Question

Free will is an important concept to individuals and societies. In the context of cognitive neuroscience, mounting evidence suggests that free will is an illusion, constructed by processes in the brain, similar to visual illusions. Recent research has demonstrated that people who believe in free will tend to also believe in the paranormal (Mogi, 2014). A psychologist at Arizona State University (ASU) wanted to replicate this study with students in the psychology major. Following the procedure of Mogi (2014), an anonymous survey was sent to students with a call to participate in a “study of free will.” There was no mention of paranormal beliefs at this stage. One thousand and thirty-eight (1038) students completed the following survey. First, subjects were asked a series of questions regarding their belief in free will. After the free will questions, subjects were asked a series of questions regarding their belief in the paranormal. Care was taken so that the questions related to the paranormal was not phrased in a way that suggested a correlation between free will and the paranormal. Below are the findings:

		Belief in Paranormal
	ntotal = 1038	Yes	No
Belief in Free Will	Yes	446	172	618
	No	298	122	420
		744	294

1. (Test of Independence) The researcher now wants to look at just the psychology students at ASU. Does this data suggest a significant relationship between belief in free will and belief in the paranormal amongst the budding psychologists at ASU?
   
   1. Which variables are being tested in this Test of Independence?
      
   2. What are the hypothesis (H₁), the null hypothesis (H₀), and alpha level?
      

3. What is the df value for the chi-square statistic?
4. What is the population size?
5. Using SPSS and the dataset, ParaFW.csv, conduct a Test of Independence. What is the chi-square statistic and p-value?
   

1. 6. BY HAND! Calculate the chi-square statistic for this test of independence with α = .05.
      
2. 7. Conduct a measure the Effect Size. Is this effect size small, medium, or large?
      

State your decision: Based on your statistical analysis, does this data suggest a significant relationship between belief in free will and belief in the paranormal amongst the budding psychologists at ASU?

Answer 1

a.

The variables being tested in this Test of Independence are belief in free will and belief in the paranormal amongst the budding psychologists at ASU.

b.

Let p_AB be the proportion of students who believe in free will and believe in the paranormal.

Let p_Ab be the proportion of students who does not believe in free will and believe in the paranormal.

Let p_aB be the proportion of students who believe in free will and does not believe in the paranormal.

Let p_ab be the proportion of students who does not believe in free will and does not believe in the paranormal.

Let p_A be the proportion of students who belief in the paranormal.

Let p_a be the proportion of students who does not believe in the paranormal.

Let p_B be the proportion of students who believe in free will.

Let p_b be the proportion of students who does not believe in free will.

Null Hypothesis H₀: p_ij = p_i * p_j   i,j = A,B,a,b

Alternative Hypothesis H₁: p_ij p_i * p_j for at least one i,j = A,B,a,b

c.

For a rs contingency table, df value for the chi-square statistic = (r-1)(s-1)

For the given 22 contingency table, df value for the chi-square statistic = (2-1)(2-1) = 1

d.

The population size is equal to the number of budding psychologists at ASU = 1038