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Overview of Quantitative Overview of Quantitative Research MethodsResearch Methods
Florida Legislature Office of Program Policy Analysis & Government Accountability
Training OverviewTraining Overview
Describes when quantitative Describes when quantitative analyses are appropriateanalyses are appropriate
Provides an overview of four Provides an overview of four techniquestechniques•Describing the central tendency and Describing the central tendency and
variation in a groupvariation in a group
•Analyzing trends in program Analyzing trends in program expendituresexpenditures
•Regression analysisRegression analysis
•Survival analysisSurvival analysis2
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Elements of a FindingElements of a Finding
CriteriaCriteria ConditionCondition SignificanceSignificance CauseCause RecommendationRecommendation
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Questions Addressed by Questions Addressed by Quantitative AnalysisQuantitative Analysis
How typical?How typical? What fraction? What fraction? How many or how much?How many or how much? What has changed?What has changed? How does one group compare How does one group compare
with other groups?with other groups?
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The Power of The Power of Quantitative AnalysisQuantitative Analysis
Where anecdotes can provide rich Where anecdotes can provide rich descriptions of a few, quantitative descriptions of a few, quantitative analysis can be used to describe analysis can be used to describe large aggregateslarge aggregates
Quantitative analysis enjoys the Quantitative analysis enjoys the legitimacy of the “objectivity” legitimacy of the “objectivity” promised by mathematical promised by mathematical analysisanalysis
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TechniquesTechniques
Describing groups - central Describing groups - central tendency and variationtendency and variation
Analyzing trends in program Analyzing trends in program expendituresexpenditures
Regression analysisRegression analysis Survival analysisSurvival analysis
Florida Legislature Office of Program Policy Analysis & Government Accountability
Central Tendency and Central Tendency and VariationVariation
Mean Mean (average)(average)
MedianMedian ModeMode RangeRange
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Teacher Salaries: District Teacher Salaries: District AA
Avg. = $40,300
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Teacher Salaries: District Teacher Salaries: District BB
Avg. = $40,300
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Teacher Salaries: District Teacher Salaries: District CC
Avg. = $40,300
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Teacher Salaries: District Teacher Salaries: District DD
Avg. = $40,300
Florida Legislature Office of Program Policy Analysis & Government Accountability
Analyzing Trends in Analyzing Trends in ExpendituresExpenditures
Annual percent changeAnnual percent change Average annual percent changeAverage annual percent change Disaggregating expendituresDisaggregating expenditures
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Measures of ChangeMeasures of Change
Annual percent changeAnnual percent change
($($T2T2 - $ - $T1T1) / $) / $T1T1 or ($ or ($T2T2 / $ / $T1T1) - 1) - 1
Average annual percent changeAverage annual percent change
($($T5T5 / $ / $T1T1)) 1 / (# years*) 1 / (# years*) – 1 – 1
* # of years = 4 in this case* # of years = 4 in this case
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Trends in Medicaid Trends in Medicaid ExpendituresExpenditures
Fiscal Year
Total Medicaid Expenditures
Average Annual % Increase
Medicaid Prescription Drug Expenditures
Average Annual % Increase
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
21.2%
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Disaggregating Disaggregating Expenditures Into Factors Expenditures Into Factors
Driving ExpendituresDriving Expenditures
Factors Driving Drug Expenditures
FY1995-96
FY1999-00 Average Annual % Increase
Total Expenditures(Volume x Price)
$608,513,970
$1,313,358,605
21.2%
Volume (# of prescriptions)
17,689,068
22,158,912 5.8%
Population (# enrollees) 1,150,162 1,155,079 0.1%
Utilization (scripts / enrollee)
1.28 1.60 5.7%
Price $34.40 $59.27 14.6%
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Regression AnalysisRegression Analysis
Y = a + B(X1) + B(X2) + B(X3) + . . .Y = a + B(X1) + B(X2) + B(X3) + . . .
