Overview of Quantitative Research Methods

Florida Legislature Office of Program Policy Analysis & Government Accountability

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Overview of Quantitative Overview of Quantitative Research MethodsResearch Methods


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


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


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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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


Survival AnalysisSurvival Analysis

Kaplan-MeierKaplan-Meier Cox regressionCox regression

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Survival Analysis – How Long Survival Analysis – How Long Until?Until?


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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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%


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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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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Documents

Overview of Quantitative Research Methods