PA551

PA551

Analytic Methods in PA 1

Class Lectures Outline

Note: Files also supplementing these lecture notes include:

· PowerPoint files

· Class session instructor notes

Slide 1

Basic Statistics

Measurement

-- Professor Stipak presents --

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Slide 2

Simple Statistics Example

•

How do we report motor vehicle theft rates?

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Slide 3

Simple Statistics Example

•

How do we report motor vehicle theft rates?

•

Accepted practice: Thefts per 1000

population

•

Alternative: Thefts per 1000 motor vehicles

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Slide 4

Motor Vehicle Theft Rates:

Thefts / 1000 Population

22

Detroit

20

Los Angeles

19

Philadelphia

16

Chicago

12

New York City

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Slide 5

Motor Vehicle Theft Rates:

Thefts / 1000 Motor Vehicles

53

New York City

49

Philadelphia

47

Detroit

45

Chicago

34

Los Angeles

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Slide 6

Measurement:

Importance

Measurement

Data

Statistics

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Slide 7

Measurement:

Overview

•

Basic Concepts

•

Levels of Measurement

•

Validity/Reliability

Basic Concepts:

Objects……….UOA / Cases

Attributes……….Variables

A measuring process assigns a value to each attribute for each case.

Structure of data sets:

Rows – Cases

Columns – Variables

PA examples:

· Fire calls

· Employee records

· Client records

· Daily record of library use (time series data)

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Recording Data

· Show IBM Card, discuss as a medium for recording data

· Today: Enter data at a computer into a program—database, statistical, spreadsheet.

· What to enter?

· Numerical coding schemes

· Give example entering data from students

· Use both ratio and nominal data

· Lead into concept of levels of measurement

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

· Slide 9

Measurement:

Levels

•

Ratio

•

Interval

•

Ordinal

•

Nominal

Reference: Triola text, pp. 7-9; Statsoft Electronic Statistics Textbook, “Elementary Concepts—Measurement Scales”

Give Examples:

· Ratio: all counting variables--# of employees, size of budget

· Interval: temperature F(

· Ordinal: rating scales in questionnaire items

· Nominal: demographic and other classifications

Note: Different statistical methods require different levels of measurement.

Also note: Discrete vs. Continuous variables

____________________________________________________________________________________________________________________________________________________________________________________________________________________

Slide 10

Data In Public Agencies

•

Types of data in agencies

•

Sources of data

•

Types of datasets, examples:

census data, merged data

Distinctions for characterizing datasets:

· The UOA

· The variables

· Level of measurement of the variables

· Sample data vs. population data

· Cross-section vs. time series data

· Aggregated data vs. individual-level data (note aggregation changes UOA)

· Merged data vs. data from one source

· Types of merged datasets

1. several sources, same UOA

2. different UOA, aggregate up

· Example: school-level achievement and socio-demographic data

3. different UOA, append contextual data

Survey Research using Interviews / Questionnaires

· A very common way of data gathering

· Open vs. closed ended questions

· Art of designing questions: simple, clear, unbiased

· Examples of problem questions (real examples from questionnaires):

· “Does your department have a special recruitment policy for racial minorities and women?” (double-barreled)

· “Is anyone in your family a dipsomaniac?”

· “You don’t smoke, do you?”

· Strive for: short, simple, neutral wording

Examples Showing Complexity of Interpreting Interview Data

· “Metallic Metals Act” survey

· Most people are in favor of the Metallic Metals Act.

· Split ballot question on a national survey (1940)

· “Do you think the United States should forbid public speeches against democracy?”

· 54% Yes, 46% No

· “Do you think the United States should allow public speeches against democracy?”

· 25% Yes, 75% No

· Slide 11

Measurement:

Quality

•

Reliability of Measurement

•

Validity of Measurement

•

Measurement Error

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Measurement Quality

- Reliability, Validity, Measurement Error -

Reliability

· Refers to how consistent is a measure: repeatability

· Informal def.: How well we are measuring, whatever we are measuring

Validity

· Refers to whether a measure is measuring what it is supposed to measure

· A measure can be reliable, but not valid:

· Example: A count of the number of people entering a park would be an invalid measure of the frequency of park users if most people entering the park were merely walking through the park to go somewhere else.

· Note validity is in reference to a purpose.

· A person’s measured height could be a valid measure of one aspect of physical size, but not a valid measure of intelligence.

· Note validity problems for many PA purposes.

· E.g. measuring performance

· Performance measures for police agencies, ad hoc interpretation of crime statistics

· Use of spending figures for performance measures

· E.g. per capita student expenditures

Measurement Error

· Closely related to reliability and validity

· Sources of error:

· Recording errors

· Coding errors

· Response errors

· (Note: Sampling error is not a measurement error)

· High visibility / controversial examples in PA

· Census undercounts

· Crime rates: UCR vs. NCS

· Random error sources: mainly reliability threat

· Systematic (non-random) error sources: validity threat

· Example: Case Manager (COCAAN self-sufficiency program) asks clients each week in an assessment procedure about drug use.