Regression analysis estimates Y Regression analysis estimates Y given values of X1, X2, X3, etc. given values of X1, X2, X3, etc. The Bs indicate the independent The Bs indicate the independent effect the Xs have on Y.effect the Xs have on Y.
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Estimating Hospice Estimating Hospice ExpendituresExpenditures
Total Total ExpendituresExpenditures
Hospices Hospices reporting reporting expenditures expenditures (N=37)(N=37)
$910,272,301$910,272,301
Hospices not Hospices not reporting reporting expenditures expenditures (N=6)(N=6)
$0$0
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Estimating Hospice Estimating Hospice ExpendituresExpenditures
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Estimating Hospice Estimating Hospice ExpendituresExpenditures
Total Total ExpendituresExpenditures
Hospices Hospices reporting reporting expenditures expenditures (N=37)(N=37)
$910,272,301$910,272,301
Hospices not Hospices not reporting reporting expenditures expenditures (N=6)(N=6)
$193,073,565$193,073,565
TotalTotal $1,103,345,866$1,103,345,866
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Average 3-Yr. Costs Per Average 3-Yr. Costs Per PersonPerson
Total Total $$
NursinNursing g Home Home $ $
Waiver Waiver $$
Other Other $$
Non-Non-waiverwaiver
$39,8$39,89696
$25,55$25,5566 $0$0
$14,34$14,3400
WaiverWaiver$59,4$59,4
9797 $3,937$3,937$53,57$53,57
55 $1,985$1,985
Examining Cost Examining Cost EffectivenessEffectiveness
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Avg. Avg. Total Total
$$
Avg. Avg. MontMonths hs
Avg. Avg. Monthly Monthly
$$
Adj. Adj. Monthly Monthly
$$
Non-Non-waivewaiverr
$39,8$39,89696 19.519.5 $2,046$2,046 $2,558$2,558
WaivWaiverer
$59,4$59,49797 26.226.2 $2,271$2,271 $2,657$2,657
DifferenceDifference $225$225 $99$99
Examining Cost Examining Cost EffectivenessEffectiveness
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Survival AnalysisSurvival Analysis
Kaplan-MeierKaplan-Meier Cox regressionCox regression
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Survival Analysis – How Long Survival Analysis – How Long Until?Until?
Florida Legislature Office of Program Policy Analysis & Government Accountability
ReviewReview
1.1. Under what conditions is the Under what conditions is the mean (average) not the best mean (average) not the best measure of central tendency?measure of central tendency?
2.2. What are the best measures What are the best measures of central tendency under of central tendency under these conditions?these conditions?
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Florida Legislature Office of Program Policy Analysis & Government Accountability
ReviewReviewWhy is using the geometric mean for Why is using the geometric mean for
the average annual percent the average annual percent change more appropriate than change more appropriate than average of the annual percent average of the annual percent changes in column B?changes in column B?
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Year
Expenditures
Annual percent change
Avg. annual percent change (geometric mean)
2006 $500,000
2007 $525,000 5.00%
2008 $526,000 0.19%
2009 $535,000 1.71%
2010 $542,000 1.31% 2.04%
Florida Legislature Office of Program Policy Analysis & Government Accountability
ReviewReview
What are some instances where What are some instances where it would be important to adjust it would be important to adjust for the characteristics of for the characteristics of members of a group when members of a group when comparing multiple groups on an comparing multiple groups on an outcome (e.g., cost outcome (e.g., cost effectiveness)?effectiveness)?
Would regression analysis be Would regression analysis be appropriate?appropriate?
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Florida Legislature Office of Program Policy Analysis & Government Accountability
ReviewReview
Survival analysis techniques are a Survival analysis techniques are a better alternative to estimating better alternative to estimating how long it takes an event to how long it takes an event to occur (e.g., release from a occur (e.g., release from a treatment facility). What is the treatment facility). What is the disadvantage of the more disadvantage of the more commonly used average length of commonly used average length of stay for persons released in a stay for persons released in a year?year?
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