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Topics

- Statistical terminology
- Descriptive statistics
- Probability and distribution functions
- Inferential statistics
- Estimation (confidence intervals)
- Hypothesis testing

- Simple linear regression and correlation

STA 291 Summer 2010 Lecture 1

Why study Statistics?

- Research in all fields is becoming more quantitative
- Research journals
- Most graduates will need to be familiar with basic statistical methodology and terminology

- Newspapers, advertising, surveys, etc.
- Many statements contain statistical arguments

- Computers make complex statistical methods easier to use

STA 291 Summer 2010 Lecture 1

Lies, Damn Lies, and Statistics

- Many times statistics are used in an incorrect and misleading manner
- Purposely misused
- Companies/people wanting to further their agenda
- Cooking the data
- Completely making up data

- Massaging the numbers
- Altering values to get desired result

- Cooking the data

- Companies/people wanting to further their agenda
- Accidentally misused
- Using inappropriate methods
- Vital to understand a method before using it

- Using inappropriate methods

STA 291 Summer 2010 Lecture 1

What is Statistics?

- Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data
- Applicable to a wide variety of academic disciplines
- Physical sciences
- Social sciences
- Humanities

- Statistics are used for making informed decisions
- Business
- Government

STA 291 Summer 2010 Lecture 1

General Statistical Methodology

STA 291 Summer 2010 Lecture 1

Basic Terminology

- Population
- Total set of all subjects of interest
- Entire group of people, animals, products, etc. about which we want information

- Total set of all subjects of interest
- Elementary Unit
- Any individual member of the population

- Sample
- Subset of the population from which the study actually collects information
- Used to draw conclusions about the whole population

STA 291 Summer 2010 Lecture 1

Basic Terminology

- Variable
- A characteristic of a unit that can vary among subjects in the population/sample
- Ex: gender, nationality, age, income, hair color, height, disease status, state of residence, grade in STA 291

- A characteristic of a unit that can vary among subjects in the population/sample
- Parameter
- Numerical characteristic of the population
- Calculated using the whole population

- Numerical characteristic of the population
- Statistic
- Numerical characteristic of the sample
- Calculated using the sample

- Numerical characteristic of the sample

STA 291 Summer 2010 Lecture 1

Data Collection and Sampling Theory

- Why take a sample? Why not take a census? Why not measure all of the units in the population?
- Accuracy
- May not be able to find every unit in the population

- Time
- Speed of response from units

- Money
- Infinite Population
- Destructive Sampling or Testing

- Accuracy

STA 291 Summer 2010 Lecture 1

Example

- University Health Services at UK conducts a survey about alcohol abuse among students
- 200 of the students are sampled and asked to complete a questionnaire
- One question is “have you regretted something you did while drinking?”
- What is the population?
- What is the sample?

STA 291 Summer 2010 Lecture 1

‘Flavors’ of Statistics

- Descriptive Statistics
- Summarizing the information in a collection of data

- Inferential Statistics
- Using information from a sample to make conclusions/predictions about the population
- Ex: using a sample statistic to estimate a population parameter

- Using information from a sample to make conclusions/predictions about the population

STA 291 Summer 2010 Lecture 1

Example

- The Current Population Survey of about 60,000 households in the United States in 2002 distinguishes three types of families: Married-couple (MC), Female householder and no husband (FH), Male householder and no wife (MH)
- It indicated that 5.3% of “MC”, 26.5% of “FH”, and 12.1% of “MH” families have annual income below the poverty level
- Are these numbers statistics or parameters?

- The report says that the percentage of all “FH” families in the USA with income below the poverty level is at least 25.5% but no greater than 27.5%
- Is this an example of descriptive or inferential statistics?

STA 291 Summer 2010 Lecture 1

Scales of Measurement

- Quantitative or Numerical
- Variable with numerical values associated with them

- Qualitative or Categorical
- Variables without numerical values associated with them

STA 291 Summer 2010 Lecture 1

Qualitative Variables

- Ordinal
- Disease status, company rating, grade in STA 291
- Ordinal variables have a scale of ordered categories, they are often treated in a quantitative manner (A = 4.0, B = 3.0, etc.)
- One unit can have more of a certain property than another unit

- Ordinal variables have a scale of ordered categories, they are often treated in a quantitative manner (A = 4.0, B = 3.0, etc.)

- Disease status, company rating, grade in STA 291
- Nominal
- Gender, nationality, hair color, state of residence
- Nominal variables have a scale of unordered categories
- It does not make sense to say, for example, that green hair is greater/higher/better than orange hair

- Nominal variables have a scale of unordered categories

- Gender, nationality, hair color, state of residence

STA 291 Summer 2010 Lecture 1

Quantitative Variables

- Quantitative
- Age, income, height
- Quantitative variables are measured numerically, that is, for each subject a number is observed
- The scale for quantitative variables is called interval scale

- Quantitative variables are measured numerically, that is, for each subject a number is observed

- Age, income, height

STA 291 Summer 2010 Lecture 1

Example

- A study about oral hygiene and periodontal conditions among institutionalized elderly measured the following
- Nominal (Qualitative): Requires assistance from staff?
- Yes
- No

- Ordinal (Qualitative): Plaque score
- No visible plaque
- Small amounts of plaque
- Moderate amounts of plaque
- Abundant plaque

- Interval (Quantitative): Number of teeth

- Nominal (Qualitative): Requires assistance from staff?

STA 291 Summer 2010 Lecture 1

Example

- A birth registry database collects the following information on newborns
- Birth weight: in grams
- Infant’s Condition:
- Excellent
- Good
- Fair
- Poor

- Number of prenatal visits
- Ethnic background:
- African-American
- Caucasian
- Hispanic
- Native American
- Other

- What are the appropriate scales? Quantitative (Interval) Qualitative (Ordinal, Nominal)

STA 291 Summer 2010 Lecture 1

Importance of Different Types of Data

- Statistical methods vary for quantitative and qualitative variables
- Methods for quantitative data cannot be used to analyze qualitative data
- Quantitative variables can be treated in a less quantitative manner
- Height: measured in cm/in
- Interval (Quantitative)

- Can be treated at Qualitative
- Ordinal:
- Short
- Average
- Tall

- Nominal:
- <60in or >72in
- 60in-72in

- Ordinal:

- Height: measured in cm/in

STA 291 Summer 2010 Lecture 1

Other Notes on Variable Types

- Try to measure variables as detailed as possible
- Quantitative

- More detailed data can be analyzed in further depth
- Caution: Sometimes ordinal variables are treated as quantitative (ex: GPA)

STA 291 Summer 2010 Lecture 1

Discrete Variables

- A variable is discrete if it can take on a finite number of values
- Gender
- Nationality
- Hair color
- Disease status
- Grade in STA 291
- Favorite MLB team
- Qualitative variables are discrete

STA 291 Summer 2010 Lecture 1

Continuous Variables

- Continuous variables can take an infinite continuum of possible real number values
- Time spent studying for STA 291 per day
- 43 minutes
- 2 minutes
- 27.487 minutes
- 27.48682 minutes
- Can be subdivided into more accurate values
- Therefore continuous

- Time spent studying for STA 291 per day

STA 291 Summer 2010 Lecture 1

Examples

- Number of children in a family
- Distance a car travels on a tank of gas
- % grade on an exam

STA 291 Summer 2010 Lecture 1

Discrete or Continuous

- Quantitative variables can be discrete or continuous
- Age, income, height?
- Depends on the scale
- Age is potentially continuous, but usually measured in years (discrete)

- Depends on the scale

STA 291 Summer 2010 Lecture 1

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