Mellott & Associates LLC www.mellottandassociates.com
Statistics for the Healthcare Quality Professional
Susan Mellott PhD, RN, CPHQ, FNAHQ
Mellott & Associates LLC www.mellottandassociates.com
Objectives
Use basic statistical techniques to describe data and to evaluate data
Use or coordinate the use of statistical process control components
Use or Coordinate the use of process analysis tools to display data
Mellott & Associates LLC www.mellottandassociates.com
Mom
Baseball
Apple PieStatistics
Mellott & Associates LLC www.mellottandassociates.com
What Type of Data?
The type of data that you have controls what tools, statistics and display format are utilized
Everything is driven from this
Mellott & Associates LLC www.mellottandassociates.com
Type of Data
Category – Count Data Categories or groups Histogram Percentage Chi Squared
Measured Data Time, Volume, Money,
Scores Run Chart Control Chart Mean, Median, Mode,
Range T-test
Mellott & Associates LLC www.mellottandassociates.com
Categorical Data Examples
Men vs Women Age Ranges (0-30, 31-50, 51-70, 71+) DRGs Types of falls Types of injuries Diagnosis Complications
Mellott & Associates LLC www.mellottandassociates.com
Measured Data Examples
Temperature LOS Average daily census Scores on a test Pre and Post Test scores Anything over time
Mellott & Associates LLC www.mellottandassociates.com
In Healthcare Quality
Use more measured data than categorical data, but there is a place for each
Use more Run and Control charts than Histograms
Mellott & Associates LLC www.mellottandassociates.com
And then there are other Problem Solving Tools
Cause & effect diagram
Pareto diagram
Scatter diagram
Regression analysis
Mellott & Associates LLC www.mellottandassociates.com
But First…… Some Basics
Mellott & Associates LLC www.mellottandassociates.com
Reliability and Validity
Reliability – The ability to get the same answer time and time
again if nothing changes
Validity– To be sure you are counting or measuring what
you intended to count or measure
Mellott & Associates LLC www.mellottandassociates.com
Reliability and Validity
Must have reliability before you can have validity
HINT: R comes before V in the alphabet
Mellott & Associates LLC www.mellottandassociates.com
Reliability
Test / Retest reliability
Inter-Rater reliability ***
Mellott & Associates LLC www.mellottandassociates.com
Validity
Face Validity– Lowest level
Criterion Validity ***– Based on criteria
Construct Validity– Hardest to obtain
Mellott & Associates LLC www.mellottandassociates.com
Sampling
How you pick your sample influences what you can do with your results – Can you generalize the findings outside of the
sample you used– Are you confined to use your findings only in
relation to the sample itself
Probability vs Non-Probability– Usually use of combination of each type
Mellott & Associates LLC www.mellottandassociates.com
Probability Sampling
You probably will be able to generalize your findings
Simple Random– All items have an equal chance of being chosen
Stratified Random– Creating 2 or more homogeneous groups and then
randomly selecting items– Men vs Women
Systemic Random– Every n’th case
Mellott & Associates LLC www.mellottandassociates.com
Non-Probability Sampling
You probably will not be able to generalize your findings
Convenience– Using data readily available
Quota– Set number of data sets
Purposive– Demonstrate a desired characteristic– Expert sampling– Men vs Women
Mellott & Associates LLC www.mellottandassociates.com
Data Collection
Must assure that measuring what you intend to measure– Pre-test your data collection tool!– Verify collection questions with requestor of the data
Must assure that all data collectors collect the data from the same places and in the same manner
Mellott & Associates LLC www.mellottandassociates.com
Before Collect Data, Must:
Know how you want to manipulate data;
Know how you want to display data;
Know how you want to report data;
All of which is based on type of data!
