A Statistical Investigation

1. State your claim

2. Collect your data

3. Calculate the appropriate values

4. Run the tests to see if we accept or reject the claim

A Statistical Investigation

Starts with a claim

• South students are smart!!

• “But all the kids have their own car!!”

Or a question

• Are Japanese cars safer than European cars?

• Is chocolate more popular that vanilla?

Claims need to be…

• Specific– We need a specific definition of the attribute

• Measurable and comparable– The attribute has to be numerically measureable.

– Comparing two measurements has to be meaningful

• Have a benchmark– We have to compare our measurement with some value, or

– With another measurement from some other group

Claims:

• Specific

• Measurable and comparable

• Have a benchmark

Claims:

• Specific

• Measurable and comparable

• Have a benchmark

Claims:

• Specific

• Measurable and comparable

• Have a benchmark

Claims:

• Specific

• Measurable and comparable

• Have a benchmark

Homework

• Rewrite the following claims so that they are specific, measureable, and comparable with a benchmark etc.– Most students can access the internet

– Swine flu is dangerous

– Manny Ramirez is a good hitter

– The planet is getting warmer

– Movies starring George Clooney are popular

– A man’s best friend is his dog

– Blondes have more fun

Basic Definitions: Population

• Population– The entire group to be studied

• Census– A collection of data and information from the population

• Parameter– A numeric measurement or calculation of census data

– Quantifies an attribute of the population

Basic Definitions: Sample

• Fundamental concept– A census may not be possible or practical

• Sample– (Noun) A subset of a population that (we hope) represents

the population

– (Verb) The process of collecting data from the subset.

• Statistic– A numeric measurement or calculation of sample data

– Estimates the parameter of a population

Another Fundamental Concept

• We are never 100% sure that our sample exactly represents the population

• So a statistic is just an estimate

• We will learn many techniques to deal with this uncertainty

Classifying data

• Data classification determines the parameters or statistics we can calculate.

• Evaluate the quality of the data– Does the reported value match the characteristic?

– Does the reported value have the correct precision?

• Three classifications:– Quantitative or qualitative

– Continuous or discrete

– Nominal, ordinal, interval, or ratio

1. Classifying Data: Quantitative or qualitative

• Quantitative– Measurements or counts

• Qualitative– Choices

2. Classifying Data: Discrete or continuous

• Discrete– Finite set of values

– Gaps in the sequence

– “Integer” (Fractions don’t make sense)

– Counts

• Continuous– Infinite set of values

– “Decimal”

– Measurements

3. Classifying Data: Nominal, ordinal, interval, ratio

• Nominal– Can not be ordered, or ordering the data doesn’t make

sense, except to make it easier to locate

– Example: Favorite color

• Ordinal measurements– Can be ordered

– The differences between two measurements is meaningless

– Example class rank

Classifying Data

• Interval measurements– Measurements can be ordered and the interval between

measurements is meaningful

– E.g., temperature

• Ratio measurements– A zero measurement means ‘none’

– E.g., Income

For example

Measurement Qualitative or quantitative

Discrete or continuous

Nominal, ordinal, interval, or ratio

Approval rating

pH

Velocity

Homework

• On-line, go to the web site