The document discusses the chi-square test of independence, which determines if there is a relationship between two categorical variables. It explains that the chi-square test compares observed and expected category frequencies to assess if the null hypothesis of independence is true. An example calculates the chi-square test to see if gender and education level are related using a sample of 45 people's education data. The chi-square test value is greater than the critical value, so the null hypothesis of no relationship is rejected.

1. B U L A H A N A N D D A L U M P I N E S
CHI-SQUARE
CHI-SQUARE
TEST OF
TEST OF
INDEPENDENCE
INDEPENDENCE
B S P S Y C H O L O G Y 1 - B

2. WHAT IS CHI-SQUARE?
2
IT IS A NON-PARAMETRIC TEST AND CAN ALSO BE CALLED AS A
DISTRIBUTION FREE TEST.
IT IS USEFUL IN ANALYZING CROSS TABLATIONS OF SURVEY
RESPONSE DATA.
DETERMINES WHETHER THERE IS A RELATIONSHIP OR AN
ASSOCIATION BETWEEN TWO CATEGORICAL VARIABLES.

3. CONDITIONS IN USING NON-
PARAMETRIC TESTS:
2
1. THE LEVEL OF MEASUREMENT OF ALL THE VARIABLES
IS NOMINAL OR ORDINAL.
2. THE SAMPLE SIZES OF THE STUDY GROUPS ARE
UNEQUAL.
3. THE ORIGINAL DATA WERE MEASURED AT AN
INTERVAL OR RATIO LEVEL, BUT VIOLATED ONE OF THE
FOLLOWING ASSUMPTION OF A PARAMETRIC TEST.

4. THINGS TO CONSIDER WHEN USING
CHI SQUARE TEST
C H I S Q U A R E T E S T O N L Y A S S E S S E S
I N D E P E N D E N C E O F T W O V A R I A B L E S I N A
B I N A R Y F O R M A T .
C H I S Q U A R E R E Q U I R E S T H E U S E O F
N U M E R I C A L V A L U E S , E S P E C I A L L Y F R E Q U E N C Y
C O U N T S , R A T H E R T H A N R A T I O S .

5. TYPES OF CHI-
SQUARE TESTS
C H I S Q U A R E T E S T S I S U S E D T O C O M P A R E
Y O U R O B S E R V E D V A L U E S D A T A T O Y O U R
E X P E C T E D V A L U E S S O T H A T Y O U W O U L D S E E
I F T H E N U L L H Y P O T H E S I S I S T R U E .
T H E R E A R E T W O C O M M O N L Y U S E D C H I -
S Q U A R E T E S T S : T H E C H I - S Q U A R E G O O D N E S S
O F F I T T E S T A N D T H E C H I - S Q U A R E T E S T O F
I N D E P E N D E N C E .

7. CHI-SQUARE TEST
CHI-SQUARE TEST
OF INDEPENDENCE
OF INDEPENDENCE
The Chi-square (χ2) test of independence is a
statistical hypothesis test used to determine
whether there is a significant relationship between
two nominal variables.

8. CHI-SQUARE TEST
CHI-SQUARE TEST
OF INDEPENDENCE
OF INDEPENDENCE
The frequency of each category for one nominal
variable is compared across the categories of
the second nominal variable.

9. CHI-SQUARE TEST
CHI-SQUARE TEST
OF INDEPENDENCE
OF INDEPENDENCE
It is also called Pearson’s chi-square test or the
chi-square test of association that is used to
discover if there is a relationship between two
categorical variables.

10. EXAMPLE
Is sex independent of education level? A
random sample of 45 people was
surveyed, and each person was asked to
report the highest education level they
obtained.
Are sex and education levels
dependent at a 5% level of significance? In
other words, given the data collected, is
there a relationship between the sex of an
individual and the level of education that
they have obtained?

11. Educational Level
Sex Bachelor High School Masters
Female 11 8 6
Male 10 5 5

12. 1. State your null and alternative hypothesis
Ho’=There is no relationship between the gender of an
individual and the level of education.
H1’=There is a relationship between the gender of an
individual and the level of education.
2. Significance level
α = 0.05
3. Statistical tool
Chi-square of independence
Step 1: df: (r−1) × (c−1)

13. Step 1: df: (r−1)×(c−1)
where r is total number of rows and c is the total
number of columns
r=? (male and female) and c=? (bachelor, high
school, and masters)

14. Step 1: df: (r−1)×(c−1)
where r is total number of rows and c is the total
number of columns
r=2 (male and female) and c=3 (bachelor, high
school, and masters)
df=(r−1)×(c−1)=(2−1)×(3−1)=(1×2)=2
df=2

15. df=2, and
α=0.05
the critical
value is 5.991
(5.99).
Decision rule: Reject Ho’, if the test value is greater than
5.99, otherwise, do not reject Ho’

16. Educational Level
Sex
Bachel
or
High
School
Master
Row
Total
Female 11 8 6
Male 10 5 5
Column
Total

17. O Educational Level
Sex
Bachel
or
High
School
Master
Row
Total
Female 11 8 6 25
Male 10 5 5 20
Column
Total
21 13 11 45

20. CHI-SQUARE TEST VALUE

21. O Educational Level
Sex
Bachel
or
High
School
Master
Row
Total
Female 11 8 6 25
Male 10 5 5 20
Column
Total
21 13 11 45

22. E Educational Level
Sex
Bachel
or
High
School
Master
Row
Total
Female 11.677 7.2 6.111 25
Male 9.333 5.778 4.889 20
Column
Total
21 13 11 45

24. USING JASP
USING JASP

25. USING JASP
USING JASP

26. USING JASP
USING JASP

27. DECISION AND
CONCLUSION

28. THANK YOU
THANK YOU
SO MUCH!
SO MUCH!