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CHAPTER 1
INTRODUCTION TO STATISTICS AND
LEVELS OF MEASUREMENT
HOW TO FIGURE THINGS OUT.
OBJECTIVES
By the end of this chapter students will be able to:
• State the question that statistics is always trying to answer.
• Define the empirical method.
• Compare quantitative and qualitative variables.
• Differentiate a population from a sample and a statistic from a parameter, giving an
example of each.
• Explain the difference between an independent and a dependent variable, citing
examples of each.
• Identify continuous and categorical variables accurately.
• Distinguish the four levels of measurement and describe each.
• Apply several beginning-level statistical techniques to further develop understanding
of the concepts discussed in this chapter.
KEY TERMS
Categorical variable
A variable that has a finite number of classification groups or categories, which are usually
qualitative in nature.
Continuous variable
A variable that has an infinite number of potential values, with the value being measured
falling somewhere on a continuum containing in-between values.
Dependent variable
The outcome variable or final result.
Empirical method
Gathering information through systematic observation and experimentation.
Estimate
A preliminary approximation.
Independent variable
A variable measured or controlled by the experimenter; the variable that is thought to affect
the outcome.
Interval data
Data whose categories are exhaustive, exclusive, and rank ordered, with equally spaced
intervals.
Nominal data
Data that indicates a difference only, with categories that are exhaustive and exclusive, but
not rank ordered.
Ordinal data
Data whose categories are exhaustive, exclusive, and rank ordered.
Parameter
Descriptive result for the whole group.
Population
The whole group.
Probability
How likely it is that an outcome will occur.
Qualitative measure
A measure that describes or characterizes an attribute.
Quantitative measure
A measure that reflects a numeric amount.
Ratio data
Data whose categories are exhaustive, exclusive, and rank ordered with equally spaced
intervals and a point at which the variable does not exist.
Sample
A group selected from the population.
Statistic
An estimate derived from a sample.
Variable
The changing characteristic being measured.
INTRODUCTION
So here you are. You’ve worked hard, you are in nursing school, and are ready to
begin your studies. But wait! What do you mean you have to take statistics? Why does
a nurse need to understand all those numbers and equations when you just want to
help people?
Most nursing students experience a mild sense of panic when they discover they have
to take statistics—or any other kind of math for that matter. That reaction is
commonplace. Here is a calming thought to remember: You already practice statistics,
but you just don’t know it. Statistics boils down to doing two things:
• Looking at data.
• Applying tests to find out either (1) that what you observe is what you expected or
(2) that your observation differs enough from what you expected that you need to
change your expectations.
You might be convinced that you don’t use statistics in your life, so let me give you
an example. New York State, where I live, has four seasons. The summer is usually
June, July, and August. Fall is September, October, and November. Winter is
December, January, and February. And that leaves March, April, and May for the
spring. If you walk outside in July and find it to be 80° and humid, you would draw an
unspoken conclusion that what you just observed is what you were expecting, and you
would put on your sunglasses. However, what if you walk outside in January and find
it to be 80° and humid? You would probably be startled, take off your overcoat and
boots, and read up on global warming. The difference between the weather you expect
in January and what you actually encounter is so different that you might need to
change your expectations. You are already practicing statistics without knowing it!
Of course, that day in January might just be a fluke occurrence (a random event), and
the temperature could be below freezing again the next day. That is why we need to
use the empirical method, otherwise known as systematic observation and
experimentation. The empirical method allows you to determine whether the
temperature observed is consistently different from what you expect. To use the
empirical method, you need to check the temperature on more than one day. So you
might decide to monitor the temperature for the whole month of January to see
whether readings are consistently different from what you expect. In this scenario, you
would be using the empirical method to practice statistics.
POPULATION VERSUS SAMPLE
To answer questions in research, we need to set up a study of the concepts we’re
interested in and define multiple variables, that is, the changing characteristics being
measured. In our example, the temperature is a variable, a measured characteristic.
