Quantitative Methods & Analysis



“The government is very keen on amassing statistics.  They will collect them, raise them to the nth power, take the cube root, and prepare wonderful diagrams.  But you must never forget that every one of these figures comes in the first instance from the village watchman, who just puts down what he pleases.” 

Sir Josiah Stamp, Inland Revenue Department, England (1896-1919)


Research methods & techniques (see http://krypton.mnsu.edu/~tony/courses/609Design.html%20)

·        Control/randomization

·        Cross-sectional & longitudinal design

·        Quasi-experimental design

·        Operational definition

·        Variables:  independent (x), dependent (y), intervening

·        Relationships:  linear, curvilinear, bivariate, multivariate

·        Spurious relationships

·        Validity:  internal (control), external (representativeness)

·        Reliability (replicability)

Collecting Data

·        Nominal (categories)

·        Ordinal (rank order)

·        Interval & ratio

Analyzing Information

Descriptive Statistics (see http://krypton.mnsu.edu/~tony/courses/609StatsI.html%20)

·        Parameter (scale factor) vs. statistic (summary measure)

·        Range & variance

·        Measures of central tendency: 

o       Mean, median, mode

o       Standard deviation & coefficient of variation (sd/mn)

·        Kurtosis (platykurtic [flat], leptokurtic [peaked], & skew)

Significance Testing

·          Null hypothesis

·        Significance level

·        Type I (reject true null) & Type II (accept false null) error

·        One-tail/two-tail test

·        Sample size

·        Standard error of mean (confidence interval)

·        T-test of difference of means

·        Central limit theorem

·        Significance vs. measures of association

Nonparamteric Statistics

·        Chi-square

·        Rank-order correlation (Spearman’s r)

Parametric Statistics (see http://krypton.mnsu.edu/~tony/courses/609StatsII.html )

·        Normal curve (50+ observations)

·        General linear model (regression line)

·        Homoscedasticity & independence

·        Scattergram

·        Correlation (y=a+bx+u)

·        Multiple regression (y=a+b1x1+b2x2…+u)

·        Partial correlation coefficient & beta weight

·        Analysis of variance

·        Factor analysis

·        Logit/analysis of covariance

·        Data transformations & z-scores



Choosing Inductive Statistics:



                                      categorical               interval





R, r








Teri Renner, Statistics Unraveled  (Washington, DC:  ICMA, 1988)


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Population Projection

(see http://krypton.mnsu.edu/~tony/courses/609Pop.html )


·                    Simple

    • Linear

o       Exponential

o       Modified exponential

o       Gompertz

·                                                                    Composite

Composite Method

·                                                                                            P = P + NI + NM

·                                                                                            Net Migration (NM) = inmigration – outmigration

·                                                                                            Natural Increase (NI) = births – deaths

·                                                                                            Births = Women of childbearing age * net reproduction rate

·                                                                                            Net reproduction rate = fertility – infant mortality

·                                                                                            Replacement rate

Cohort Survival Method

·        Cohort

·        Survival rate

·        Population pyramids


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Employment Projection

Economic Base (Export Base) Models

·        Basic & nonbasic employment

·        Basic (export) multiplier

·        Methods

o       Survey

o       Location quotient

o       Minimum requirements

o       assumptions

·        Location Quotient

o       LQ = local share / national share


Shift-Share Analysis

·          National share

·          Industry shift


Employment Projection & Impact Analysis

·          Employment = Total Output / Output per Worker

·          Allocate base employment

·          Allocate basic housing

·          Allocate service employment

·          Allocate service housing



Michael Greenberg, et alii, Local Population and Employment Projection Techniques (Rutgers NJ:  CUPR Press, 1978)


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Program Analysis

(see http://krypton.mnsu.edu/~tony/courses/609Benefit.html )

Benefit/Cost Analysis

Ratio of benefits to costs


·                                   All costs & benefits are explicit, finite, and quantifiable

