Overview of Quantitative
Research Methods
Florida Legislature Office of Program Policy Analysis & Government Accountability
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Training Overview
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Describes when quantitative analyses
are appropriate
Provides an overview of four
techniques
• Describing the central tendency and variation
•
•
•
in a group
Analyzing trends in program expenditures
Regression analysis
Survival analysis
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Elements of a Finding
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Criteria
Condition
Significance
Cause
Recommendation
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Questions Addressed by
Quantitative Analysis
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How typical?
What fraction?
How many or how much?
What has changed?
How does one group compare with
other groups?
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The Power of Quantitative
Analysis
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Where anecdotes can provide rich
descriptions of a few, quantitative
analysis can be used to describe large
aggregates
Quantitative analysis enjoys the
legitimacy of the “objectivity” promised
by mathematical analysis
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Techniques
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Describing groups - central tendency and
variation
Analyzing trends in program
expenditures
Regression analysis
Survival analysis
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Central Tendency and
Variation
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Mean (average)
Median
Mode
Range
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Teacher Salaries: District A
Avg. = $40,300
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Teacher Salaries: District B
Avg. = $40,300
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Teacher Salaries: District C
Avg. = $40,300
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Teacher Salaries: District D
Avg. = $40,300
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Analyzing Trends in
Expenditures
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Annual percent change
Average annual percent change
Disaggregating expenditures
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Measures of Change
Annual percent change
($T2 - $T1) / $T1 or ($T2 / $T1) - 1
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Average annual percent change
($T5 / $T1) 1 / (# years*) – 1
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* # of years = 4 in this case
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Trends in Medicaid
Expenditures
Fiscal Year
Total Medicaid
Expenditures
Average
Annual %
Increase
Medicaid
Prescription Drug
Expenditures
1995-96
$6,139,478,988
$608,513,970
1996-97
$6,281,428,233
$730,569,270
1997-98
$6,611,527,446
$845,774,833
1998-99
$6,946,629,422
$1,027,454,370
1999-00
$7,763,865,817
6.0%
$1,313,358,605
Average Annual
% Increase
21.2%
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Disaggregating Expenditures
Into Factors Driving
Expenditures
Factors Driving Drug
Expenditures
FY1995-96
FY1999-00
Average
Annual %
Increase
Total Expenditures
(Volume x Price)
$608,513,9
70
$1,313,358,6
05
21.2%
Volume (# of prescriptions)
17,689,068
22,158,912
5.8%
Population (# enrollees)
1,150,162
1,155,079
0.1%
1.28
1.60
5.7%
$34.40
$59.27
14.6%
Utilization (scripts / enrollee)
Price
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Regression Analysis
Y = a + B(X1) + B(X2) + B(X3) + . . .
Regression analysis estimates Y given
values of X1, X2, X3, etc. The Bs
indicate the independent effect the
Xs have on Y.
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Estimating Hospice
Expenditures
Total Expenditures
Hospices reporting
expenditures (N=37)
$910,272,301
Hospices not
reporting
expenditures (N=6)
$0
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Estimating Hospice Expenditures
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Estimating Hospice
Expenditures
Hospices reporting
expenditures (N=37)
Hospices not
expenditures (N=6)
Total
Total Expenditures
$910,272,301
$193,073,565
$1,103,345,866
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Examining Cost Effectiveness
Average 3-Yr. Costs Per Person
Nursing
Total $ Home $
Waiver $ Other $
Nonwaiver
$39,896
$25,556
$0
$14,340
Waiver
$59,497
$3,937
$53,575
$1,985
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Examining Cost Effectiveness
Avg.
Avg.
Total $ Months
Nonwaiver
Waiver
Avg.
Monthly $
Adj.
Monthly $
$39,896
19.5
$2,046
$2,558
$59,497
26.2
$2,271
$2,657
Difference
$225
$99
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Survival Analysis
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Kaplan-Meier
Cox regression
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Survival Analysis – How Long Until?
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Review
1. Under what conditions is the mean
(average) not the best measure of
central tendency?
2. What are the best measures of
central tendency under these
conditions?
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Review
Why is using the geometric mean for
the average annual percent change
more appropriate than average of
the annual percent changes in
Year
Expenditures
Avg. annual percent change
column
B? Annual percent
change
2006
$500,000
2007
$525,000
5.00%
2008
$526,000
0.19%
2009
$535,000
1.71%
2010
$542,000
1.31%
(geometric mean)
2.04%
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Review
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What are some instances where it
would be important to adjust for the
characteristics of members of a
group when comparing multiple
groups on an outcome (e.g., cost
effectiveness)?
Would regression analysis be
appropriate?
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Review
Survival analysis techniques are a
better alternative to estimating how
long it takes an event to occur (e.g.,
release from a treatment facility).
What is the disadvantage of the
more commonly used average
length of stay for persons released
in a year?
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