Advanced_Statistics_Chi-Square_Test_Repo

statistics

1. GUESS THE PICTURE

2. CHI-SQUARE

3. HYPO NULL HYPOTHESIS

4. DEGREES OF FREEDOM

5. ALPHA LEVEL

6. Chapter 10 Chi-Square

7. Objectives To learn Chi Square Statistics Does a Chi-Square Statistic Tell You Use of the Chi squared tests

8. ( x²) statistic is a test that measures how expectations compare to actual observed data (or model results). FORMULA: where: c=Degrees of Freedom O=Observed Value(s) E=Expected Value(s) Chi-Square Statistic

9. One of the most common forms can be used for contingency tables: Where O is the observed value, E is the expected value and “ i ” is the “ ith ” position in the contingency table. Chi-Square Statistic

10. A chi-square goodness of fit test A chi-square test for independence A very small chi square test statistic  A very large chi square test statistic Types of Chi-Square Test

11. Example BLACK WHITE RED BLUE TOTAL MALE 48 12 33 57 150 FEMALE 34 46 42 26 148 TOTAL 82 58 75 83 298 H₀:Gender and preferred shirt color are independent. Hₐ:Gender and preferred shirt color are not independent. BLACK WHITE RED BLUE MALE FEMALE BLACK WHITE RED BLUE MALE FEMALE   The formula for expected Frequency

12. BLACK WHITE RED BLUE TOTAL MALE 48 12 33 57 150 FEMALE 34 46 42 26 148 TOTAL 82 58 75 83 298 BLACK WHITE RED BLUE MALE FEMALE BLACK WHITE RED BLUE MALE FEMALE OBSERVED VALUE EXPECTED VALUE x²   x²=1.0867 + 10.1315 + 0.0095 + 5.5272 + 1.1029 + 10.2722 + 0.6194 + 5.6077 x²=34.9572

13. df=(number of rows-1)(number of columns-1) =(2-1)(3) df=3 BLACK WHITE RED BLUE MALE FEMALE BLACK WHITE RED BLUE MALE FEMALE

14. df =3 CRITICAL VALUE LEVEL: 5%(  α =0.050)=7.815

15. CONCLUSION CHI SQUARE CRITICAL VALUE 34.9572  > 7. 815 Therefore, Gender and preferred shirt color are not independent

16. Chi-Square P-Values - tell you if your test results are significant or not. 1. Degrees of freedom. 2. The alpha level(α).

17. For example, the following chi-square shows 6 df:x²₆. And this chi square shows 4 df:x²₄. is a special case of the gamma distribution; A chi square distribution with n degrees of freedom is equal to a gamma distribution with a = n / 2 and b = 0.5 (or β = 2) Chi-square Distribution

18.  Confidence interval  Independence of two criteria of classification of qualitative variables.  Relationships between categorical variables (contingency tables).  Sample variance  Tests of deviations a goodness of fit test. Uses

19. A similar distribution is the chi distribution. This distribution describes the square root of a variable distributed according to a chi-square distribution.; with df = n > 0 degrees of freedom has a probability density function of: For values where x is positive Chi Distribution

20. Thank you