Math 132B

Class 3

The Infant Cognition Study Again

Infant Cognition Study

A study performed in 2007 by the Infant Cognition Center at the Yale University presented 16 10-months old infants with a puppet show depicting a character trying to climb a hill.

  • In one situation, another character helped the climber ascend the hill.
  • In the other situation, a different character pushed the climber down the hill, hindering it and preventing it from ascending.

The infants were then asked to select one of the two characters (triangle and square) to play with, and their choice was recorded.

The Results

Out of the 16 infants that participated in the study, 14 chose the friendly character.

Can you think of some reasons why?

Two Questions in Statistical Analysis

  • Can the thing we observed in the sample be generalized to the whole population?

  • Is the observed effect caused by the treatment?

    • Did the helpful behavior in the puppet shows cause the infants to choose the friendly character?
    • Did the difference in the flu vaccine cause the difference in the flu infection rates?
    • Did the memory training games caused the improvement in the IQ scores?

Confounding

  • Response variable is the effect you want to observe or the outcome of the process you are studying.
  • Explanatory variable is what you believe causes the effect, or may cause the effect.
  • Confounding variable (confounder) is another variable that may be associated with both the explanatory and response variable.
  • Lurking variable is confounding variable that is not mentioned among the variables in the study.

Two explanations left

after eliminating confounders:

  • The infants can recognize the friendly behavior and choose the character based on that.

  • The infants are choosing randomly.

Techniques to minimize confounding

Repetition:

  1. Include a large number of diverse subjects, with wildly varying values of the confounding variables, to see if the effect you are looking for is present regardless of the values of the confounders. (Sample size)

  2. Repeat the whole study again with a different set of subjects. It is likely that the confounders will have different values, so if the result is similar, it makes it seem more likely that the effect is due to the treatment. (Replication)

Techniques to minimize confounding

Control:

  1. Fix the value of some potentially confounding variables, so that they do not vary and therefore cannot influence the results in different ways. (controlling the variables)

  2. Include a control group with the confounding variables still present, but with no treatment, to see is the effect will show even without the treatment.

Techniques to minimize confounding

Randomization:

  1. Randomize the values of the confounding variables that cannot be controlled. That way the influence of the confounders will be reduced to a random “noise”, which can be analyzed mathematically.

  2. Select the sample randomly, so that even the variables that are inherently present in the subjects themselves will be randomized.

Techniques to minimize confounding

Special techniques for some special cases of confounding variables: blinding, double blinding, binning, …

Important Question:

Are the researchers doing the study actually able to use these techniques?

Do they have enough control over the variables to be able to either control or randomize them?

An Example

A doctor at a university affiliated hospital wants to do a study that compares two different procedures that are both designed to alleviate certain condition. After securing all the necessary permissions, she randomly divides her patients into two groups, and performs one procedure on the patients in group 1, and the other procedure on the patients in group 2. She then compares the results.

Another Example

A researcher at a College of Health and Human Services at certain university wants to do a study that compares two different medical procedures that are both designed to alleviate certain condition. They contact doctors at 200 different hospitals that perform these procedures, and asks the doctors to report the results of the procedures to them.

Third Example

A group of medical professionals wants to do a study that compares two different medical procedures that are both designed to alleviate certain condition. Under the directions of a doctor, they perform one of the two procedures on 35 patients, and the other one on 17 patients, and compare the results.

Types of studies

  • Experiment: The researchers have control over all or most of the possible confounding variables, and are able to use some techniques to minimize confounding. When comparing multiple treatments, they can decide which subject gets which treatment.

  • Observational study: The researchers do not have control over the possible confounding variables. They cannot decide how the subjects will be divided into groups. These decisions are either not made at all, or someone else makes them, for reasons other that the study itself.

Example of an Observational Study

An observational study is conducted where two medical procedures alleviating the same condition are compared:

  • One procedure is cheap and quick, and is performed on 350 patients in the study.

  • The other one is much more expensive, takes much longer, and is much more invasive than the first one. It is performed on 72 patients in the study.

  • The first procedure is successful in 342 of the patients.

  • The second one is successful in 35 of the patients.

Can you conclude that the first procedure is better than the second one?

Back to the Two Questions

Can the result of the study be generalized to the whole population?

Can the study establish a causal relationship between the treatment and the effect?