Each variable has an associated probability for each of its possible outcomes, that is,
how likely it is the outcome will occur. For example, how likely is it that the
temperature will be below freezing as opposed to in the eighties? In your study, you
recorded the temperature for only the month of January, and those readings make up a
sample of all the days of the year. The manner in which you collect your sample is
dependent on the purpose of your study.
A sample is always a subset of a population, or an overall group (sometimes referred
to as the reference population). In this case, our population includes all the days of the
year, and the subset, or sample, is all the days in January. If you calculate the average
temperature based on this sample data, you create what is called a statistic, which is
an estimate generated from a sample.
A measured characteristic of a population is called a parameter. In our example, if
you measured the temperature for the whole year and then calculated the average
temperature, you would be determining a parameter. A really good way to remember
the relationships among these four terms is with the following analogy: Statistic is to
sample as parameter is to population.
QUANTITATIVE VERSUS QUALITATIVE
While you are collecting the weather data, you may realize that the data can be
recorded in several ways. You could write down the actual temperature on that day,
which would be a quantitative measurement, or you could describe the day as
“warm” or “cold,” which would be a qualitative measurement. A numeric amount or
measure is associated with quantitative measurement (such as 80°F), and qualitative
measures describe or characterize things (such as, “So darn cold I can’t feel my toes”).
Be careful with this difference: You can easily get confused. Qualitative variables do
not contain quantity information, even if numbers are assigned. The assigned numbers
have no quantitative information, rank, or distance. For example, a survey question
asks, “What color scrubs are you wearing?” and lists choices numbered 1–3. Even if
you selected choice 2, neon orange, you do not necessarily have any more scrubs than
someone who chooses 1, lime green (although both respondents may want to purchase
new scrubs). Even though these qualitative variables have numbers assigned to them,
the numbers simply help with coding. The variables are still qualitative.
INDEPENDENT VERSUS DEPENDENT VARIABLES
Being as inquisitive as you are, you have probably asked yourself a number of times
about a relationship you observe in your patients. For example, you notice that many
supportive family members visit Sally Smith after her hip replacement recovery and
that she is discharged 3 days after her surgery. Joanne Jones, on the other hand, has no
visitors during her hip replacement recovery and is not discharged until day 6. As an
observant nurse researcher, you have been wondering how variable x (the
independent variable, which is measured or controlled by the experimenter) affects
variable y (the dependent variable, or outcome variable). You wonder, does having
family support (the independent variable) affect the duration of a hospital stay (the
dependent, or outcome, variable)?
To answer this question, you create a study. Obviously, other factors might be
involved as well, but in your experiment you are interested in how family support, the
independent variable, impacts hospital stay, the dependent variable. If you are correct,
then the duration of the hospital stay depends on family support. The independent
variable can be the suspected causative agent, and the dependent variable is the
measured outcome or effect.
Note: Additional criteria must be met to say a variable is causative, so I refer here
only to the “suspected” causative agent.
CONTINUOUS VERSUS CATEGORICAL VARIABLES
Some data have an infinite number of potential values, and the value you measure
falls somewhere on a continuum containing in-between values. These values are
called continuous variables. As a nurse, when you measure your patient’s
temperature, you are measuring a continuous variable. The reading could be 98° or
98.6° or 98.66666°. The infinite possibilities are all quantitative in nature. Actually,
the only limit to the measurement is the accuracy of the measuring device. If, for
example, you have a thermometer that measures only in whole degrees, you will not
have as much information as you would using a thermometer that measures to the
one-thousandth of a degree.
FROM THE STATISTICIAN
Brendan Heavey
What is a Statistic?
As a student of statistics, you will run into questions regarding parameters and statistics all
the time. Determining the difference between the two can be difficult. To get a concrete idea
of the difference, let’s look at an example. According to the Bureau of Labor Statistics,
registered nurses constitute the largest healthcare occupation, with 2.7 million jobs
nationwide. Because this text is primarily designed for nursing students, let’s use this number
for our example.
