chapter 1 introduction to statistics 1 larson/farber 4th ed. 1.1 an overview of statistics 1.2 data...

Chapter 1Introduction to Statistics

1Larson/Farber 4th ed.

• 1.1 An Overview of Statistics

• 1.2 Data Classification

• 1.3 Experimental Design

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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DefinitionsPopulation 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.

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.

3. A fashion magazine gathers data on the price of women’s jeans.

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 Data2. 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

Quantitative DataQuantitative data: Numerical measurements or counts.

Age Weight of a letter Temperature

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Common statistic calculated: averages

Quantitative Data:Discrete vs. Continuous

Discrete data: finite number of possible data values: 0, 1, 2, 3, 4….

ex: Number of classes a student is taking

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Continuous data: infinite number of possible data values on a continuous scale

ex: Weight of a baby

Parameters and StatisticsParameter 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 characteristicfrom 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.

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. N=471 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%

Branches of StatisticsDescriptive 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.

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

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

Misuses of Statistics

Misuse: Bad Samples

• Voluntary response sample : Respondents themselves decide whether to be included in the sample

• Ex. Online surveys• Ex. Ratemyprofessor.com

• 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”

Misuse: Misleading Graphs

CNN/USA Today Gallup poll on Terri Schiavo (March 2005)

CNN/USA Today Gallup poll on Terri Schiavo

(March 2005) Reprinted

Misuse: Pictographs

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: )

Misuse: Loaded Questions

Misuse: Correlation does not imply Cause and Effect

Misuses: Self Interest and Deliberate Distortions

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 CollectionConsider 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.

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)

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.

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.

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

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

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 sampleResponse Bias- bad data: incorrect

responses, inaccurate measurements, etc.)