nferential Statistics - Non-parametric test (Chi Square Test)

Inferential Statistics - Nonparametric test used to compare observed results with expected results. The purpose of this test is to determine if a difference between observed data and expected data is due to chance, or if it is due to a relationship between the variables you are studying.

1. chi- square test

2. Objectives Understand what the chi-square test is and how it works Learn about the different types of Chi-Square tests Be able to calculate the chi-square value using the chi-square formula

3. Statistical analysis is a key tool for making sense of data and drawing meaningful conclusions.

4. is a statistical test used to determine if there is a significant association between two categorical variables. It is a non-parametric test, meaning it does not make assumptions about the underlying distribution of the data. CHI- SQUARE TEST

5. There are three main types of chi-square tests commonly used in statistics: 1.Pearson’s Chi-Square Test: This test is used to determine if there is a significant association between two categorical variables in a single population. It compares the observed frequencies in a contingency table with the expected frequencies assuming independence between the variables. 2.Chi-Square Goodness of Fit Test: This test is used to assess whether observed categorical data follows an expected distribution. It compares the observed frequencies with the expected frequencies specified by a hypothesized distribution. 3.Chi-Square Test of Independence: This test is used to examine if there is a significant association between two categorical variables in a sample from a population. It compares the observed frequencies in a contingency table with the expected frequencies assuming independence between the variables.

6. Chi-Square Test For mula where, χ 2 = Chi-Square value Oi = Observed frequency Ei = Expected frequency

7. A research scholar is interested in the relationship between the placement of students in the statistics department of a reputed University and their C.G.P.A (their final assessment score). He obtains the placement records of the past five years from the placement cell database (at random). He records how many students who got placed fell into each of the following C.G.P.A. categories – 9-10, 8-9, 7-8, 6-7, and below 6. HO: There is no relationship between the placement rate and the C.G.P.A. H1: There is a statistically significant relationship between the placement rate and the C.G.P.A of students

8. Chi-Square Test For mula where, χ 2 = Chi-Square value Oi = Observed frequency Ei = Expected frequency

9. Step 1 : Subtract each expected frequency from the related observed frequency

10. Step 2: Square each value obtained in step 1 .

11. Step 3: Divide all the values obtained in step 2 by the related expected frequencies.

12. Step 4: Add all the values obtained in step 3 to get the chi-square test statistic value

13. Step 5: Once we have calculated the chi-square value, we will compare it with the critical chi-square statistic value df= N-1 = 4

14. Therefore, we can say that the observed frequencies from the sample data are significantly different from the expected frequencies. In other words, C.G.P.A is related to the number of placements that occur in the department of statistics.