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Essentials of Applied Quantitative Methods for Health Services Managers Class Slides

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Chapter 2: Working with Numbers Learning Objectives: 1.To Be Able to Calculate and Use Descriptive Statistics 2.To Be Able to Compare Different Types of Data Using Statistical Inference and Hypothesis Testing 3.To Be Able to Present Data Effectively and Efficiently in Visual Form

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Functions of Managerial Statistics 1.Describe certain data elements 2.Compare two points of data 3.Predict data

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Types of Data Variables 1.Nominal – non-overlapping categories, no ranking, and mutually exclusive; e.g., eye color 2.Ordinal – measure categories, but categories have ranks; e.g., satisfaction surveys 3.Interval/Ratio – continuously measured, with equal distance between categories

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Descriptive Statistics with One Variable Insurance type by patient 1 United 8 BC/BS 2 Medicare 9 Medicaid 3 Medicaid 10 Uninsured 4 Medicare 11 Medicare 5 BC/BS 12 Uninsured 6 United13 United 7 BC/BS14 MBCA

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Measures of Central Tendency Mean – Mathematical Center (Average) Median – Center of a Distribution of Data, When Arranged from Lowest to Highest Mode – Most frequently reported data point

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Measures of Spread Range – Difference between Maximum and Minimum Value Standard Deviation – Average Distance of a Given Data Point to the Mean

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Working with Samples Samples are Inherently More Variable than Populations Impossible to Know the “Truth” about Current and/or Future Population Data – Create an Interval that We Can Say with Some Level of Confidence Contains the True Population Mean Formula for Constructing a Confidence Interval: Mean = +/- 1.96 * Standard Error, Where Standard Error = Standard Deviation/√n

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Working with Bivariate Data Hypothesis Testing Null Hypothesis: The Hypothesis of No Association or Difference Alternative Hypothesis: The Converse of the Null Hypothesis; i.e., There Is Some Association or Difference - When the Direction of the Difference Doesn’t Matter A Two-Tailed Test. If Direction Does matter, the Test Is One-Tailed Test

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More on Hypothesis Testing Can Never Be Certain What Relationship Truly IS Between Two Variables So, We Use Hypothesis Testing and Statistics to Make Probabilistic Inferences about Relationships

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The Normal Distribution 68-95-99.7 Rule 62” 64” 66” 68” 70” 72” 74”

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Comparing Continuous Data Correlation: A Statistical Measure of Association between Two Phenomena – Not a Causal Relationship r = Correlation Coefficient R = +1.0 = Perfectly Positive Correlation R = - 1.0 = Perfectly Negative Correlation Can Apply Principles of Hypothesis Testing to Correlation to Assess if There Is a Relationship. (Use Table of Critical Values (Table 2-4)

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The t-test Compare Differences between Means between Groups Types: - Paired - Assuming Equal Variances - Assuming Unequal Variances

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Comparative Monthly Births Port City Hospital US for similar size hospitals January2422 February2521 March3326 April3527 May3731 June3825 July4136 August3527 September4539 October3935 November4234 December5023 Mean3729

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Sample t-test Report t-Test: Two-Sample Assuming Unequal Variances Port CityUS Mean3728.8 Variance5636.0 Observations12 Hypothesized Mean Difference0 df21 t Stat2.9499 P(T<=t) one-tail0.0038 t Critical one-tail1.7207 P(T<=t) two-tail0.0076 t Critical two-tail2.0796

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Comparing Categorical Data Often Measured in Rates or Proportions Chi-Square Statistic (X 2 ): Compares Observed Differences in Proportions with What Would Be Expected if Proportions Were Equal

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2 X 2 Contingency Table Group 1Group 2 Total variable 1aba+b variable 2cdc+d Totala+cb+da+b+c+d

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Patient Satisfaction Comparison Using Chi Square East Campu s West Campu s Total Satisfied361753 Not satisfied303565 Total6652118

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The Chi-Square Formula X 2 = Σ((Observed – Expected) 2 ) Expected Where the Expected Count Is Row Total * Column Total n

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Chi-Square Calculations for Patient Satisfaction Data ObservedExpectedO-E(O-E) 2 (O-E) 2 /E 3629.66.4040.961.38 1723.4-6.4040.961.75 3036.4-6.4040.961.13 3528.66.4040.961.43 Total118 0.00163.845.69

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Summary of Methods ContinuousCategorical Descriptive mean, median,mode, standard deviation, range, variance counts, percents, rates and proportions Comparisons ContinuousCategorical Same variable Different variable Same variable Different variable Continuoust-testcorrelation-t-test Categorical- chi-square t-test

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Percent of Patients Overweight or Obese by BMI Score Port City Hospital, 2008 Age group Percent(95% CI)Sample Size (n) 18-2436.7 (30.2, 43.3)93 25-3448.6 (44.3, 53.0)289 35-4456.6 (53.2, 60.1)519 45-5465.3 (61.7, 69.0)488 55-6468.1 (63.8, 72.3)353 65 and older59.7 (55.6, 63.8)389 BMI > 25 is considered overweight, as BMI > 30 is considered obese.

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A Bar Chart

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Another Bar Chart

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Raw Data 2007 Expenditure Categories Port City Hospital Med SurgICU Supplies $ 189,654.00 $ 210,157.00 Professional $ 1,085,623.00 $ 1,527,560.00 Pharmacy $ 228,290.00 $ 142,152.00 Ancillary $ 45,620.00 $ 33,158.00 Facilities $ 624,877.00 $ 218,906.00 Administrative $ 328,176.00 $ 3,235,148.00 Total $ 2,502,240.00 $ 5,367,081.00

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Pie Chart

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Raw Data Port City Hospital Births, 2005-2008 2005200620072008 Jan21253039 Feb25303542 Mar21313751 Apr24344153 May35 4257 Jun14203044 Jul21232741 Aug27253140 Sep33374555 Oct37405060 Nov30384262 Dec36454858

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Line Graft

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Raw Data FTE employees and total expenditures by department Port City Hospital 2008 FTE employeesTotal Expenditures Med/Surg23 $ 5,645,230.00 ED14 $ 825,180.00 ICU17 $ 1,236,450.00 Neonatal12 $ 1,647,264.00 Radiology6 $ 546,230.00 Lab6 $ 427,451.00

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Dual Axis Graft

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Copyright © 2012 Wolters Kluwer Health | Lippincott Williams & Wilkins Chapter 16 Descriptive Statistics.

Copyright © 2012 Wolters Kluwer Health | Lippincott Williams & Wilkins Chapter 16 Descriptive Statistics.

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