MATH225 Week 1 Assignment Variables and Measures of Data (July 2019)

MATH 225 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