BIOSTATISTICS

2. BIOSTATISTICS 5.6 TEST OF HYPOTHESIS

3. BIOSTATISTICS • TERMINAL OBJECTIVE: • 5.6 Perform a test of significance on a hypothesis using Chi-square test.

4. BIOSTATISTICS • STATE THE PURPOSE OF A: 5.6.1 2X2 contingency table. 5.6.2 2x2 expected table.

5. Purpose - Contingency • General • Public health professionals use contingency tables to display data used in calculating measures of association and tests of statistical significance.

6. Purpose - Contingency • Used to study the association between exposure and disease with the observed frequencies. In basic terms, the observed table shows a relationship between exposure and outcome (ill or well).

7. Purpose - Expected • General • Computes the frequencies we would if there is no relationship between exposure and outcome. • Determines which test statistic is used on the hypothesis. • Chi-square • Fisher's exact test

8. BIOSTATISTICS • 5.6.3 Complete a 2x2 contingency table from observed data.

9. Completing A 2x2 Contingency Table • Data is derived from frequency distribution table, such as a Food Specific Attack Rate Table, or other two variable table.

10. Completing A 2x2 Contingency Table • Basic Format • Composed of four outlined square cells. • Disease status is designated at the top of table. • Exposure status is designated along side of table.

11. Completing A 2x2 Contingency Table Format

12. Completing A 2x2 Contingency Table • Presenting a 2x2 contingency table • Title • Appropriate for identification. Addresses what, where, and when. • Follows rules of table construction.

13. Completing A 2x2 Contingency Table • Headings • Rows and columns labeled for exposure and outcome, respectively.

14. Completing A 2x2 Contingency Table • Printing • Double line above header, single line below. • No internal lines are needed. • Single line below the row for totals.

15. Completing A 2x2 Contingency Table Example

16. Computing A 2x2 Expected Table • COMPUTE: 5.6.4 Data for a 2x2 expected table.

17. Computing A 2x2 Expected Table • Obtain data from observed table. • Format

18. Computing A 2x2 Expected Table Format

19. Computing A 2x2 Expected Table • Formula • a´ = (H1)(V1)/N • b´ = (H1)(V2)/N • c´ = (H2)(V1)/N • d´ = (H2)(V2)/N • Note: Row and column totals equal the observed totals.

20. Computing A 2x2 Expected Table • Evaluation • If any one of the cells (a´ through d´) is less than 5, the Fisher's exact test is used. • When all cells are 5 or greater, the Chi-Square test is used.

21. Computing A 2x2 Expected Table • Example of expected table

22. Computing A 2x2 Expected Table • a' = (133)(99)/158 = 83.34 • b' = (133)(59)/158 = 49.66 • c' = (25)(99)/158 = 15.66 • d' = (25)(59)/158 = 9.34

23. Computing A 2x2 Expected Table • 5.6.5 The value of Chi-square from a 2x2 contingency table.

24. Calculating Chi-square • Once the 2X2 contingency table is completed, Chi-Square is computed by substituting the values in the table into the Chi-Square equation.

25. Calculating Chi-square Equation 2= N[|(a d)-(b c)|-N/2]2 (a+b)(c+d)(a+c)(b+d)

26. Calculating Chi-square • Steps: • Substitute the values into the equation. • Perform the functions in the parentheses first. • Subtract one-half of N from this total. • Square the value within the brackets.

27. Calculating Chi-square • Multiply that number by "N". • Simplify the denominator by multiplying the totals. • Carry out the remaining division. • Round off to the nearest hundredth.

28. Calculating Chi-square • Example using TABLE 5.6A χ2= 158[((97*23)-(2*36))-158/2]2 • 158[2159-158/2]2 • 158[2080]2 • 158[4326400]

29. Calculating Chi-square • 683571200 • 19421325 • 683571200/19421325 = 35.1969 = 35.20

30. Calculating Chi-square • 5.6.6 Define the null (HØ) and alternative (HA) hypotheses.

31. Defining Hypothesis • Definition (statistical) • Statement about the relationship between probability distributions. • Educated guess or an idea as to what may be going on in a particular situation.

32. Defining Hypothesis • Two types • Null (HØ) • Alternate (HA)

33. Defining Hypothesis • Null hypothesis: • There is no association between two factors under consideration. It may be due to chance.

34. Defining Hypothesis • Alternate hypothesis: • There is an association between the factors under consideration. It is not due to chance.

35. Hypothesis • 5.6.7 Interpret the test of significance on the null hypothesis.

36. Hypothesis • Chi-Square test: • Either proves or disproves the null hypothesis. • When the null hypothesis is disproved, then the alternative hypothesis is selected.

37. Interpreting The Test Of Significance • Test of significance • Either proves or disproves the null hypothesis. • When the null hypothesis is disproved, then the alternate hypothesis is selected.

38. Interpreting The Test Of Significance • P value • The P value is the probability that our result will occur due to chance. • Chi-square calculates a value which represents a known P value.

39. Interpreting The Test Of Significance • Interpretation • If the Chi-Square value is greater than 3.84 (P  0.05), then the null hypothesis is rejected and the alternate hypothesis is accepted. • There is a statistically significant association between the two factors.

40. Interpreting The Test Of Significance • If the Chi-Square value is less than or equal to () 3.84, the alternative hypothesis is rejected in favor of the null hypothesis. • The association between the two factors is NOT statistically significant.

41. Interpreting The Test Of Significance • A Chi-Square value > 6.63 (P  0.01) is considered highly significant.

42. You have just finished the last presentation in Biostatistics!Tomorrow: Practice

44. You have just finished the last presentation in Biostatistics!Tomorrow: Practice