·                                   Comparable projects

·                                   Optimality

·                                   “do-nothing” option

·                                   No complementarities



·               Market prices

·               Dead-weight loss

·               Intangibles

·               Differential impacts (use weights)

·               Externalities (sum weighted effects)

·               Project constraints (linear programming)

·               Indivisibilities (treat as a constraint)

·               Cost vs. “negative benefit”


Long-Term Analysis

·               Time-value of money

·               Discounting (PV = FV / (1+i)^n)

·               Opportunity costs

·               Inflation

Cost-Effectiveness Analysis

Benefits not calibrated in monetary units—programs must have similar goals

Cost-Revenue Analysis

Benefits measured only by discounted future stream of revenues—focus on profitabiilty

Fiscal Impact Analysis

(see http://krypton.mnsu.edu/~tony/courses/609Fiscal.html )

Estimation of difference between public costs and public revenues generated by a development project for the locality in which it occurs.

·          Case Study Method

1.      Most accurate

2.      Most expensive

·          Average Cost Methods (Per Capita Multiplier; Service Standards)

1.      Steady growth (+/-)

2.      Past predicts the future

3.      Usually for residential projects

·          Marginal Cost Methods (Comparable City; Employment Anticipation)

1.      Large project—past is no guide

2.      Significant unused capacity or no remaining marginal capacity



J.A. Schofield, Cost Benefit Analysis in Urban & Regional Planning (London:  Allen & Unwin, 1987)

Edith Stokey & Richard Zeckhauser, A Primer for Policy Analysis (NY:  WW Norton, 1978)


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Capital Improvement Programming (CIP)

(see http://krypton.mnsu.edu/~tony/courses/609CIP.html )


Essentially, a political process of trying to determine who will get what when and how:

·        Generate a list of projects (and their costs)

·        Rank the projects

o       Criteria

o       Weights

·        Allocate available funds

o       By fund

o       Debt capacity

·        Capital reserve account



Project Management

(see http://krypton.mnsu.edu/~tony/courses/609PERT.html )

PERT (Program Evaluation & Review Technique)

  1. define tasks
  2. link in sequence
  3. estimate time to complete each task
  4. estimate
  5. find slack time (difference between expected time and latest time)
  6. find probability of meeting expected time


CPM (Critical Path Method)—“Crashing”

Revise PERT estimates to arrive it minimum time, neither wasting nor sparing costs.

  1. estimate time & cost, “crashed” and normal
  2. determine cost-per-week for crashing (crashed costs/time saved)
  3. crash cheapest path on the critical path
  4. recalculate project network
  5. continue 3 & 4 until all paths are crashed
  6. ease up on noncritical paths, until all paths are critical
  7. illustration



·          All activities have distinct beginning and end points

·          Time estimates are well defined

·          Resources must be able to be shifted from one activity to another

·          Linear programming may be used, if cost is direct function of time and there are no indivisibilities in activities

·          No discounting, indirect costs, or time benefits



Krueckeberg & Silvers, Urban Planning Analysis:  Methods & Models (NY:  Wiley, 1974)


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Budget Analysis

Line-Item Budget (functional areas, like “personnel,” “supplies,” “space”)

Project Budget (evaluate & rank outcomes—value of results—rather than inputs—costs)

Performance Budget (MBO—Management by Objectives)

§         Determine organizational goals

§         Convert goals into performance objectives for individuals

§         Measure performance against stated results or standards

PPBS (Planning, Programming & Budgeting System)

§         “Horizontal comprehensive”—compare alternatives to determine which best contributes to larger program objectives

§         Organize spending by program rather than by function

§         Extend programs far enough into future to determine spending implications (justify costs against established needs)

§         Subject all programs to explicit quantitative analysis (measure cost of meeting needs)

ZBB (Zero-Based Budgeting)

§         Starts from assumption of “zero funding” for each year

§         “Vertical comprehensive”—compare alternative funding levels for same program

§         Shifts burden of proof to each manager to justify why money should be spent



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Last revised: 3/12/02  AJF