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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: X2 contingency table x2 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 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: 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 = –b' = (133)(59)/158 = –c' = (25)(99)/158 = –d' = (25)(59)/158 = 9.34

23 Computing A 2x2 Expected Table 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  2 = N[|(a d)-(b c)|-N/2] 2 (a+b)(c+d)(a+c)(b+d) Equation

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[ /2]2 – 158[2080]2 –158[ ]

29 Calculating Chi-square – – – / = = 35.20

30 Calculating Chi-square Define the null (H Ø ) and alternative (H A ) 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 (H Ø ) –Alternate (H A )

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 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

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