Introduction to Statistics
•
1.1 An Overview of Statistics
•
1.2 Data Classification
•
1.3 Experimental Design
Larson/Farber 4th ed.
1

Larson/Farber 4th ed.
An Overview of Statistics
Classifying Data
Critical Thinking
2

The science of collecting, organizing, analyzing, and interpreting data in order to make decisions.
Larson/Farber 4th ed.
3

The collection of all outcomes, responses, measurements, or counts that are of interest.
The collection of data from a subset of the population.
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.

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
Larson/Farber 4th ed.
6

Qualitative Data : Consists of non-numeric, categorical attributes or labels
Major Place of birth Eye color
Common statistic calculated: percentages

Quantitative data: Numerical measurements or counts.
Age
Weight of a letter Temperature
Common statistic calculated: averages
Larson/Farber 4th ed.
8

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
Larson/Farber 4th ed.
9

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
11

Decide whether the numerical value describes a population parameter or a sample statistic.
1.
The average credit load of all HCC fulltime 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
Rudy Giuliani
Mike Huckabee
Mitt Romney
Fred Thompson
Ron Paul
Duncan Hunter
Other (vol)
None (vol.)
Unsure
22%
20%
17%
12%
9%
4%
1%
1%
2%
12%

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.

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)
Larson/Farber 4th ed.
15

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)
Larson/Farber 4th ed.
16

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

• 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

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

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

“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: )

Larson/Farber 4th ed.
Experimental Design
30

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
Larson/Farber 4th ed.
31

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?
Larson/Farber 4th ed.
32

• Observational study
• Survey
• Experiment
• Simulation
Larson/Farber 4th ed.
33

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.
Larson/Farber 4th ed.
34

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.
Larson/Farber 4th ed.
35

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.

• Random versus Non-Random Samples
• Convenience Samples
• Simple Random Samples
• Systematic Samples
• Cluster Samples
Larson/Farber 4th ed.
37

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.
38 Larson/Farber 4th ed.

• 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)

• 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. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

• 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.

Choose a starting value at random. Then choose every k th member of the population.
• example: Select every 3 rd patient who enters the ER.

• 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

• 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

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 Biasbad data: incorrect responses, inaccurate measurements, etc.)