1. What is Chi-Square and its used in Hypothesis? Kinza malik 1

2. Chi-Square (χ 2 ) Definition ‘’ Chi square (χ 2 ) is simply an extension of a cross-tabulation that gives you more information about the relationship. However, it provides no information about the direction of the relationship(positive or negative) between the two variables.’’ Where o is the observed value E is the expected value I have not filled in all of the information because we need to talk about two concepts before we start calculations: Degrees of Freedom :In any table, there are a limited number of choice for values in each cell. DF=(c-1)x(r-1) Marginals : Total frequencies in columns and rows. 2

3. Hypothesis Definition A hypothesis is a tentative answer to a research problem. A tentative statement which may or may not be true. Examples : higher the education higher will be the income. Types of hypothesis 1:Null hypothesis( no relationship between two or more variables is called null hypothesis. This hypothesis is denoted by Ho) 2:Alternative hypothesis(Assumes that there is an association between the two variables is called alternative hypothesis. This hypothesis is denoted by H1) 3

4. Chi-square test used in hypothesis We can summarize two categories variables within a two-way table, also called a r*c contingency table, where r=numbers of rows, c=numbers of columns. The chi-square test statistic is used by using the formula. Where o is represents the observed frequency. E is the expected frequency under the null hypothesis and computed by: E = row total X column total sample size The critical value for the chi-square statistic is determined by the level of significance (typically.05) and the degrees of freedom. If the observed chi-square test statistic is greater than the critical value, the null hypothesis can be rejected 4

5. Example Education Income High Low Total High401050 Low104050 Total50 100 Degree of freedom=(c-1)x(r-1) DF=(2-1)x(2-1)=(1)x(1)=1 Level of significant(0.05) 5

6. Chi-square calculation is Expected value E = row total X column total sample size Cell 1 E= 50x50 = 100 25 Cell 2 E= 50x50 = 100 25 Cell 3 E= 50x50 = 100 25 Cell 4 E= 50x50 = 100 25 6

7. Chi-square 1 x² = 25(40-25)² = 25 9 2 x²= 25(10-25)² = 25 9 3 x²= 25(10-25)² = 25 9 4 x² = 25(40-25)² = 25 9 36 7

8. Table 8

9. Result At 0.05, DF=1,chi-square must be larger than 3.84 to be statistically significant. Its mean null hypothesis is rejected or alternative is accepted. 9