07 Jan discrete quantitative

MATH399 Applied Managerial Statistics

Week 1 Variables and Measures of Data

Question A biologist samples and measures the length of the fish in a lake. What is the level of measurement of the data?

Nominal

Ordinal

Interval

Ratio

QuestionA 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

QuestionA track runner keeps track of how long it takes her to run the 200 meter dash. What is the level of measurement of the data?

Nominal

Ordinal

Interval

Ratio

QuestionJason is collecting data on the number of books students read each year. What type of data is this?

qualitative

discrete quantitative

continuous quantitative

none of the above

QuestionIs the statement below true or false?

Continuous is the type of quantitative data that is the result of counting.

True

False

QuestionWhich 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

QuestionThe 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.

QuestionResearchers 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

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

QuestionYou 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.

QuestionJacqueline is investigating if age has any effect on the number of hours of sleep. Which of the following gives the explanatory and response variables respectively?

the number of people that are being studied and the number of hours of sleep

the number of hours of sleep and age

age and the number of hours of sleep

the number of people that are being studied and age

QuestionJanice 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

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

qualitative

discrete quantitative

continuous quantitative

none of the above

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

Nominal

Ordinal

Interval

Ratio

QuestionMichelle is investigating if gender has any effect on political party associations. What is the explanatory variable?

political party associations

gender

the number of people that are being studied

none of the above

QuestionA 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 Timothy is collecting data on the number of dental cavities. What type of data is this?

qualitative

discrete quantitative

continuous quantitative

none of the above