What is the Difference
Between a Percentage and a Rate?
Often we hear the question, "What is the
difference between a percentage and a rate?"
They are both calculated using a numerator
and a denominator. However, the relationship
between the numerator and denominator makes
the difference.
Percentages
Indicators which use percentage are the most
commonly used indicator type in healthcare.
Most of the Joint Commission measures monitor
percentages to measure compliance. A percentage
measures the number of a certain set of events
which have a particular outcome when there are
two outcomes possible, either Yes or No. For
example, either the AMI patient received aspirin
on arrival or they did not. For each of these
outcomes (received aspirin or did not receive
aspirin), there can never be more than 100 percent.
We cannot see a situation where 110% of the
patients admitted received aspirin on arrival.
Guidelines for Percentages:
 Numerator and denominator are the same unit
of measure
 Both the numerator and denominator are positive
whole numbers
 The numerator is never greater than the denominator
Example: An AMI patient is admitted.
Did that patient receive aspirin on arrival?
If we look at all the AMI patients admitted
during a period, some subset of those patients
receive aspirin on arrival. To get the percentage,
we divide the number of AMI patients admitted
and who received aspirin (numerator) by the
total number of AMI patients admitted (denominator).
The patients who received aspirin are a subset
of the patients admitted.
Percentages are charted on a p chart, where
p stands for proportion. Statit piMD™
translates that to a percentage, a simple transformation
that has no effect on the results except to
provide the viewer a standard view that is easier
to understand.
Rates
A rate, on the other hand, does not have the
same numeratordenominator relationship as a
percentage. For example, if we look at falls
per patient days, the patient days did not fall.
So the numerator is not a subset of the denominator;
that is, it does not have the same unit of measure.
If we answer the question, "Can an outcome
happen more than once in an area of opportunity?"
in the affirmative, then we are talking about
a rate.
We probably cannot count the number of opportunities
for a patient to fall, so we use a surrogate
measure that will give us an indication of the
magnitude of the area of opportunity. Patient
days fits well with several such measures. Using
such surrogate measures produces standard measures
across different size hospitals with different
numbers of patients.
Guidelines for rates:
 Numerator and denominator do not use the same
unit of measure
 There can be more than one countable outcome
for a unit in the denominator
 We may not be able to count the opportunities
for the outcome
Example:
We might measure the number of falls per 1000
patient days. The numerator is the number of
falls during the period. The denominator is
the number of patient days in that period divided
by 1000. We use the 1000 patient days as a denominator
to produce a number that will make a little
more sense to the viewer. Four (4) falls per
1000 patient days seems to make more sense to
the human mind than .04 falls per patient day.
You would probably choose the denominator (1000
patient days or 100 patient days) based on how
you would want to compare your measures to other
hospitals. If most of the hospitals you are
comparing are using 1000 patient days, then
you would probably want to use 1000 patient
days.
This type of data is charted on a u chart where
the u stands for unit, as in number of defects
per unit. An important thing to remember is
that there can be more than one defect per unit.
In the above example, the unit is 1000 patient
days and the defect is falls.
The rate might be expressed in a form that
looks like a percentage but is not and can produce
confusion. For example, falls per 1000 patient
days is a rate not a percentage. The number
produced is not the number of patient days that
fell but is the rate of falls per 1000 patient
days.
Let me give you one more example that may help
to illustrate the difference. With med errors,
each dose could have more than one error. We
administer a dose of medicine. There could be
more than one error with that dose, such as
wrong time, wrong dose, wrong patient, or wrong
delivery. A percentage would be the number of
doses that were in error divided by the total
number of doses administered. Doses in error
would be any dose that had a least one error.
A rate would be the count of individual errors
divided by the number of doses. The percentage
would be expressed as the percent of doses that
had at least one error. The rate would be expressed
as the number of individual errors per 1000
doses.
The Statit
piMD online demo and the 10
Minute guided tour of Statit piMD give you
some illustration of the use of these measures.
Most of the indicators under the group Competency
are percentage type; however, Adverse Drug Events
is a rate type. Please take a look at these
charts for a better understanding of the difference
between the two types.
A more indepth discussion of these data and
chart types can be found at:
http://www.statit.com/support/quality_practice_tips/ucharts_pcharts_icharts.shtml.
