HM404

1. © 2017 American Health Information Management Association
© 2017 American Health Information Management Association
Health Informatics Research Methods:
Principles and Practice, Second Edition
Chapter 9: Applied Statistics

2. © 2017 American Health Information Management Association
Learning Objectives
• Select descriptive and inferential statistics
appropriate to the research question, the type
of data, and other aspects of the population
or the research design.
• Choose parametric or nonparametric
statistical tests appropriately.
• Justify the selection of a statistical analytic
test.
• Use key terms associated with quantitative
statistical tests appropriately.

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Why We Study Statistics
• To benefit from and to make sense of the
numerical data that surround us

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Definition of Statistics
• Statistics is the science of collecting,
classifying, displaying, analyzing, and
interpreting numerical data
– Biostatistics is a specialized branch of
statistics that applies statistical tests to
biological data, such as the data obtained
from experiments on humans and animals

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Goals of Quantitative Researchers
and Related Processes
• Goals for quantitative
researchers:
– Be able to state that the
researchers’ intervention
contributed to or was the
cause of the change in
the dependent variable
– Be able to state that their
findings can be
generalized to a
population
• Probability: Likelihood of
outcome; separating
chance from contributing
factors or cause
• Random sampling
– Unbiased selection of
subjects from a population
with every member having
an equal chance of selection
– Statistics: Numerical
characteristics
– Uncertainty: Making
estimates and assumptions

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Level of Data
• Level of data affects the types of statistical tests that can be applied
to data
• Other terms for level of data: Scale of data, type of data, level of
measurement, and scale of measurement
– Nominal data
• Named or labeled, such as sex or job title
– Ordinal data
• Sequence of ranking showing relationships, such as usability on a scale of 1 to 5
or such as level agreement from strongly agree, agree, neutral, disagree, to
strongly disagree
– Interval data
• Evenly distributed scale that does not begin at true zero, such as interval between
1985 –1990 and 2011–2016
– Ratio data
• Evenly distributed scale beginning at true zero, such as height and weight

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Other Terms Associated with
Level of Data
• Discrete data vs. continuous data
– Discrete: Separate and distinct values or observations, e.g. number of clinic visits
– Continuous: Observation that can have an infinite number of points
• Numeric data vs. categorical data
– Numeric data can have mathematical operations applied (interval and ratio)
– Categorical data are grouped data, such as race or age group (youth, adult)
(nominal or ordinal)
• Quantitative data vs. qualitative data
– Quantitative data include interval and ratio data, and may be discrete or
continuous
– Qualitative data include categorical data (nominal or ordinal)
• Metric data vs. nonmetric data
– Metric data are interval and ratio data
– Nonmetric data are nominal or ordinal data

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Parametric Data Versus
Nonparametric Data
• Parametric data
– Continuous data, interval
data, and ratio data
– Distributions are assumed to
be normal (normal or bell
curve)
• Nonparametric data
– Discrete data, nominal data,
and ordinal data
– No assumptions are made
about their distributions
Different statistical tests are used for parametric and
nonparametric data

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Associations (Relationships)
among Variables
• Associations (relationships) among variables can be linear or
nonlinear
• Linear and nonlinear associations require different statistical
tests
• Linearly associated (related) variables cluster around a
straight line when they are graphed, known as linearity
– Positive (direct)
– Negative (inverse)
• Nonlinear associations are
– Curvilinear
– Less common than linear associations

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Examples of Associations
(Relationships)
Positive (direct) linear
association
Negative (inverse) linear
association
Curvilinear association
(s-curve)

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Factors in Selecting a Statistical
Test
• Purpose of the research
– Difference or relationship
• Type of variable (level of variable)
– Nominal, ordinal, interval, or ratio
• Number of variables
• Nature of the target population
– Parametric or nonparametric
• Number, size, and independence of groups
– Independent sample or dependent sample