Approaches to Assessing Reliability and Validity

Reliability

· Test-retest approach

· Split-half approach / Cronbach’s alpha

· Reliability coefficients

Validity

· Face validity

· Consensual validity

· Content validity (e.g. educational tests)

· Correlational validity / Predictive validity

· Compare measure to a criterion

· Example: Challenge to civil service tests based on lack of predictive validity

Computer Use

-- Professor Stipak presents --

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Computing Overview

General / Historical

· Mainframes, 1950’s

· PC’s, 1980’s

· Changes in user interface with computer

· Changes in computer applications

· 50’s: billing, scientific res

· 80’s: word processing, spreadsheets

· 90’s: internet applications

Computer Use in Public Agencies

· Ask class: examples of what you do

· Note applications people use

Computer Use in PA551

· Note two possible purposes

· Personal skill development

· Understanding

· Spreadsheet Software

· Statistical Analysis Software

Spreadsheet Use Overview

· Resources: Triola, Dretzke, other

· Set up Remedial Lab Session

General Spreadsheet Concepts / Excel Demo

· Two activities: executing commands, entering/editing cell contents

· Cell addresses

· Cell entries

· Numbers

· Text/labels

· Formulas, including functions

· How to tell what is in a cell?

· Excel spreadsheet: CellContents.xls

· Copying cells

· Relative vs. absolute cell references

Basic Statistics

Descriptive

Statistics

-- Professor Stipak presents --

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Descriptive Statistics

Compare to Inferential Statistics

Purpose: Summarize, Describe

Frequency Distribution Tables

· Raw frequency distribution (count)

· Cumulative frequency distribution

· Percent frequency distribution

· Relative frequency distribution—use proportions, not percents

· Cumulative percent frequency distribution

Graphs of Frequency Distributions

· Most common—bar graph, a histogram

· Frequency polygon leads to idea of line graph of frequency distribution, pictures of distributions

Characteristics of Frequency Distributions

1. Shape

2. Central Tendency

3. Spread

Shape of Frequency Distribution

· Symmetrical vs. skewed

· Bi-modal, multi-modal

Measures of Central Tendency

· Mean

· Median (50th percentile)

· Mode

· Relate to level of measurement

· Relate to shape of distribution, skew, outliers

Measures of Spread

· Range

· Standard deviation, spread

Exploratory Data Analysis as an alternative to classic statistics (Triola, p. 109)

Concept of a z-score, a standardized score

· See Triola, Formula 5-2, p. 256

· See Triola, alternative 5-2 formula, p. 265

Basic Statistics

Inferential

Statistics

-- Professor Stipak presents --

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Probability

Expresses likelihood on a 0-1 scale.

Relative frequency distribution shows the probability of different values.

· Can call it a probability distribution

Empirical (actual) probability distributions

· Many different shapes

Tabled, mathematical probability distributions as tools

· To study real distributions

· To study special distributions in statistical inference—sampling distributions

Normal Probability Distribution—most important tabled distribution

· Must be able to read table for the Standard Normal Distribution

· Must be able to work simple problems with this table

· Triola, pp. 254-256, 261-264, 268-270

· SHOW Triola VIDEO: CD 5, file 5_1

· Also show: 5_2 and 5_3, beginning, for other instructorss

Sampling Distributions

Population parameters vs. sample statistics

· Carefully use different symbols to distinguish sample mean vs. population mean, sample standard deviation vs. population standard deviation

Definition of a sampling distribution: distribution of a sample statistic across repeated samples

Attempt to clarify concept of a sampling distribution:

· Three distributions in any problem of statistical inference:

1. Population distribution

2. Sample distribution

3. Sampling distribution

· Try to visualize idea of a sampling distribution with an in-class demo

Sampling Distribution of the Mean (Triola, p. 272)

· Shape: CLT ~normal (if n large)

· Mean = population mean (under CRS)

· Standard deviation = sigma/sq rt(n)

Sampling Distribution of the Proportion

· Shape: ~normal (if n large)

· Mean = population proportion (under CRS)

· Standard deviation = sqrt(P*(1-P)/n)

Work Sampling Distribution Problems

· For mean (Triola, pp. 278-281)

· For proportion

PAGE

28

_1063127566.ppt

Motor Vehicle Theft Rates:

Thefts / 1000 Motor Vehicles

Los Angeles34

Chicago45

Detroit47

Philadelphia49

New York City53

_1063128570.ppt

Measurement: Levels

Ratio

Interval

Ordinal

Nominal

_1063140629.ppt

Computer Use

-- Professor Stipak presents --

1.bin

_1063140720.ppt

Basic Statistics

Descriptive Statistics

-- Professor Stipak presents --

1.bin

_1063140838.ppt

Basic Statistics

Inferential Statistics

-- Professor Stipak presents --

1.bin

_1063138987.ppt

Basic Statistics

Measurement

-- Professor Stipak presents --

1.bin

_1063127571.ppt

Measurement: Overview

Basic Concepts

Levels of Measurement

Validity/Reliability

_1063128569.ppt

Data In Public Agencies

Types of data in agencies

Sources of data

Types of datasets, examples: census data, merged data

_1063128568.ppt

Measurement: Quality

Reliability of Measurement

Validity of Measurement

Measurement Error

_1063127569.ppt

Measurement: Importance

Measurement

Data

Statistics

_1063127562.ppt

Simple Statistics Example

How do we report motor vehicle theft rates?

Accepted practice: Thefts per 1000 population

Alternative: Thefts per 1000 motor vehicles

_1063127564.ppt

Motor Vehicle Theft Rates:

Thefts / 1000 Population

New York City12

Chicago16

Philadelphia19

Los Angeles20

Detroit22

_1063127560.ppt

Simple Statistics Example

How do we report motor vehicle theft rates?