Let’s say you are a consultant working for a fledgling company that is planning to make
scrubs for nurses. Let’s call this company Carol’s Nursing Scrubs, Inc. Scrubs at Carol’s will
come in small, medium, and large. The company will offer all kinds of styles and prints, but
the underlying sizes are intended to remain the same. Carol just received her first bit of seed
money to mass-produce 20,000 pairs of scrubs. Carol, an overly demanding boss, wants the
medium-size scrubs to fit as many nurses nationwide as possible. To make that happen, she
needs to know the average height and weight of nurses nationwide, so she has instructed you
to conduct a nationwide poll. She thinks you should ask every nurse in the country his or her
height and weight and then calculate the average of all the numbers you get.
Now, you are an intelligent, well-grounded employee who’s in demand everywhere and
working for Carol only because her health plan comes with a sweet gym membership and
you get a company car. So you realize it would be pretty difficult to set up a nationwide poll
and ask all the nurses in the country for their height and weight. Even if you tried a mass
mailing, the data returned to you would be filled with so many incompletes and errors that it
wouldn’t be trustworthy.
So what are you to do? Your first instinct might be to respond to your boss by saying, “Geez,
Carol, that’s so absurd and impossible I don’t even know where I’d start,” and then finish
your day on the golf range. However, after this course you’ll be not only a nurse, but a nurse
with some training in statistics. You’ll be able to deal with this situation in a more effective
way.
Jenna the Statistical
Carol, I recommend we take a few samples of nurses nationwide and survey the
Nursing Guru (you):
rather than attempting to contact every nurse in the country. Then we could esti
the true average height and weight based on our samples.
How would that work, Jenna?
Carol:
Jenna:
Well, I’d go down to the University Hospital and poll 30 RNs on their height an
weight. Then I’d go to the next state and do the same. My third and final sample
would contain 30 RNs from a hospital in Springfield. I’d calculate the average f
my total sample (90 RNs), which is a statistic, and use that to estimate the overa
average in the United States, which is a parameter of the total population.
You see, Carol, any time you calculate an estimate with data from a sample or l
data from the sample itself, you calculate a statistic. If you calculate an estimate
data in an entire population, you’re calculating a parameter.
Continuous variables can be contrasted with categorical variables, sometimes called
discrete variables, which have a finite number of classification groups, or categories,
that are usually qualitative in nature. For example, as part of your research you may
need to collect information about your patients’ racial background. The choices
available are African American, Native American, Caucasian, Asian, Latino, mixed
race, and other. Race is an example of a categorical variable, a measurement that is
restricted to a specific value and does not have any fractional or in-between values.
LEVELS OF MEASUREMENT
Let’s say your interest in the relationship between family support (the independent
variable) and duration of stay (the dependent variable) is extensive enough that you
apply for a program at your hospital that includes a small research fellowship. You
win the fellowship and proceed to collect data about each patient admitted to your
orthopedic unit for hip replacement over a 3-month period. The study protocol calls
for you to complete the usual admission forms and then for patients to complete a
short survey about perceived family support. After your institutional review board
approves your study, you begin. The level of measurement of your data determines
what type of analysis you are able to perform in your study, so let’s look at the
different types and what makes each level unique.
Your first question asks the patient’s gender: male or female. The data you gather for
this question is an example of nominal data; it simply indicates a difference between
the two answers. One is neither greater nor less than the other, and they are not in any
particular order. Also, the categories are exclusive and exhaustive; that is, the patient
cannot answer “both” or “neither.”
You then ask the patient to rate his or her family support level as low, medium, or
high. This question is an example of ordinal data. Ordinal data must be exhaustive
and exclusive, just like nominal data, but the answers are also rank ordered. With
rank-ordered data, each observation/category is higher or lower or better or worse
than another, but you do not know the level of difference between the
observations/categories. In this example, a high level of family support indicates a
greater quantity of the variable in question than does a low level of family support.
