Statistics for Behavioral Science Practice Exam Questions with Answers - Chi- Square and Pearson Correlation

Test questions for Lessons 3-4 – Chi Square and Pearson correlation

Chi Square


1. Researcher A wanted to test the correlation between extroversion and sexual orientation.
She sampled 100 participants and measured their extroversion levels. She then divided
them to two equal groups, based on their score – a “high extroversion” group and a “low
extroversion” group. She also measured the sexual orientation of the participants and
classified them to two groups: heterosexuals and LGBT (gays, lesbians, bisexuals and
transgenders). Researcher B used to same data to examine whether the sexual orientations
in the “high-extroversion” group are distributed the same as in the population (90%
heterosexuals, 10% LGBT). Researcher A should conduct a _______ and Researcher B
should conduct a ________.

a) Chi-Squared test for independence; Chi-Squared test for goodness of fit
b) Chi-Squared test for goodness of fit; Chi-Squared test for independence
c) Pearson’s r; Chi-Squared test for goodness of fit
d) Pearson’s r; Chi-Squared test for independence
e) Chi-squared test for independence; Chi-squared test for independence

Explanation:
Researcher A wanted to test the correlation between two variables that are categorical –
extroversion (low\high) and sexual orientation (heterosexual\LGBT). Thus, researcher A
should conduct a chi-squared test for independence. Researcher B focused on one group
only – the high extroversion group, and wanted to test the distribution of sexual
orientation in this group against a known distribution in the population. That is, he only
measured the sexual orientation variable (which is categorical). Therefore he should use
chi-squared test for goodness of fit.

2. A researcher wanted to test whether having a pet (yes/no) is correlated with a person’s
character (altruistic/egocentric/loner). The following table describes the frequency of
participants in each group:

Altruistic Egocentric Loner Total
Frequency
Has a pet 20 15 18 53
Does not have a pet 10 12 17 39
Total Frequency 30 27 35 92

The researcher calculated the appropriate Chi-Squared test. What is the value of the
statistic he obtained?

a) -0.01
b) 0.1
c) 1.6

, d) 3.6

Explanation:
There are two categorical variables whose correlation is tested. Therefore, the appropriate
test here is Chi-Squared test for independence. First, we need to calculate the expected
frequencies, and then compare the observed and the expected frequencies using the Chi-
Squared formula:

Observed:
Altruistic Egocentric Loner Total
Frequency
Has a pet 20 15 18 53
Does not have 10 12 17 39
a pet
Total 30 27 35 92
Frequency
Expected:
Altruistic Egocentric Loner
Has a pet 53*30/92=17.28 53*27/92=15.55 53*35/92=20.16
Does not have a pet 39*30/92=12.72 39*27/92=11.45 39*35/92=14.84
(Oi  Ei ) 2
2   Ei

(20  17.28) 2 (10  12.72)2 (15  15.55) 2 (12  11.45) 2 (18  20.16)2 (17  14.84)2
2      
17.28 12.72 15.55 11.45 20.16 14.84

 2  0.43  0.58  0.02  0.03  0.23  0.31  1.6




3. A researcher wanted to know whether the desire to have children (yes / no) is dependent
on sexual orientation (gay / bisexual / heterosexual). He sampled 1000 people and asked
them to report their desire to have children and their sexual orientation. Which test should
the researcher conduct? How many degrees of freedom will he have?
a. Chi-Squared test for independence; 1
b. Chi-Squared test for goodness of fit; 2
c. Chi-Squared test for independence; 2
d. Chi-Squared test for goodness of fit; 6

Explanation:
The researcher has to categorical variables: desire to have children (yes/no) and sexual
orientation (gay / bisexual / heterosexual). He wants to test the correlation between these
categorical variables, and therefore should use Chi-Squared test for independence. DF =
(c – 1) * (r – 1) = (2-1) * (3-1) = 2.