Section 2.1 Material in these slides is taken from the following - - PowerPoint PPT Presentation

Section 2.1

Material in these slides is taken from the following text: Contemporary Mathematics: Contemporary Mathematics at Nebraska by Michelle Homp, Alyssa Seideman, and Sean Gravelle It is available online at https://mathbooks.unl.edu/Contemporary/index.html

[ do questions 1,2 in the workbook ]

Observational Study

• So far, we have primarily discussed
• bservational studies: studies in which

conclusions would be drawn from observations

• f a sample or the population.

Experiments

• In contrast, it is common to use experiments

when exploring how subjects react to an

• utside influence. In an experiment, some kind
• f treatment is applied to the subjects and the

results are measured and recorded. By applying some treatment to the subjects, the researchers are controlling one of the variables, which does not occur in an observational study.

Example Experiments

• A pharmaceutical company tests a new medicine for

treating Alzheimers disease by administering the drug to 50 elderly patients with recent diagnoses. The treatment here is the new drug.

• A gym tests out a new weight loss program by enlisting

30 volunteers to try out the program. The treatment here is the new program.

• You test a new kitchen cleaner by buying a bottle and

cleaning your kitchen. The new cleaner is the treatment.

• A psychology researcher explores the effect of music on

temperament by measuring peoples temperament while listening to different types of music. The music is the treatment.

Which is Which?

• The weights of 30 randomly selected people

are measured.

• Subjects are asked to do 20 jumping jacks, and

then their heart rates are measured.

• Twenty people are told to drink coffee and

twenty are told to drink tea. They are then given a concentration test.

• Researchers survey 100 students, asking

whether they drink coffee or tea. They then give these 100 people a concentration test.

Which is Which?

• The weights of 30 randomly selected people are
• measured. [Observational study]
• Subjects are asked to do 20 jumping jacks, and

then their heart rates are measured. [Experiment; the treatment is the jumping jacks]

• Twenty people are told to drink coffee and twenty

are told to drink tea. They are then given a concentration test. [Experiment; the treatments are coffee and tea]

• Researchers survey 100 students, asking whether

they drink coffee or tea. They then give these 100 people a concentration test. [Observational study]

Experiments vs Observational Studies

• Experiments can often yield more robust results

than observational studies.

• Observational studies are sometimes

necessary for ethical or logistical reasons.

– For example, suppose researches are studying the

effects of smoking. They could not ethically ask an experimental group to start smoking, so they would have to perform an observational study instead.

• Cause and effect conclusions can only be

drawn from experiments!

Experiments vs Observational Studies

• Consider the previous example and suppose

that people who smoked were more likely to have lung cancer. The researchers CANNOT conclude that smoking causes lung cancer.

Smoking Lung Cancer

Experiments vs Observational Studies

• Consider the previous example and suppose

that people who smoked were more likely to have lung cancer. The researchers CANNOT conclude that smoking causes lung cancer.

Smoking Genetics Lung Cancer

Maybe there was a genetic reason that people were both prone to smoking and to getting lung cancer

Correlation

• The tendency for two values or variables to

change together, in either the same or opposite

• way. (Definition from wordnik.com)
• Not the same as causation!

– In the previous example, (where we said that for

sake of example, genetics cause both a tendency to smoke and a risk for lung cancer) smoking was correlated with lung cancer, but was not the cause

• f lung cancer. (Note this is an example and we are

not making any real genetic or medical claims.)

• There are a number of reasons that variables

can be correlated, causation is just one...

Correlation: Coincidence

Image from http://tylervigen.com/spurious-correlations

Correlation: Confounding

• Confounding occurs when there are two

potential variables that could have caused the

• utcome, and it is not possible to determine

which actually caused the result.

– Researchers conduct an experiment to determine

whether students will perform better on an arithmetic test if they listen to music during the test. They first give the student a test without music, then give a similar test while the student listens to music. In this case, the student might perform better on the second test, regardless of the music, simply because it was the second test and they were warmed up.

Example of Confounding

• Consider a researcher attempting to assess the

effectiveness of drug X, from population data in which drug usage was a patient's choice. The data shows that gender (Z) differences influence a patient's choice of drug as well as their chances of recovery (Y). In this scenario, gender Z confounds the relation between X and Y since Z is a cause of both X and Y:

Example from https://en.wikipedia.org/wiki/Confounding

Example of Confounding

• Data shows that gender (Z) differences

influence a patient's choice of drug as well as their chances of recovery (Y). In this scenario, gender Z confounds the relation between X and Y since Z is a cause of both X and Y:

Example from https://en.wikipedia.org/wiki/Confounding

Experiments: Control and Treatment Groups

• In some experiments the participants are

divided into two or more groups, typically a control group and a treatment group. The treatment group receives the treatment being tested; the control group does not receive the treatment.

• This allows for the possibility of drawing the

conclusion that the treatment caused an

• bserved difference between the groups.

– If the participants were randomized between the

groups, variables other than the treatment should be consistent between the groups.

[ back to workbook ]

[ extra slides ]

Correlation: Coincidence

Image from http://tylervigen.com/spurious-correlations

Correlation: Causation (?)

Image from xkcd.com/523/

Correlation: Causation (?)

Image from xkcd.com/523/

Correlation: Causation (?)

Image from xkcd.com/523/

Correlation: Causation (?)

Image from xkcd.com/552/

Correlation: Causation (?)

Image from xkcd.com/552/

Correlation: Causation (?)

Image from xkcd.com/552/

Correlation: Causation (?)

Image from xkcd.com/552/

Correlation: Causation (?)

Image from xkcd.com/552/