Sta 291 summer 2010
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STA 291 Summer 2010. Lecture 1 Dustin Lueker. Topics. Statistical terminology Descriptive statistics Probability and distribution functions Inferential statistics Estimation (confidence intervals) Hypothesis testing Simple linear regression and correlation. Why study Statistics?.

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STA 291 Summer 2010

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Sta 291 summer 2010

STA 291Summer 2010

Lecture 1

Dustin Lueker


Topics

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

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

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

  • Accidentally misused

    • Using inappropriate methods

      • Vital to understand a method before using it

STA 291 Summer 2010 Lecture 1


What is statistics

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

General Statistical Methodology

STA 291 Summer 2010 Lecture 1


Basic terminology

Basic Terminology

  • Population

    • Total set of all subjects of interest

      • Entire group of people, animals, products, etc. about which we want information

  • 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 terminology1

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

  • Parameter

    • Numerical characteristic of the population

      • Calculated using the whole population

  • Statistic

    • Numerical characteristic of the sample

      • Calculated using the sample

STA 291 Summer 2010 Lecture 1


Data collection and sampling theory

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

STA 291 Summer 2010 Lecture 1


Example

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

‘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

STA 291 Summer 2010 Lecture 1


Example1

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

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

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

  • 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

STA 291 Summer 2010 Lecture 1


Quantitative variables

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

STA 291 Summer 2010 Lecture 1


Example2

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

STA 291 Summer 2010 Lecture 1


Example3

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

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

STA 291 Summer 2010 Lecture 1


Other notes on variable types

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

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

  • 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

STA 291 Summer 2010 Lecture 1


Examples

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

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)

STA 291 Summer 2010 Lecture 1


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