Math 205 Introduction to Statistical Methods

Online homework: My webpage: people.adams.edu/~rjastalos

“There are three kinds of lies: lies, damned lies, and statistics.” Mark Twain

How to lie with statistics Darrell Huff, 1954 How to tell the liars from the statisticians Robert Hooke, 1983 Book Titles

“You can make statistics show anything!”

On a piece of paper: No names or identifying numbers! 1. height (inches)

On a piece of paper: No names or identifying numbers! 1. height (inches) 2. eye color

On a piece of paper: No names or identifying numbers! 1. height (inches) 2. eye color 3. age

On a piece of paper: No names or identifying numbers! 1. height (inches) 2. eye color 3. age 4. IQaverage is 100 Einstein was probably 160 – 170 pretty smart ~

On a piece of paper: No names or identifying numbers! 1. height (inches) 2. eye color 3. age 4. IQaverage is 100 Einstein was probably 160 – 170 pretty smart ~ shoe size

On a piece of paper: No names or identifying numbers! 1. height (inches) 2. eye color 3. age 4. IQaverage is 100 Einstein was probably 160 – 170 pretty smart ~ shoe size 6. gender

On a piece of paper: No names or identifying numbers! 1. height (inches) 2. eye color 3. age 4. IQaverage is 100 Einstein was probably 160 – 170 pretty smart ~ shoe size 6. gender 7. state of birth (or country, if outside U.S.)

Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions. Individuals are the people or objects included in the study A variable is the characteristic of the individual to be measured

A quantitative variable has a value or numerical measurement for which mathematical operations make sense A qualitative variable describes an individual by placing the individual into a category or group

Personal Data: 1. height 2. eye color 3. age 4. IQ 5. shoe size 6. gender 7. state of birth

In population data, the variable is measured for every individual of interest “population” = every individual of interest In sample data, the variable is measured for only some individuals of interest “sample” = a subset of the population

A parameter is a numerical description of a population characteristic. A statistic is a numerical description of a sample characteristic. parameter  population statistic  sample

A statistic is assumed to be an approximation of a parameter.

Descriptive statistics involves methods of organizing, picturing, and summarizing information from samples or populations Inferential statistics involves methods of using information from a sample to draw conclusions regarding the population Probability is a basic tool of inferential statistics.

Nominal level of measurement: Qualitative only Categorized using names, labels, or qualities NO mathematical computations can be made

Nominal level of measurement: Qualitative only Categorized using names, labels, or qualities NO mathematical computations can be made Ordinal level of measurement: Qualitative or quantitative Can be arranged in order Differences between data entries are not meaningful

Personal Data: 1. height 2. eye color 3. age 4. IQ 5. shoe size 6. gender 7. state of birth

Interval level of measurement: Quantitative Can be ordered & subtracted The zero is arbitrary

Interval level of measurement: Quantitative Can be ordered & subtracted The zero is arbitrary Ratio level of measurement: Quantitative, similar to interval data Can be ordered, subtracted, & divided Zero really means zero!

Personal Data: 1. height 2. eye color 3. age 4. IQ 5. shoe size 6. gender 7. state of birth

Level of measurement Put data in categories Arrange data in order Subtract data values Determine if one value is a multiple of another NominalYesNo OrdinalYes No IntervalYes No RatioYes