The chi-square test is used to determine if there is a significant relationship between two categorical variables. There are three main types: test of goodness-of-fit examines the difference between observed and expected frequencies; test of homogeneity compares differences between two or more groups; and test of independence examines the association between two variables. The chi-square test calculates a test statistic and p-value to determine if the null hypothesis that there is no relationship can be rejected.

1. JONATHAN BITOON BALOLOY
Discussant

2. 1. WHAT IS CHI SQUARE TEST?
2. WHEN TO USE CHI-SQUARE TEST?
3. TYPES OF CHI-SQUARE TEST
4. SCENARIO OR TOPICS INCORPORATING
CHI-SQUARE TEST

3. ▪Generating inferential results from different
types of data might be too confusing.
▪In every type of data, there is a specific
inferential statistical tool for a certain type of
data.
▪this also applies whether how many group or
variables you considered on your study.

4. ▪An inferential statistical tool that is used to
determine relationship or difference among
data collected.
▪It is a non-parametric tool.
▪It is used to identify the relationship or
difference between two nominal or ordinal
variables.

5. ▪Used to test the null hypothesis.
▪When t-test can’t be used.
▪When the variable is a nominal or ordinal variable.
▪Data are consist of variables distributed across
various categories.
▪Helps us to know whether that distribution is
different from what one would expect by chance.

6. Where:
Oi = observed value
Ei = Expected value

7. 1. Define null and alternative hypothesis
2. State alpha
3. Calculate degrees of freedom
4. State decision rule
5. Calculate test statistics
6. State results
7. State conclusion

8. ▪Test of goodness-of-fit
▪Test of homogeneity
▪Test of independence

9. ▪This is a test of difference between the
observed frequencies and the expected
frequencies
▪This test is used when ratio is employed.
▪It claims about population proportions.

10. When do we use the test of goodness-of-fit?
The test is used when ratio is employed.
How do we use the test of goodness-of-fit?
Use the formula (if computed manually)

11. Let’s take as an example the theory of Mendel
regarding crossing of peas. According to Mendel’s
theory, the yellow color is dominant over green, and in
terms of skin, smooth skin is dominant over wrinkled
skin.
In this case, the theory (expected) is
compared with the actual experiment
(observed).

12. The theory of Mendel regarding crossing of peas is in
the ratio of 9:3:3:1, meaning 9 peas are smooth
yellow, 3 parts smooth green, 3 parts wrinkled
yellow, and 1 part wrinkled green.
The researcher conducted an experiment and the
result was that out of 560 peas, 310 were smooth
yellow, 100 were wrinkled yellow, 110 were smooth
green, and 40 were wrinkled green.

13. Attributes Ratio (Actual Result) Observed (Theory) Expected
Smooth Yellow 9 310 315
Wrinkled Yellow 3 100 105
Smooth Green 3 110 105
Wrinkled Green 1 40 35
Total 16 560 560
Use the formula :

14. ▪This test concerned with two or more
samples, with only one criterion variable
▪It is used to determine if two or more
population are homogenous.
▪Is applied when we have two categorical
variables from a single population.

15. ▪It is used to determine whether there is a
significant association between the two
variables.
▪This test is applicable when the observations
are independent.
▪It is also called a contingency table Chi-square
test.

16. ▪The chi-square test of homogeneity is used in comparing
significant difference between two or more groups.
▪Chi-square test of homogeneity uses the formula for a 2x2
contingency table.
Where: X2 = chi – square test
N = grand total
Klmn = product of rows and column
N(ad-bc)2
klmn
X2 =

17. Example 2.
Evaluate the value of sample of Lakas and Laban
parties on issues of peace and order in Mindanao. To
carry out such study, a separate random sample of
members of each party is drawn from the nationwide
population of Lakas and Laban and each individual in
both samples responds to the scale. Scores are then
classified into “favorable” or “unfavorable” categories:
The following frequencies are obtained.

18. Favorable Unfavorable Total
Lakas 65
a
35
b
100
K
Laban 50
c
50
d
100
L
Total 100
m
85
n
200
N

19. Favorable Unfavorable Total
Lakas 65
a
35
b
100k
Laban 50
c
50
d
100l
Total 115
m
85
n
200
N

20. ▪The test of independence is different from the test of
homogeneity. The sample in this test consists of members
randomly drawn from the same population.
▪This test is used from the same population.
▪This test is used to look into whether the measures taken on
the two – criterion variables are either independent or
associated with one in a given population using such variables
as level of education and income, performance in class and IQ,
etc.

21. ▪The chi-square test of independence is used when we try to
find out if there is a significant relationship between two
variables.
How do we use the chi-square test of independence?
▪The calculation of this test is similar to the test of goodness-of-
fit and the test of homogeneity.

22. Example 3. Ninety individuals, male and female, were given a
test in psychomotor skills and their scores were classified into
high and low.
▪Is there significant relationship between sex and score in
psychomotor skills?
SEX
PSYCHOMOTOR SKILLS
TOTAL
HIGH LOW
O E O E
MALE 18 28 46
FEMALE 32 12 44
TOTAL 50 40 90

23. Statistics :chi-square test of independence
Computation :
Sex Psychomotor Skills
High Low Total
O E O E
Male 18 (25.56) 28 (20.44) 46
Femal
e
32 (24.44) 12 (19.56) 44
Total 50 40 90

25. ▪Chi-Square gives a P-value to help you know the
correlation if any.
▪A very small chi-square test statistics indicated
that the collected data matches the expected data
extremely well.
▪A very large chi-square test statistic indicated that
the data does not match very well. If the chi-
square value is large, the null hypothesis is
rejected

26. ▪Used by biologists to determine if there is significant
association between two variables, such as association
between two species in a community.
▪Used by genetic analysts to interpret numbers in various
phenotypic classes.
▪Used in various statistical procedures to help to decide if
to hold onto or reject the hypothesis.
▪Used in medical literature to compare the incidence of
the same characteristics in two or more groups.

27. ▪Chi-square is an inferential statistics tool which is used for non-
parametric distributions and nominal and ordinal data.
▪There are 3 types: Test of goodness-of-fit, test of homogeneity and
test for independence.
▪Test of goodness-of-fit is used when there are 2 independent
groups
▪Test of homogeneity is used when there are 2 or more independent
groups with 1 criterion
▪Test of independence is used when there is 1 independent and 1
dependent variable.