of the study represents the
  descriptive branch of statistics. What
  conclusions might be drawn from the study using
  inferential statistics?

A sample of 471 registered republicans showed
that 22 would pick John McCain as the republican
nominee for president. (Margin of error 5).
(Source USA Today/CNN poll)
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Uses of Statistics

• Almost all fields of study benefit from the
  application of statistical methods
• Statistics often lead to change

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Misuses of Statistics

• Bad Samples
• Small Samples
• Misleading Graphs
• Pictographs
• Loaded Questions
• Correlation Causality
• Self Interest Study

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Misuse Bad Samples

• Samples must be unbiased and fairly represent the
  entire population.
• If the data is not collected appropriately, the
  data may be completely useless. Garbage in,
  garbage out

• Voluntary response sample Respondents
  themselves decide whether to be included in the
  sample
• Ex. Online surveys
• Ex. Ratemyprofessor.com

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Misuse Misleading Graphs
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CNN/USA Today Gallup poll on Terri Schiavo (March
2005)
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CNN/USA Today Gallup poll on Terri Schiavo
(March 2005) Reprinted
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Misuse Pictographs
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Misuse Loaded Questions
Should the President have the line item veto to
eliminate waste? (97 said yes
) Should the President have the line item
veto? (57 said yes )
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Misuse Loaded Questions
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Misuse Correlation does not imply Cause and
Effect
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Misuses Self Interest and Deliberate Distortions
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Section 1.3

• Experimental Design

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Designing a Statistical Study

1. What is it you want to study?
2. What is the population to gather data from?
3. Collect data. If you use a sample, it must be
   representative of the population.
4. Descriptive Statistics organize, present,
   summarize data
5. Inferential Statistics draw conclusions about
   the population based on sample data

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Things to Consider with Samples

1. The sample must be unbiased and fairly represent
   the entire population.
2. If the data is not collected appropriately, the
   data may be completely useless. Garbage in,
   garbage out
3. Want the maximum information at the minimum cost.
   What sample size is needed?

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Methods of Collecting Data

• Observational study
• Survey
• Experiment
• Simulation

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Methods of Collecting Data

• Observational study
• A researcher observes or measures characteristics
  of interest of part of a population but does not
  change any existing conditions.
• Experiment
• A treatment is applied to part of a population
  and responses are observed.

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Methods of Collecting Data

• Survey
• An investigation of one or more characteristics
  of a population, usually be asking people
  questions.
• Commonly done by interview, mail, or telephone.
• Simulation
• Uses a mathematical or physical model to
  reproduce the conditions of a situation or
  process. Often involves the use of computers.

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Example Methods of Data Collection

• Consider the following studies. Which method of
  data collection would you use to collect data for
  each study?

1. A study of salaries of NFL players.
2. A study of the emergency response times during a
   terrorist attack.
3. A study of whether changing teaching techniques
   improves FCAT scores.
4. A study of whether Tampa residents support a mass
   transit system.

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Sampling Techniques

• Random versus Non-Random Samples
• Convenience Samples
• Simple Random Samples
• Systematic Samples
• Cluster Samples

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Random and Non-Random Sampling

• Random Sampling
• Every member of the population has an equal
  change of being selected.
• Non-Random Sampling
• Some members of the population have no chance of
  being picked. Often leads to biased samples.

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Convenience Samples

• Data is collected that is readily available and
  easy to get.
• Self-selected surveys or voluntary response
  surveys (online surveys, magazine surveys,
  1-800-Verdict, Ratemyprofessor.com)

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Simple Random Sample

• A random sample where every member of the
  population and every group of the same size has
  an equal chance of being selected.
• Usually involves using a random number generator.

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Simple Random Sampling

• Number each element of the population from 1 to
  N.
• Use a random number generator (table, calculator,
  computer) to randomly selected a sample of size
  n.
• TI-83/4 randint (1,N,n), or
• Table 1 in text. Pick a random start.

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Systematic Sampling

• Choose a starting value at random. Then
• choose every kth member of the population.

• example Select every 3rd patient who enters the
  ER.

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Stratified Sampling

• Divide a population into at least 2 different
  subgroups (strata) that share the same
  characteristics (age, gender, ethnicity, income,
  etc) and select a random sample from each group.
  
• Advantages More information

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Cluster Sampling

• Divide the population into many like subgroups
  (clusters) randomly select some of those
  clusters, and then select all of the members of
  those clusters to be in the sample.
• Advantage geographically separately populations

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Sources of Error in Sampling

• Sampling Error
• the expected difference between a sample result
  and the true population result. (e.g.
  Margin of error).

• Non-Sampling Error
• sample data is incorrectly gathered, collected,
  or recorded.
• Selection Bias - bad sample
• Response Bias- bad data incorrect responses,
  inaccurate measurements,
• etc.)