Question

1. A researcher wants to test the hypothesis that increasing temperature and physical exercise increases the body’s skin conductivity (as measured by a galvanometer). A sample of 24 males, all 21 years old is randomly selected, and the subjects are randomly assigned to four treatment conditions. Group A is subjected to high temperature and physical exercise (jogging in place for 10 minutes). Their GSR (Galvanic skin response) scores in decivolts are 9, 8, 8, 10, 7, and 8. Group B is subjected to low temperature and physical exercise (again, jogging in place for 10 minutes). Their GSR scores are 7, 6, 5, 5, 4, and 5. Group C is subjected to high temperature without exercise. Their GSR scores are 5, 3, 3, 4, 3, and 4. Group D is subjected to low temperature without exercise. Their GSR scores are 3, 2, 2, 1, 2, and 1. (High scores indicate greater skin conductivity. Test the hypothesis...

Independent variable/s _____________________________________________________

Levels of independent variable/s _____________________________________________

Dependent variable/s ______________________________________________________

Test to use ______________

Does temperature affect GSR scores? _________________________________________

Value of your test statistic ______________

p-value from test ___________

Does exercise affect GSR scores? ____________________________________________

Value of your test statistic ______________

p-value from test _______________

Answer 1

The tabulation is as follows:

The summary statistics are as follows

The ANOVA table is attached below:

1) INDEPENDENT VARIABLES

There are two independent variables : Temperature and Exercise

2) LEVELS OF INDEPENDENT VARIABLES

Both factors have two levels each

Temperature : High and Low

Exercise: 10 min and No Exercise

3) DEPENDENT VARIABLES

GSR SCORE (Galvanic Skin Response) is the response variable or dependent variable

4) TEST TO USE

We have to use Two Factor ANOVA with 6 observations per cell, or it is directly the case of 2*2 Factorial Experiment.

We conduct 3 F tests and hypothesis as follows:

Ho (Interaction) = There is no interaction between the two factors

Ho (Temp) = The temperature levels are homogeneous in nature and hence do not impact the response variable significantly.

Ho (Exercise) = The exercise levels are homogeneous in nature and hence do not impact the response variable significantly.

It is to be noted that interaction p value is 0.1350 > Level of Significance (0.05) Hence we accept the null hypothesis and assume that the interaction is 0, and we can now proceed to individual F tests for both factors.

5) DOES TEMP AFFECT GSR SCORE?

As p value = 0.000 < 0.05 (LOS), we reject the null hypothesis, and conclude that temperature does impact the GSR score.

6) VALUE OF TEST STATISTIC

F = 41.6336

7) P VALUE FROM THE TEST

p value = 0.000

8) DOES EXERCISE AFFECT GSR SCORE?

As p value = 0.000 < 0.05 (LOS), we reject the null hypothesis, and conclude that exercise does impact the GSR score.

9) VALUE OF TEST STATISTIC

F = 118.8614

10) P VALUE FROM THE TEST

p value = 0.000