Question

MATH225 Statistical Reasoning for the Health Sciences

Week 1 Assignment Variables and Measures of Data

Question Thomas is investigating if gender has any effect on
political party associations. Which of the following gives the
explanatory and response variables respectively?

the number of people that are being studied and
political party associations

the number of people that are being studied and gender

gender and political party associations

political party associations and gender

Question Karen is investigating if age has any effect on
political party preferences. What is the explanatory variable?

the number of people that are being studied

age

political party preferences

none of the above

Question True or False? An explanatory variable is a
value or component of the independent variable applied in an
experiment.

True

False

Question To determine whether or not grade level
influences time spent studying, Samuel has designed a survey. What
is the response variable?

grade level

time spent studying

the number of people surveyed

none of the above

Question To determine whether or not number of siblings
influences grade point average, Charles has designed a survey. What
is the explanatory variable?

number of siblings

grade point average

the number of people surveyed

none of the above

Question A market researcher finds the price of several
brands of fabric softener. What is the level of measurement of the
data?

nominal

ordinal

interval

ratio

Question A political researcher asks people if they Strongly
Disagree, Disagree, Agree, or Strongly Agree with various policy
decisions. What is the level of measurement of the data?

nominal

ordinal

interval

ratio

Question Which of the following scale levels would be best to
measure the data below?

The Carnival Cruise Line surveys its passengers after their
trip and asks them about the friendliness and hospitality of
various staff, such as the guest services desk staff, the
housekeeping staff, and the bar staff. The passengers rate each
staff group as

•
“Very Friendly,”

•
“Somewhat Friendly,”

•
“Somewhat Unfriendly,” or

•
“Not at all Friendly.”

nominal scale level

ordinal scale level

interval scale level

ratio scale level

Question In 2014, the website PhoneArena polled users,
asking them which smartphone company had the best phone that year.
The responses were the company names, such as Apple, Motorola,
Nokia, Samsung, and Microsoft.

Which of the following scale levels describes the data in
this poll?

nominal scale level

ordinal scale level

interval scale level

ratio scale level

Levels of Measurement

Levels of Measurement

The way a set of data is measured is called its level of
measurement. Researchers must be familiar with the levels of
measurement in order to use the correct statistical procedures. Not
every statistical operation can be used with every set of data.
Data can be classified into four scale levels of measurement:
nominal scale, ordinal scale, interval scale, and ratio scale.

Nominal scale level—Data that is measured using this
scale is qualitative and not ordered.

Categories, colors, names, labels, and favorite foods, along
with yes or no responses, are examples of nominal level data. For
example, trying to classify people according to their favorite food
does not make any sense. Putting pizza first and sushi second is
not meaningful.

Ordinal scale level—Data that is measured using this
scale can be ordered. This is the one major difference it has from
nominal scale data. Like nominal scale data, ordinal scale data
cannot be used in calculations.

An example of ordinal scale data is a list of the top five
national parks in the United States. The top five national parks
can be ranked from one to five, but we cannot measure differences
between the data.

Interval scale level—Data that is measured using this
scale has a definite order, and the differences between interval
scale data can be measured. However, the data does not have a
starting point.

For example, temperature scales (Celsius and Fahrenheit) are
measured using the interval scale. In both temperature
measurements, 40° is equal to 100° minus 60°. Here, differences
make sense. But 0° is not necessarily the starting point because in
both scales 0° is not the absolute lowest temperature.
(Temperatures like -10° and -15° exist and are colder than 0°.)

*Note: Interval level data can be used in calculations, but a
ratio comparison cannot be made. 80° is not four times as hot as
20° (in either temperature measure). There is no meaning to the
ratio of 80 to 20 (or 4 to 1).

Ratio scale level—Data that is measured using this
scale addresses ratios and gives you the most information about the
data. Ratio scale data is like interval scale data, but it has a
starting point (also known as a “0 point”) and ratios between the
differences can be calculated.

For example, four multiple-choice statistics final exam
scores are 80, 68, 20, and 92 (out of a possible 100 points). The
data can be put in order from lowest to highest (20, 68, 80, 92),
and the differences between the data have meaning. The score 92 is
more than the score 68 by 24 points. Since there is a starting
point (the smallest score is 0), ratios can be calculated. So, 80
is 4 times 20. The score of 80 is 4 times better than the score of
20.

Question A zoologist measures the birthweight of each cub in
a litter of lions. What is the level of measurement of the data?

nominal

ordinal

interval

ratio

Question A restaurant asks its patrons to rate the
speed of the service. The options are Very Slow, Somewhat Slow,
Somewhat Fast, Very Fast. What is the level of measurement of the
data?

nominal

ordinal

interval

ratio

Question A new mother keeps track of the time when her
baby wakes up each morning. What is the level of measurement of the
data?

nominal

ordinal

interval

ratio

Question Patrick is collecting data on shoe size. What
type of data is this?

qualitative data

discrete quantitative data

continuous quantitative data

none of the above

Question Janice is investigating if grade level has any
effect on time spent studying. What is the explanatory variable?

time spent studying

grade level

the number of people that are being studied

none of the above

Question Margaret is investigating if gender has any
effect on political party associations. What is the response
variable?

political party associations

gender

the number of people that are being studied

none of the above

Question What is the independent variable in an
experiment?

lurking variable

treatment

explanatory variable

response variable

Question Which of the following best describes the term
explanatory variable?

the dependent variable in an experiment

a value or component of the independent variable
applied in an experiment

a variable that has an effect on a study even though it
is neither an independent nor a dependent variable

the independent variable in an experiment

Question The Smell & Taste Treatment and Research
Foundation conducted a study to investigate whether smell affects
learning. The subjects completed a maze on paper while
wearing floral-scented masks and a different maze while wearing
unscented masks. The order of the masks is randomly assigned to the
subjects. All subjects were tested in the same location.
Researchers found that it took longer to complete the maze while
wearing the floral-scented mask as compared to the unscented masks.
Is the location of subject’s home a lurking variable in this study?

