Question

Experiment 1: Billy Rae Thompson wanted to test a new "singalong" method to teach math to...

Experiment 1: Billy Rae Thompson wanted to test a new "singalong" method to teach math to sixth graders (e.g., "All the integers, are natural numbers" to the tune of "Call me Maybe"). He used the singalong method in his first period class. His sixth period students continued solving math problems with the old method. At the end of the term, Mr. Rogers found that the first period class scored significantly lower than the sixth period class on a mathematics achievement test. He concluded that the singalong method was a total failure.

1. Identify the independent variable(s). (2 points)
2. Identify the dependent variable(s). (2 points)
3. Identify whether there are any confounding variable(s) and what they are. (5 points)
4. Identify two possible sources of error variance (or “noise”). (6 points)
5. Propose a method to "unconfound" the experiment. (10 points)

Experiment 3: An airport administrator investigated the attention spans of air traffic controllers to determine how many incoming flights the average controller can coordinate at the same time. Each randomly selected controller was tested, without his or her knowledge, by a computer program that fed false flight information to a computer terminal. The controller first "received" information from one plane, and then two planes, and so on. By the end of an hour the controller was coordinating 10 planes simultaneously. The administrator analyzed the errors collected by the computer program. The analysis revealed that the maximum number of planes a controller could handle without making potentially fatal errors was six planes. Also, no errors occurred when only one to three planes were incoming. He concluded that a controller should never coordinate more than six incoming flights.

1. Identify the independent variable(s). (2 points)
2. Identify the dependent variable(s). (2 points)
3. Identify whether there are any confounding variable(s) and what they are. (5 points)
4. Identify two possible sources of error variance (or “noise”). (6 points)
5. Propose a method to "unconfound" the experiment. (10 points)

1.

dependent variable - score in mathematics test (continuous)

independent variables - class (categorical) , how did students solved the problem (binary categorical - old vs singalong method)

Confounding variables - Here, the first graders are likely to perform comparatively lower than sixth graders. Also, the tendency to sing for both the classes differs significantly.

Real experiment is to check whether singing has an effect on score but class of the student is likely to give a false estimate of results and therefore - class is the confounding variable

Possible sources of variance (or noise) - different songs being played for different classes (One class gets boring class and thereby uses the old method whereas other class gets interesting song and thereby uses singalong method)

Unconfounding the experiment - We are interested in studying the effect of new singalong method on scores. We want to control the experiment for unintended biases. Therefore, selecting students from only one class will help unconfounding the experiment as students from the same class are likely to perform equally in the test.

3.

dependent variable - attention span (continuous)

independent variables - number of planes, gender, hour of the day, time of the season

Confounding variables - Here, the controllers in the seasons with no fog, clear sky are likely to perform comparatively lower than other controllers.

Real experiment is to check whether number of airplanes has an effect on attention span but checking the effect in different season is likely to give a false estimate of results and therefore - season of experiment is the confounding variable

Possible sources of variance (or noise) - different controllers being observed under different environmental (controllers in the winter morning are more likely to have lesser attention span due to adverse conditions such as fog, cold etc.)

Unconfounding the experiment - We are interested in studying the effect of number of planes on attention span. We want to control the experiment for unintended biases. Therefore, selecting controllers from only a particular season will help unconfounding the experiment as controllers in the same season are likely to perform equally.