Essentials of Applied Quantitative Methods for Health Services

ManagersClass Slides

Chapter 2: Working with Numbers

Learning Objectives:

1.To Be Able to Calculate and Use Descriptive Statistics2.To Be Able to Compare Different Types of Data Using Statistical Inference and Hypothesis Testing3.To Be Able to Present Data Effectively and Efficiently in Visual Form

Functions of Managerial Statistics

1. Describe certain data elements2. Compare two points of data3. Predict data

Types of Data Variables

1. Nominal – non-overlapping categories, no ranking, and mutually

exclusive; e.g., eye color2. Ordinal – measure categories, but categories have ranks;

e.g., satisfaction surveys3. Interval/Ratio – continuously measured, with equal

distance between categories

Descriptive Statistics with One Variable

Insurance type by patient 1 United 8 BC/BS2 Medicare 9 Medicaid3 Medicaid 10 Uninsured4 Medicare 11 Medicare5 BC/BS 12 Uninsured6 United 13 United 7 BC/BS 14 MBCA

Measures of Central Tendency

Mean – Mathematical Center (Average)

Median – Center of a Distribution of Data, WhenArranged from Lowest to Highest

Mode – Most frequently reported data point

Measures of Spread

Range – Difference between Maximum and Minimum Value

Standard Deviation – Average Distance of a Given Data Point to the Mean

Working with SamplesSamples are Inherently More Variable than Populations

Impossible to Know the “Truth” about Current and/orFuture Population Data – Create an Interval that We Can Say withSome 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

Working with Bivariate DataHypothesis 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

More on Hypothesis Testing

Can Never Be Certain What Relationship Truly IS Between Two Variables

So, We Use Hypothesis Testing and Statistics to Make ProbabilisticInferences about Relationships

The Normal Distribution

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

Comparing Continuous DataCorrelation: 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)

The t-test

Compare Differences between Means between Groups

Types:- Paired

- Assuming Equal Variances

- Assuming Unequal Variances

Comparative Monthly Births

 Port City Hospital

US for similar size hospitals

January 24 22February 25 21March 33 26April 35 27May 37 31June 38 25July 41 36August 35 27September 45 39October 39 35November 42 34December 50 23Mean 37 29

Sample t-test Reportt-Test: Two-Sample Assuming Unequal Variances

  Port City USMean 37 28.8Variance 56 36.0Observations 12 12Hypothesized Mean Difference 0df 21t Stat 2.9499P(T<=t) one-tail 0.0038t Critical one-tail 1.7207P(T<=t) two-tail 0.0076t Critical two-tail 2.0796

Comparing Categorical Data

Often Measured in Rates or Proportions

Chi-Square Statistic (X2): Compares Observed Differences in Proportions with What Would Be Expected if Proportions Were Equal

2 X 2 Contingency Table

Group 1 Group 2 Total

variable 1 a b a+b

variable 2 c d c+d

Total a+c b+d a+b+c+d

Patient SatisfactionComparison Using Chi Square

East Campu

s

West Campu

s Total

Satisfied 36 17 53Not satisfied 30 35 65Total 66 52 118

The Chi-Square Formula

X2 = Σ((Observed – Expected)2) Expected

Where the Expected Count Is

Row Total * Column Totaln

Chi-Square Calculations forPatient Satisfaction Data

Observed Expected O-E (O-E)2 (O-E)2/E

36 29.6 6.40 40.96 1.38

17 23.4 -6.40 40.96 1.75

30 36.4 -6.40 40.96 1.13

35 28.6 6.40 40.96 1.43

Total 118 118 0.00 163.84 5.69

Summary of Methods Continuous Categorical

Descriptivemean, median,mode, standard deviation,

range, variance

counts, percents, rates and proportions

ComparisonsContinuous Categorical

Same variable

Different variable

Same variable

Different variable

Continuous t-test correlation - t-test

Categorical - 

chi-square chi-square t-test

Percent of Patients Overweight orObese by BMI Score

Port City Hospital, 2008 Age group Percent (95% CI) Sample Size (n) 18-24 36.7 (30.2, 43.3) 9325-34 48.6 (44.3, 53.0) 28935-44 56.6 (53.2, 60.1) 51945-54 65.3 (61.7, 69.0) 48855-64 68.1 (63.8, 72.3) 35365 and older 59.7 (55.6, 63.8) 389BMI > 25 is considered overweight, as BMI > 30 is considered obese.

A Bar Chart

Another Bar Chart

Raw Data 2007 Expenditure Categories

Port City Hospital Med Surg ICU

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

Pie Chart

Raw DataPort City Hospital Births, 2005-2008

2005 2006 2007 2008Jan 21 25 30 39Feb 25 30 35 42Mar 21 31 37 51Apr 24 34 41 53May 35 35 42 57Jun 14 20 30 44Jul 21 23 27 41Aug 27 25 31 40Sep 33 37 45 55Oct 37 40 50 60Nov 30 38 42 62Dec 36 45 48 58

Line Graft

Raw Data

FTE employees and total expenditures by departmentPort City Hospital 2008

FTE employees Total ExpendituresMed/Surg 23 $ 5,645,230.00

ED 14 $ 825,180.00 ICU 17 $ 1,236,450.00 Neonatal 12 $ 1,647,264.00

Radiology 6 $ 546,230.00

Lab 6 $ 427,451.00

Dual Axis Graft