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Descriptive Statistics
• Descriptive statistics
– Describe what is by classifying, organizing, and summarizing
numerical data about a particular group of observations (also
called summary statistics)
– Frequency distributions, tables, graphical displays, measures of
central tendency, measures of dispersion, and some correlations
• Purposes of descriptive statistics
– Examine raw data
– Summarize data
– Conduct exploratory data analysis
– Verify accuracy of data entry
– Assess distribution of data as normal or nonnormal

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Frequency Distribution
• Frequency distribution is the frequency with
which values of a variable occur in a sample
or population
• Tables
– Counts and percentages
• Graphs
– Bar charts and histograms
– Values along x-axis and frequencies along y-axis

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Normal Distribution
• Normal distribution
– Graphing the frequencies of the variables’ values
results in a bell-shaped curve called a “normal
curve,” a “bell curve,” or a Gaussian distribution
– Normal distribution determined by mean and
standard deviations
– Underlies many statistical tests
– Symmetrical and extends to infinity in both
directions

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Normal Distribution (cont.)
• Mean, median, and mode are all the same and cut the curve in half
• One standard deviation on either side of the mean includes 68
percent of values, two standard deviations on either side include 95
percent of values, and three standard deviations include 99 percent
of values Mean, median, and mode

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Properties of Nonnormal Distributions
• Kurtosis: Measure of
heaviness of both tails of
curve
– Platykurtic (negative
kurtosis) excessively
heavy in tails (broad
and flattened)
– Leptokurtic (positive
kurtosis) excessively
light in tails (tall and
peaked)
• Skewness:
Nonsymmetrical slant or tilt
of distribution; uneven
distribution of values in tails
– Mean, median, and mode
different values
– Values clustered in left tail
= negatively skewed
– Values clustered in right
tail = positively skewed
• Bimodal (two modes)
• Multimodal (three or more
modes)

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Nonnormal Distributions (cont.)

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Tables
• Tabular presentations of frequency distributions
• Grid or matrix of raw counts or percentages

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Tables (cont.)
• Contingency table
– Visually presents information on two or more
categorical variables
– Also known as frequency tables, cross-
tabulation tables, and cross-classification
tables
– Number of cells depends on number of
variables and values (often dichotomous
variables with two values: yes or no)

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Tables (cont.)

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Tables (cont.)

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Bar Chart
• Bar chart: Visual
presentation of data
– Showing comparisons
between and among
variables
– Illustrating major
characteristics in
distribution of data
– Height of bar
corresponds to the
frequency of value’s
occurrence
– Gaps can exist
between bars
– Nominal or ordinal data

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Histogram
• Histogram: visual
presentation of the
frequency distributions
of continuous data
– Data are divided into
ranges of data called
bins or class intervals
– Height of bar
corresponds to
frequency of the
value’s occurrence
– Bars are adjoining
with no gaps between
bars

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Line Graph
• Line graph shows
trends for one
variable over time
– X-axis represents
time and the y-axis
represents the
frequency of an event
– May also compare
trends for multiple
variables with each
variable having its
own line

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Scatter Graph
• Scatter graphs (plots
or diagrams) show the
association between
two variables
– Clustering or dispersion
(scattering) of the data
points shows association
– Association can be linear
or nonlinear
– Positive linear
association between
variable a and variable b

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Pie Chart
• Pie charts visually
show proportions
(percentages) of a
variable in each value,
relationships among
the values, and the
whole
– Proportions are pie
slices and whole is the
whole circle of pie.
– Adding percentages of
all values should
equal 100 with “slices”
creating a complete
“pie”

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Graphical Display and
Investigation
• Stem-and-leaf diagram (plot)
– Summarize data while
maintaining all individual data
points
– Stem column is unique elements
after removing last digit(s)
– Leaves column is final digits
placed in row next to appropriate
stem column
– Row 7|1455 represents 71, 74,
75, 75 in A
– Row 45 |7|15 represents 71, 74,
75, 75 in B Back-to-back stem and leaf plot
A
B

