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Essentials of Applied Quantitative Methods for Health Services Managers

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Essentials of Applied Quantitative Methods for Health Services Managers. Class Slides. Chapter 2: Working with Numbers. Learning Objectives: To Be Able to Calculate and Use Descriptive Statistics

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chapter 2 working with numbers
Chapter 2: Working with Numbers
  • Learning Objectives:
  • To Be Able to Calculate and Use Descriptive Statistics
  • To Be Able to Compare Different Types of Data Using Statistical Inference and Hypothesis Testing
  • To Be Able to Present Data Effectively and Efficiently in Visual Form
functions of managerial statistics
Functions of Managerial Statistics
  • Describe certain data elements
  • Compare two points of data
  • Predict data
types of data variables
Types of Data Variables
  • Nominal – non-overlapping categories, no ranking, and mutually
  • exclusive; e.g., eye color
  • Ordinal – measure categories, but categories have ranks; e.g., satisfaction surveys
  • Interval/Ratio – continuously measured, with equal distance between categories
descriptive statistics with one variable
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 United 13 United


measures of central tendency
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

measures of spread
Measures of Spread

Range – Difference between Maximum and Minimum Value

Standard Deviation – Average Distance of a Given

Data Point to the Mean

working with samples
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

working with bivariate data
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

more on hypothesis testing
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

the normal distribution
The Normal Distribution

62” 64” 66” 68” 70” 72” 74”

68-95-99.7 Rule

comparing continuous data
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)

the t test
The t-test

Compare Differences between Means between Groups


- Paired

- Assuming Equal Variances

- Assuming Unequal Variances

comparing categorical data
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
the chi square formula
The Chi-Square Formula

X2 = Σ((Observed – Expected)2)


Where the Expected Count Is

Row Total * Column Total