A routine part of admitting each patient also includes a baseline set of vital signs. One
of the vital signs you check is each patient’s temperature. Temperature is an example
of interval data, which is exhaustive, exclusive, and rank ordered and which has
numerically equal intervals. In this example, the interval is a degree of Fahrenheit.
After assessing each patient’s temperature, you go on to take each patient’s blood
pressure. Blood pressure is an example of ratio data, which is exhaustive, exclusive,
and rank ordered with equal intervals and a point at which the variable is absent. (If
the blood pressure reading is “absent” in any of your patients, you need to begin
CPR!)
Ratio data is the highest level of measurement you can collect and gives you the
greatest number of options for data analysis, but not all variables can be measured at
this level. As a general rule of thumb, always collect the highest-level data you can for
all your variables, especially your dependent variable. In your study of how family
support (the independent variable) impacts the duration of hospital stay (the
dependent variable), you could have measured the length of hospital stay as short,
medium, or long (ordinal) or in actual days (the interval/ratio level). Obviously, the
actual number of days gives you a higher level of measurement.
Note: A dependent variable with a higher level of measurement allows for a more
robust data analysis. Collect the highest level you can.
SUMMARY
Talk about exhausting, but you survived! So let’s wrap it up here. Statistics really
boils down to asking:
• Is what you observe what you expect?
• Or, using the empirical method, have you determined that what you observe is
different enough from what you would expect that you need to change your
expectations?
Using qualitative (descriptive) and quantitative (numeric) variables, you can assess
the impact of independent variables on dependent (outcome) variables. Always collect
the highest level of measurement possible, especially for your dependent variable.
Doing so gives you the widest range of analysis options when you are ready to
“crunch the numbers.”
If you understand these concepts, you are ready to move on to the review exercises. If
you are still struggling, don’t despair. These concepts sometimes take a while to
absorb. Read the review questions and then the chapter again, and slowly start to look
at the review questions. You will get the hang of statistics; sometimes you just need
practice. My students frequently look at me as though I am an alien when I tell them
that by the end of the course this chapter will seem really simple. You may not believe
it either. However, as you develop your understanding and apply these concepts, they
will become clearer, and you too will look back in amazement. You are a statistical
genius in the making!
CHAPTER 1 REVIEW QUESTIONS
1. A researcher asks hospitalized individuals about their comfort in a new type of hospital
gown. This is an example of what type of data?
2. If a researcher is examining how exposure to cigarette ads affects smoking behavior,
cigarette ads are what type of variable?
3. A nurse practitioner measures how many times per minute a heart beats when an
individual is at rest versus when running. She is measuring the heartbeat at what level of
measurement?
4. If a researcher is examining how exposure to cigarette ads affects smoking behavior,
smoking behavior is what type of variable?
5. The research nurse is coding adults according to size. A person with a below-average
body mass index (BMI) is coded as 1, average is 2, and above-average is 3. What level of
measurement is this?
a.
b.
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
ratio
independe
quantitativ
qualitative
qualitative
quantitativ
dependent
independe
interval/ra
nominal
independe
ordinal
ratio
independe
dependent
nominal
nominal
ratio
ordinal
interval
6. You are asked to design a study measuring how nutritional status is related to serum
lead levels in children. You assess calcium and fat intake, as well as serum lead levels in a
sample of 30 children who are 2 years old. Lead levels are measured in micrograms per
deciliter (mcg/dL). One child had a lead level of 17 mcg/dL. This is an example of what
type of variable?
Questions 7–9: You are asked to design a study to examine the relationship between
preoperative blood pressure and postoperative hematocrit.
7. What is your independent variable?
8. What is your dependent variable?
9. How will you measure each, and what level of measurement is this?
Questions 10–13: You are later asked to do a follow-up study to see whether requiring an
intraoperative blood transfusion impacted postoperative rates of poor mental health,
specifically depression.
10. What is your independent variable?
11. What is yo …
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