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Graphical Display and Investigation (cont.)
• Box-and-whisker plot
(box plot)
– Display variation in a data
set
– Summarize dataset’s key
features
• Median
• Upper and lower quartiles
• Largest and smallest
values (range)
• Outliers
– Used to
• Compare multiple datasets
• Analyze or convey
dataset’s key features
rather than detail
• Median line is center of box formed by
upper and lower quartiles
• Whiskers extend to largest and smallest
values, excluding outliers
• Outliers are asterisks (or dots)

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Ratios and Proportions
•Ratio
– Comparison of two values that
can be unrelated
– Calculated by dividing one
value by the other value
– Result can be greater or less
than one
– Written as the numerator
followed by a colon and then
the denominator
– Convention is to standardize
the statement to the lowest
terms by dividing both numbers
by the lower number
• Proportion
– Comparison of a part to the
whole
– Type of ratio in which the
numerator’s quantity is
included in the denominator
– Expressed as a decimal, a
fraction, or a percentage

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Measures of Central Tendency*
Mean
• Average calculated
by summing all the
values and dividing
by the number of
values (arithmetic
mean, other types of
means exist)
• Mean is sensitive to
outliers meaning that
the mean can be
skewed by outliers
Median
• Middle value when all
the values are placed
in numeric order
• Half the values are
above the median and
half are below
• The mean of the
middle two numbers is
calculated to
determine the median
when there are an
even number of
values
Mode
• Value that occurs most
often
• All the values are
placed in numeric
order
• Often used for
nominative data, but
can be used for all
levels of data
*Measures of central tendency are also known as measures of location
Represent clustering of the majority of the dataset’s values
around its middle value

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Measures of Dispersion*
• Range
– Difference between the
greatest and smallest
value
– Calculated for ordinal and
metric data
• Interquartile range
(IQR)
– Range within which the
middle 50 percent of values
fall
– Can be calculated for ordinal
and metric data
•Distribution of observations away from the central value
•Show the variability of the data
*Measures of dispersion are also known as measures of spread

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Measures of Dispersion (cont.)
• Standard deviation
– Average distance
from the mean that
each value lies
– Shows concentration
or dispersion of
values from
distribution’s center
– Calculated only for
metric data
• Normality of the
distribution
– Normal distribution as
greatest frequency of
values in its curve’s
middle
– Nonnormal are kurtotic
or skewed econd-hand

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Correlation
• Correlations can be descriptive statistics
when the researcher’s purpose is to describe
the association
• Often Pearson product-moment correlation
coefficient
• Bivariate
– Two variables
• Multivariate
– Multiple dependent variables

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Inferential Statistics

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Other Tests and Terms
• Sensitivity analysis
• Cox (proportional hazards regression)
model
• Hazard (function) rate
• Poisson regression
• Bonferroni correction

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Misuse of Statistics
• Misuse use of statistics can be accidental
or intentional
– Invalid statistics for ordinal data
– Lying with statistics
– Unit of analysis error
– Confusing correlation with causation
• Consequence of misuse of statistics may
be distrust of research

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Review
• Study statistics to benefit from and make sense of the numeric data around
us
• Statistics is the science of collecting, classifying, displaying, analyzing, and
interpreting numerical data; biostatistics is a specialized branch of statistics
• Probability and random sampling underpin many statistical tests
• There are four levels of data: nominal, ordinal, interval, and ratio; the level
affects the selection of statistical tests
• Properties of normal curve underlie many statistical tests; parametric tests
are used for normal distributions, nonparametric tests for nonnormal
distributions
• Descriptive statistics describe what is by classifying, organizing, and
summarizing numerical data
• Inferential statistics detect differences and associations in groups and allow
the generalization of these findings to the population of interest
• Consequence of misuse of statistics may be distrust of research