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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
Format
Outcome
Exposure
Yes
No
Total
Yes
a
b
H1
No
c
d
H2
Total
V1
V2
N
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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
Example
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
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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
Format
Disease
Exposure
Yes
No
Total
Yes
a'
b'
a' + b'
No
c'
d'
c' + d'
Total
a' + c'
b' + d'
N
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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
Equation
2= N[|(a d)-(b c)|-N/2]2
(a+b)(c+d)(a+c)(b+d)
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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!
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You have just finished
the last presentation in
Biostatistics!
Tomorrow: Practice
44