Mellott & Associates LLC www.mellottandassociates.com
Categorical Data
AKA:– Attribute, Qualitative, Nominal, Ordinal, Discrete
Examples:– # of members, patients, births, procedures,
occurrences, gender, ethnicity
Mellott & Associates LLC www.mellottandassociates.com
Categorical Data
Usually Reported as:– % in each category, whole numbers
Usually Displayed as:– Histogram, pie chart
Usual statistical test of difference between groups:– Chi Squared
Mellott & Associates LLC www.mellottandassociates.com
Measured Data
AKA:– Continuous, Variable, Quantitative
Examples:– Age, height, weight, temperature, time, charges,
LOS
Mellott & Associates LLC www.mellottandassociates.com
Measured Data
Usually Reported as:– Mean, median, mode, minimum, maximum,
percentiles, whole and fractional numbers Usually displayed as:
– Run charts, control charts Usual statistical test of difference between
groups:– T-test, or in special cases a Z-test
Mellott & Associates LLC www.mellottandassociates.com
Mean, Median, Mode
Mean:– Average– Can be influenced by outliers/extreme values
Median:– Middle of data– Best utilized when there are outliers
Mode:– Most frequently occurring numbers
Mellott & Associates LLC www.mellottandassociates.com
Examples
2, 4, 6, 8, 10– Mean:– Median:
2, 4, 6, 8, 100– Mean:– Median:
Mellott & Associates LLC www.mellottandassociates.com
Example
2, 4, 6, 7, 8, 10– Mean:– Median:
0, 0, 0, 0, 0, 7, 12, 26– Mean:– Median:
Mellott & Associates LLC www.mellottandassociates.com
Examples
2, 4, 6, 8, 10– Mode:
2, 3, 3, 4, 6, 8, 10– Mode:
2, 3, 3, 4, 4, 4, 6, 8, 10– Mode:
Mellott & Associates LLC www.mellottandassociates.com
STANDARD DEVIATION
Mellott & Associates LLC www.mellottandassociates.com
Statistical Differences between Groups
Clinical differences occur before statistical differences
Categorical data – Chi Square
Measured data – T-test
Mellott & Associates LLC www.mellottandassociates.com
Chi-Squared test
Similar to a t-test
Get an X2 value
Then look that value up on a p-value table like a t-test score
Mellott & Associates LLC www.mellottandassociates.com
T-test
Reported as a ‘p’ score Ranges from 0 to 1 0.05 and less shows statistical differences
0 10.50.25
0.05
Mellott & Associates LLC www.mellottandassociates.com
Histogram (Bar Chart)
What is it: – A display of comparisons between different
categories or groups
When used: – To look at differences between categories or
groups (non-statistical differences)
What it will tell you:– What the amount of differences look like
Mellott & Associates LLC www.mellottandassociates.com
Mellott & Associates LLC www.mellottandassociates.com
Histogram vs Run Chart vs Control Chart
Histogram – – only with categorical data
– Best to display one to three points in time
– If more than three points in time, better to use run chart
– Much more effective than a pie chart
Mellott & Associates LLC www.mellottandassociates.com
Run Chart (Line Graph)
What is it:– A line graph display of performance changes over
time When used:
– To look at data over time What it will tell you:
– What is baseline performance?– Amount and type of variation in a process?– Is process changing over time?– Is change an improvement?
