1. 2 BIOSTATISTICS 5.6 TEST OF HYPOTHESIS 3 BIOSTATISTICS TERMINAL OBJECTIVE: 5.6 Perform a test of...
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Transcript of 1. 2 BIOSTATISTICS 5.6 TEST OF HYPOTHESIS 3 BIOSTATISTICS TERMINAL OBJECTIVE: 5.6 Perform a test of...
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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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You have just finished the last presentation in
Biostatistics!
Tomorrow: Practice
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You have just finished the last presentation in
Biostatistics!
Tomorrow: Practice