No

Yes

Explanatory and Response Variables

Lurking Variables & the Importance of Blinding

Study 1

You want to investigate the effectiveness of vitamin E in
preventing disease. You recruit a group of subjects for your
sample, and ask them if they take vitamin E regularly. Analyzing
the study, you notice that the subjects who take vitamin E
regularly are healthier on average than the subjects who do not.

Does this study prove that vitamin E is effective in
preventing illness and disease?

The answer is – It does not. There are many more differences
between subjects who do and do not take vitamin E that were not
taken into account. People who take vitamin E regularly may also
take other steps to improve their health: exercise, diet, other
vitamin supplements, choosing not to smoke, etc. Any one of these
factors could also be influencing health. These additional
variables that can cloud a study are called lurking variables. So,
as described, this study does not prove that vitamin E is the key
to disease prevention.

In order to prove that the explanatory variable is the actual
cause of the change in the response variable, it is necessary to
isolate the explanatory variable.

Study 2

Researchers want to understand the effect of
performance-enhancing drugs. One group of participants were given
the active performance-enhancing drug, and the other group was
given placebo pills (pills with no active drug). The results showed
that if a person simply believed that he or she had taken the drug,
their performance times were almost as fast as those subjects who
had actually consumed the active pills with the drug. In contrast,
people who took the drug without knowing they were exhibited no
significant performance increase.

A researcher must design an experiment in such a way
that there is only one difference between the groups being
compared: the planned treatments. (In Study 2, the planned
treatments are the types of pill each subject took – pills
containing the performance-enhancing or the placebo pills.) Then a
researcher must randomly assign the treatments. When this happens,
all of the potential lurking variables are spread equally among the
groups. Now, the different outcomes measured in the response
variable, are a direct result of the different treatments. In this
way, an experiment can prove a cause-and-effect connection between
the explanatory and response variables.

The Power of Suggestion & Importance of Blinding

The power of suggestion can have an important influence on
the outcome of an experiment. Studies have shown that the
expectation of the people participating in the study can affect the
outcome just as much as the actual medication itself. So,
researchers must set aside one group as a control group. This group
is given the placebo treatment–the treatment that cannot influence
the response variable. (The control group in Study 2 is the group
that took the placebo pills.)

Blinding in a randomized experiment counteracts the altering
power of suggestion. When a person involved in a research study is
blinded, he/she does not know who is receiving the active
treatments (in the study above, this would be the
performance-enhancing drug) and who is receiving the placebo
treatment (the pills without drug). A double-blind experiment is
one where both the subjects and the researchers are blinded.

Question Researchers are investigating whether taking aspirin
regularly reduces the risk of heart attacks. Four hundred men
participate in the study. The men are divided randomly into two
groups: one group takes aspirin pills, and the other group takes
placebo pills (a pill with no aspirin in it). The men each take one
pill a day, and they do not know which group they are in. At the
end of the study, researchers will count the number of men in each
group who have had heart attacks.

Identify the explanatory and response variables in this
situation.

Explanatory variable: whether a subject had a heart attack

Response variable: the type of pill the men took each day

Explanatory variable: the type of pill the men took
each day

Response variable: whether a subject had a heart attack

Explanatory variable: the 400 men participating in the
study

Response variable: whether a subject had a heart attack

Explanatory variable: the aspirin pills

Response variable: the placebo pills (containing no aspirin)

Explanatory and Response Variables

Explanatory and Response Variables

Does aspirin reduce the risk of heart attacks? Is one
brand of fertilizer more effective at growing roses than another?
Questions like these are answered with studies using randomized
experiments. The purpose of an experiment is to investigate the
relationship between two variables:

•
An explanatory variable attempts to explain or influence changes in
another variable. Different values of the explanatory variable are
called treatments.

•
The affected variable, the variable that is changed by altering the
explanatory variable, is called the response variable.

In a randomized experiment, the researcher manipulates values
of the explanatory variable and measures any resulting changes in
the response variable.

Example

Question You want to know if there is a
relationship between the amount of time a student spends studying
for an exam and that student’s grade on the exam.

Identify the explanatory and response variables in this
situation.

Question Is the statement below true or false? A
response variable is a variable that has an effect on a study even
though it is neither an independent nor a dependent variable.

True

False

Question What is the type of quantitative data that is
the result of measuring?

qualitative

statistic

discrete

continuous

Question Which of the following is the independent
variable in an experiment?

lurking variable

explanatory variable

response variable

treatment

Question Is the statement below true or false? An explanatory
variable is the independent variable in an experiment.

True

False

Question Which of the following best describes the term
response variable?

the independent variable in an experiment

a variable that has an effect on a study even though it
is neither an independent nor a dependent variable

the dependent variable in an experiment

a value or component of the independent variable
applied in an experiment

Question A market researcher surveys users of a certain
laundry detergent about whether they think the detergent makes
their laundry smell Very Bad, Bad, Neutral, Good, or Very Good.
What is the level of measurement of the data?

nominal

ordinal

interval

ratio

Question Is the statement below true or false?
Continuous data is the type of quantitative data that is the result
of counting.

True

False

Question True or false? Discrete data is the type of
quantitative data that is the result of counting.

True

False

Question At a comic convention, a researcher asks
attendees what their favorite comic book is. What is the level of
measurement of the data?

nominal

ordinal

interval

ratio

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