Mellott & Associates LLC www.mellottandassociates.com
Histogram vs Run Chart vs Control Chart
Run Chart – – Categorical data over time
– Sequential Data points
– Display comparison between years, hospital units, stratification of data
– Prior to having enough data for Control Chart
Mellott & Associates LLC www.mellottandassociates.com
Control Chart (Line Graph)
What is it:– A line graph display that compares actual
performance to the mean and includes upper and lower control limits
When used:– To display normal variations and out-of-control
variations
What it will tell you:– Common cause or special cause variation
Mellott & Associates LLC www.mellottandassociates.com
Control Chart
Conceptually – Run chart with standard deviation curve
placed on its side
Mellott & Associates LLC www.mellottandassociates.com
0102030405060708090
100
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
Control Charts
Mellott & Associates LLC www.mellottandassociates.com
Mellott & Associates LLC www.mellottandassociates.com
Mellott & Associates LLC www.mellottandassociates.com
Mellott & Associates LLC www.mellottandassociates.com
R Chart Title
RUCL=0.395
CL=0.187
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
6/88am
10am 12pm 2pm 6/98am
10am 12pm 2pm 6/108am
10am 12pm 2pm 6/118am
10am 12pm 2pm 6/128am
10am 12pm
Date/Time/Period/Number
RangeUCL+2 sigma+1 sigmaAverage-1 sigma-2 sigmaLCL
n=19
Mellott & Associates LLC www.mellottandassociates.com
Mellott & Associates LLC www.mellottandassociates.com
Mellott & Associates LLC www.mellottandassociates.com
Regression Analysis
Simple Regression– How one variable affects another variable– Example: number of calories eaten vs weight gain
Multiple Regression– How multiple variables affect another variable– Factors related to compliance with medication
regime
Mellott & Associates LLC www.mellottandassociates.com
Regression Analysis
Scatter Diagram Pictorial representation of a simple
regression– Positive Relationship
Data goes upward in an oval shape
– Negative Relationship Data goes downward in an oval shape
– No relationship Data neither goes upward nor downward
Mellott & Associates LLC www.mellottandassociates.com
Positive Correlation
0
20
40
60
80
100
120
0 1 2 3 4 5
Mellott & Associates LLC www.mellottandassociates.com
Negative Correlation
0
20
40
60
80
100
120
0 1 2 3 4 5
Mellott & Associates LLC www.mellottandassociates.com
No Relationship or Correlation
01020304050
60708090
100
0 1 2 3 4 5
Mellott & Associates LLC www.mellottandassociates.com
Multiple Regression in Health Care Quality
Many examples where multiple regression could be an important tool: Factors related to compliance with medication
regime Factors related to infections Factors related to high cholesterol Factors related to flexibility & strength
Mellott & Associates LLC www.mellottandassociates.com
Multiple Regression
Pareto diagram Cause & Effect diagram
Mellott & Associates LLC www.mellottandassociates.com
Pareto Diagram
What is it:– Pictorial representation similar to multiple
regression When used:
– When you want to determine where to start to get the biggest ‘bang for your buck’
What it will tell you:– Where you should start in your improvement
efforts
Mellott & Associates LLC www.mellottandassociates.com
Mellott & Associates LLC www.mellottandassociates.com
Mellott & Associates LLC www.mellottandassociates.com
Mellott & Associates LLC www.mellottandassociates.com
Cause & Effect Diagram
What is it:– Pictorial representation similar to multiple
regression When used:
– When you want to determine where to start to get the biggest ‘bang for your buck’
What it will tell you:– Where you should start in your improvement
efforts
Mellott & Associates LLC www.mellottandassociates.com
Cause & Effect
Use when “bad” things happen to determine how it happened
Use when want “Good” results to determine what you need to do to get those results
Mellott & Associates LLC www.mellottandassociates.com
Cause & Effect Diagram
Effect
Cause
Mellott & Associates LLC www.mellottandassociates.com
Isolation Shallow Staffing Limited Access to Specialists Master Calendar Speed of Change Mentor Program Medical Records Soldier Assistance Board Admin CBO Info Technology Library Empowered Staff
Clinical CBO Education Program
CME OPD NCOPD SGT’s Time
Life QualityLife QualityImprovementImprovement
Showplace ofShowplace ofMedical ReadinessMedical Readiness
World ClassWorld ClassServiceService
ProfessionalProfessionalExcellenceExcellence
OasisOasisofof
CareCare
Focus Focus
Community In-processing Lack of Measurement
ResourcesTime Community Wellness PAT
Wellness Focus Info Technology
Soldier Assist Board Awards Program
AMMED Council FSG
Youth Summer Turnover
Measurement NTC Surgeon
Leadership MASCAL/EPP
Info Technology NCO Corps
Management Orientation Access Info Flow Info Technology Turnover Team Work Staffing Restraints Committed Staff EC Issues Customer Focus Lack of Measurement MC/CS Division Ambulatory Care Center
Commitment to Vision
DRETS PT Test
FSG
© M. Ellicott
Mellott & Associates LLC www.mellottandassociates.com
Summary
You first need to know what kind of data you are working with
Then you have to know the types of tools and statistics you can use with that kind of data
Then you design the data collection and plan the analysis of that data