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BIOSTATISTICS

5.6

TEST OF HYPOTHESIS

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BIOSTATISTICS

• TERMINAL OBJECTIVE:

• 5.6 Perform a test of significance on a hypothesis using Chi-square test.

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BIOSTATISTICS

• STATE THE PURPOSE OF A:

5.6.1 2X2 contingency table.

5.6.2 2x2 expected table.

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Purpose - Contingency

• General– Public health professionals use contingency

tables to display data used in calculating measures of association and tests of statistical significance.

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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).

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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

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BIOSTATISTICS

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

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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.

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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.

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Completing A 2x2 Contingency Table

Outcome

Exposure Yes No Total

Yes a b H1

No c d H2

Total V1 V2 N

Format

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Completing A 2x2 Contingency Table

• Presenting a 2x2 contingency table – Title

• Appropriate for identification. Addresses what, where, and when.

• Follows rules of table construction.

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Completing A 2x2 Contingency Table

– Headings• Rows and columns labeled for exposure and

outcome, respectively.

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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.

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Completing A 2x2 Contingency Table

OUTBREAK ASSOCIATED WITH EATING TURKEY, USS ERASMUS B DRAGON, 25 NOV 04

Gastroenteritis

Ill Well Total

Ate turkey 97 36 133

Did not eat turkey 2 23 25

Total 99 59 158

Example

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Computing A 2x2 Expected Table

• COMPUTE:

5.6.4 Data for a 2x2 expected table.

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Computing A 2x2 Expected Table

• Obtain data from observed table.

• Format

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Computing A 2x2 Expected Table

Disease

Exposure Yes No Total

Yes a' b' a' + b'

No c' d' c' + d'

Total a' + c' b' + d' N

Format

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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.

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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.

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Computing A 2x2 Expected Table

• Example of expected table

Gastroenteritis

Ill Well Total

Ate turkey 83.34 49.66 133

Did not eat turkey 15.66 9.34 25

Total 99 59 158

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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

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Computing A 2x2 Expected Table

• 5.6.5 The value of Chi-square from a 2x2 contingency table.

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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.

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Calculating Chi-square

2= N[|(a d)-(b c)|-N/2]2

(a+b)(c+d)(a+c)(b+d)

Equation

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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.

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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.

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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]

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Calculating Chi-square

– 683571200

– 19421325

– 683571200/19421325

= 35.1969

= 35.20

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Calculating Chi-square

• 5.6.6 Define the null (HØ) and alternative (HA) hypotheses.

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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.

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Defining Hypothesis

• Two types

– Null (HØ)

– Alternate (HA)

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Defining Hypothesis

• Null hypothesis:

– There is no association between two factors under consideration. It may be due to chance.

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Defining Hypothesis

• Alternate hypothesis:

– There is an association between the factors under consideration. It is not due to chance.

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Hypothesis

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

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Hypothesis

• Chi-Square test:

– Either proves or disproves the null hypothesis.

– When the null hypothesis is disproved, then the alternative hypothesis is selected.

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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.

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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.

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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.

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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.

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Interpreting The Test Of Significance

– A Chi-Square value > 6.63 (P 0.01) is considered highly significant.

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Biostatistics!

Tomorrow: Practice

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You have just finished the last presentation in

Biostatistics!

Tomorrow: Practice