Chi square

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 ꭕ . 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 Goodness of fit – It measures how much the observed or actual frequency differ from the expected or predicted frequency. 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.