The ppt cover General Introduction to the topic, Description of CHI-SQUARE TEST, Contingency table, Degree of Freedom, Determination of Chi – square test, Assumption for validity of chi - square test, Characteristics , Applications, Limitations

1. CHI-SQUARE TEST

2. Synopsis
.
 Introduction
 Description
 Contingency table
 Degree of Freedom
 Determination of Chi – square test
 Assumption for validity of chi - square test
 Characteristics
 Applications
 Limitations

3. introduction
 Chi – square test is one of the most commonly used non – parametric test.
 It is the test of significance which was first used by Karl Pearson in 1990.
 Chi – square test is a useful measure of comparing experimentally
observed result with the experimentally theoretical result or based on a
hypothesis.
 It is denoted by the Greek sign ꭕ2.
 Following is the formula:

4. DESCRIPTION
• If there is no difference between actual and
observed frequency, the value of chi-square is
zero.
• If there is difference then the value of test will
be other than zero.
• Differences may be due to sampling
fluctuations.

5. CONTINGENCY TABLE
 This term was given by Karl Pearson.
 A contingency table is a type of table in a matrix
format that displays the multivariate frequency
distribution of the variables.
 They provide a basic picture of interrelation between
two variables.
 The values depends on the number of classes.

6. Following is the 2×2 table(Four cell table)
COLUMN 1 COLUMN 2 ROW TOTAL
ROW 1 + + RT1
ROW 1 + + RT2
COLUMN TOTAL CT1 CT2

7. Degree of freedom
 In test, while comparing the calculated value with the table value, we
have to calculate the degree of freedom.
 Degree of freedom is calculated from the number of classes. Therefore
degree of freedom is equal to number of classes minus one.
 In a contingency table, the degree of freedom is calculated in a different
manner which is as follows:
D.F = (R-1)(C-1)
where R = no. of rows in a table.
C = no. of columns in a table.

8. Determination of Chi-square test
 Identify the problem.
 Make a contingency table and note the observed
frequency(o), in each classes of one event, row wise
i.e. horizontally. And then the members in each group
of other event, columnwise i.e. vertically.
 Calculate the expected frequencies (E).
 Find the difference between observed and expected
frequency in each cell (O-E)
 Calculate the chi-square value by applying the
formula. The value ranges from zero to infinite.

9. Assumption for the validity of
chi-square test
 All the observations should be independent. No individual item
should be included twice.
 The total number of observation should be large. The chi-square test
should not be used if n>50.
 For comparison purpose, the data must be in original units.
 If the theoretical frequencies is less than five then we pool it with
either preceding or succeeding frequency, so that the resulting sum
is greater than five.

10. CHARACTERISTICS
This test is based on frequencies.
Used for testing difference between the
entire set of the expected and the observed
frequency.
It is applied for testing of hypothesis but it
is not useful for estimation.

11. applications
1. Goodness of fit – It measures how much the
observed or actual frequency differ from the
expected or predicted frequency.
2. Test of Homogenity – Used to determine whether
frequency counts are distributed identically across
different samples.
3. Test of Independence – Used to explain that
variables are how much attached with each other.

12. LIMITATIONS
 Chi-square test does not give us much information
about the strength of the relationship. It only
conveys the existence or non-existence of
relationships between the variables.
 It is sensitive to sample size.
 It is also sensitive to small expected frequencies.