The document discusses the chi-square test, which is used to determine if there is a statistically significant relationship between two categorical variables. It originated from the sum of squares of independent normal variables. The chi-square test can be used for goodness of fit tests to assess differences between observed and expected values. It has a characteristic distribution represented by the symbol χ2. The test assesses how likely observed categorical data distributions are by chance alone.

1. RESEARCH METHODOLOGY
V. PRIYADHARSHINI,B.voc., M.Lib.I.Sc
Holly cross college
SFM18807
P18LSOO2

2. WHAT IS CHI-SQUARE?
 A chi-square distribution is the distribution of the
sum of squares of k independent standard normal
random variables with k degree of freedom.
 While the chi-square distribution was first
introduced by German statistician Friedrich Robert
Helmert
 The chi-square test was first used by Karl Pearson
in 1900.

3. WHAT IS THE CHI TEST USED FOR?
 Chi-Square Test for Independence.
The test is applied when you have two categorical
variables from a single population.
It is used to determine whether there is a
significant association between the two
variables.

4. WHAT IS THE USE OF CHI SQUARE IN
RESEARCH?
 Using Chi-Square Statistic in Research.
 The Chi Square statistic is commonly used for
testing relationships
between categorical variables.
 The null hypothesis of the Chi-Square test is that no
relationship exists on the categorical variables in
the population; they are independent.

5. WHAT CHI SQUARE VALUE MEANS?
 The Chi-square test is intended to test how likely it
is that an observed distribution is due to chance.
 It is also called a "goodness of fit" statistic, because
it measures how well the observed distribution of
data fits with the distribution that is expected if the
variables are independent.

6. WHAT IS THE PURPOSE OF USING THE CHI
SQUARE TEST?
 Tests for Different Purposes.
 Chi square test for testing goodness of fit is used
to decide whether there is any difference between
the observed (experimental) value and the
expected (theoretical) value.
 For example given a sample, we may like to test if
it has been drawn from a normal population.

7. WHEN SHOULD YOU USE A CHI SQUARE
TEST?
 Often, researchers choose significance levels
equal to 0.01, 0.05, or 0.10; but any value between
0 and 1 can be used.
 Test method. Use the chi-square test for
independence to determine whether there is a
significant relationship between two categorical
variables.

8. WHAT IS THE SYMBOL FOR CHI SQUARE?
 The term 'chi square' (pro- nounced with a hard
'ch') is used because the Greek letter χ is used to
define this distribution.
 It will be seen that the elements on which this dis-
Page 4 Chi-Square Tests 705 tribution is based are
squared, so that the symbol χ2 is used
to denote the distribution.

9. WHAT ARE THE CHARACTERISTICS OF CHI
SQUARE TEST?
 Characteristics of Chi square test in Statistics.
 This test (as a non-parametric test) is based on
frequencies and not on the parameters like mean
and standard deviation.
 The test is used for testing the hypothesis and is
not useful for estimation.
 This test possesses the additive property as has
already been explained

10. EXAMPLE

11. CHI-SQUARED
Advantages
 Can test association between variables
 Identifies differences between observed and
expected values
Disadvantages
 Can't use percentages
 Data must be numerical
 Categories of 2 are not good to compare
 The number of observations must be 20+
 The test becomes invalid if any of the expected
values are below 5
 Quite complicated to get right - difficult formula