2. Introduction
Data analysis can be done basically in
three ways using SPSS, as
i. Describing data through descriptive
statistics
ii. Examining relationships between
variables
iii. Comparing groups to determine
significant differences between
them
3. Introduction
Considering the third category i.e.
comparing groups, chi square and t-tests
are two of the important tests. These are
tests of significance.
4. Chi-Square Test
Chi-Square test was introduced by Karl
Pearson. It follows a specific distribution
known as chi-square distribution.
It is used to measure the differences
between what is observed and what is
expected according to an assumed
hypothesis.
5. Chi-Square Test
The Chi-Square is denoted by X² and the
formula is given as:𝑋2
=
(𝑂−𝐸)2
𝐸
Here,
O = Observed frequency
E = Expected frequency
∑ = Summation
X²= Chi Square value
A chi-square test is a statistical test
commonly used for testing independence and
goodness of fit.
6. Chi-Square Test
Testing independence determines whether
two or more observations across two
populations are dependent on each other
(i.e., whether one variable helps to estimate
the other). If the calculated value is less than
the table value at certain level of significance
for a given degree of freedom, we conclude
that null hypotheses stands which means
that two attributes are independent or not
associated. If calculated value is greater than
the table value, we reject the null
hypotheses.
7. Chi-Square Test
This test enables to explain whether or not
two attributes are associated. For instance,
suppose a study collecting data of survivors
in Titanic, for this X² test is useful.
8. Chi-Square Test
Testing for goodness of fit determines
how well the assumed theoretical
distribution (such as normal distribution)
fit to the observed data. When the
calculated value of χ2 is less than the table
value at certain level of significance, the
fit is considered to be good one and if the
calculated value is greater than the table
value, the fit is not considered to be good.
12. Chi-Square in SPSS
Independent Variable
(Gender) is in the Rows
Always show Observed
count
Optionally, show
Expected
count
Percentage across the
Rows
Click CONTINUE
In main dialogue box,
Click STATISTICS
13. Chi-Square in SPSS
Choose Chi-Square
for hypothesis test
Click Phi and
Cramer’s V for
measure of strength
of the relationship
Click CONTINUE
On main dialogue
box,
Click OK
14. Chi-Square in SPSS
Observed count (yellow highlight)
Expected count (orange highlight)
Percent within each Gender who Died or
Survived (pink highlight)
Report: “Most men on the Titanic (80.2%)
died while most women (71.6%) survived.”
gender * survival Crosstabulation
680.000 168.000 848.000
529.4 318.6 848.0
80.2% 19.8% 100.0%
126.000 317.000 443.000
276.6 166.4 443.0
28.4% 71.6% 100.0%
806.000 485.000 1291.000
806.0 485.0 1291.0
62.4% 37.6% 100.0%
Count
Expected Count
% w ithin gender
Count
Expected Count
% w ithin gender
Count
Expected Count
% w ithin gender
1 Men
2 Women
gender
Total
1 Died 2 Survived
survival
Total
15. Chi-Square Tests
332.205b
1 .000
330.003 1 .000
335.804 1 .000
.000 .000
331.948 1 .000
1291
Pearson Chi-Square
Continuity Correctiona
Likelihood Ratio
Fisher's Exact Test
Linear-by-Linear
Association
N of Valid Cases
Value df
Asymp. Sig.
(2-sided)
Exact Sig.
(2-sided)
Exact Sig.
(1-sided)
Computed only for a 2x2 tablea.
0 cells (.0%) have expected count less than 5. The minimum expected count is 166.
43.
b.
Chi-Square in SPSS
Pearson chi-square is the default test
When Sig < alpha, variables are related.
Report:
“The relationship is significant (χ2(1) = 332.205, p <
.005).”
16. Sym metric Measures
.507 .000
.507 .000
1291
Phi
Cramer's V
Nominal by
Nominal
N of Valid Cases
Value Approx. Sig.
Not assuming the null hypothesis.a.
Using the asymptotic standard error assuming the null
hypothesis.
b.
Chi-Square in SPSS
Phi for 2x2 tables
Cramer’s V for
larger tables
Both range from 0
to 1 with 0 = no
relationship
For df = 1
◦ V = 0.10 is a small
effect
◦ V = 0.30 is a
medium effect
◦ V = 0.50 is a large
effect
Report: “Gender
had a large effect
on chance of
survival for the
Titanic
passengers.”
17. t-test
The t-test is a basic test that is limited to
two groups. For multiple groups, we
should have to compare each pair of
groups, for example with three groups
there would be three tests (AB, AC, BC).
It is used to test whether there is
significant difference between the means
of two groups, e.g.:
Male v female
Full-time v part-time
18. t-test
There are three types of t-tests as below
A one sample t-test: used when we want
to know if there is a significant difference
between a sample mean and a test value
(known mean from a population or some
other value to compare with sample
mean), i.e. to compare the mean of a
sample with population mean.
19. t-test
An independent sample t-test: used to
compare the mean scores when samples
are not matched or for two different
groups of subjects i.e. to compare the
mean of one sample with the mean of
another independent sample.
20. t-test
Paired sample t-test: used to compare the
means of two variables or when samples
appear in pairs (e.g. before and after),
i.e. to compare between the values
(readings) of one sample but in 2
occasions.
30. t-test in SPSS
Choose “Use specified values”
Key in the codes for the variable “gender”
as used in the “Value Labels”. In this
case:
1 - Male
2 - Female
Click “Continue”, then “OK”
