Lesson 14 Lesson 14 Lesson 14 Lesson 14
Confidence Intervals of Confidence Intervals of
Odds Ratio and Odds Ratio and
Relative Risk
Relative Risk
Relative Risk
Relative Risk
Lesson 14 Outline Lesson 14 Outline Lesson 14 Outline Lesson 14 Outline
Lesson 14 covers Lesson 14 covers Lesson 14 covers Lesson 14 covers
Confidence Interval of an Odds Ratio Confidence Interval of an Odds Ratio
Review of Odds RatioReview of Odds Ratio
Review of Odds RatioReview of Odds Ratio
Sampling distribution of OR on natural log scaleSampling distribution of OR on natural log scale
95% Confidence Interval of OR example95% Confidence Interval of OR example
95% Confidence Interval of OR example95% Confidence Interval of OR example
Confidence Interval of Relative Risk Confidence Interval of Relative Risk
Review of Relative RiskReview of Relative Risk
Review of Relative RiskReview of Relative Risk
Sampling distribution of RR on natural log scaleSampling distribution of RR on natural log scale
95% Confidence Interval of RR example95% Confidence Interval of RR example
95% Confidence Interval of RR example95% Confidence Interval of RR example
Review: Odds Ratio and Relative Review: Odds Ratio and Relative
Ri k Ri k Risk Risk
Both Odds Ratio and Relative Risk are Both Odds Ratio and Relative Risk are
Both Odds Ratio and Relative Risk are Both Odds Ratio and Relative Risk are measures of association (or relationship) measures of association (or relationship) between two nominal variables
between two nominal variables between two nominal variables.
between two nominal variables.
The Odds Ratio is typically estimated from The Odds Ratio is typically estimated from data collected in a Case
data collected in a Case Control study Control study data collected in a Case
data collected in a Case--Control study. Control study.
The Relative Risk can be estimated from The Relative Risk can be estimated from
d t ll t d i ti t d
d t ll t d i ti t d
data collected in a prospective study.
data collected in a prospective study.
Associations between 2 nominal Associations between 2 nominal
i bl i bl variable variable
If there is no association between the two If there is no association between the two
i bl th OR RR 1
i bl th OR RR 1
variables, the OR or RR = 1 variables, the OR or RR = 1
An OR or RR > 1.0 or < 1.0 indicates a An OR or RR > 1.0 or < 1.0 indicates a possiblepossible t ti ti l l ti hi ( i ti ) b t
t ti ti l l ti hi ( i ti ) b t
statistical relationship (or association) between statistical relationship (or association) between the two variables.
the two variables.
Hypothesis tests for the OR and RR are not usedHypothesis tests for the OR and RR are not used
Hypothesis tests for the OR and RR are not used Hypothesis tests for the OR and RR are not used to determine statistical significance of the
to determine statistical significance of the association
association association association
Instead, Confidence intervals of OR or RR are Instead, Confidence intervals of OR or RR are
constructed and used to determine whether or not constructed and used to determine whether or not the association is statistically significant.
the association is statistically significant.
Confidence Interval Confidence Interval
f Odd R ti f Odd R ti
of Odds Ratio
of Odds Ratio
Review: Odds Ratio Review: Odds Ratio Review: Odds Ratio Review: Odds Ratio
Odds of an event = Odds of an event =
Odds of an event = Odds of an event =
probability that the event occurs probability that the event occurs
probability that the event does not occur probability that the event does not occur probability that the event does not occur probability that the event does not occur
Odds Ratio Odds Ratio
odds of event for group 1
odds of event for group 1 g g p p
odds of event for group 2
odds of event for group 2
Review: Disease OR for ‘Exposed’
Review: Disease OR for ‘Exposed’
d t ‘N t E d’
d t ‘N t E d’
compared to ‘Not Exposed’
compared to ‘Not Exposed’
Disease
Disease No DiseaseNo Disease TotalTotal Disease
Disease No DiseaseNo Disease TotalTotal Exposed Group
Exposed Group
a a b b a+b a+b
Not Exposed Not Exposed Group
Group
c c d d c+d c+d
Odds of Disease for Exposed = a/(a+b) b/(a+b) = a/b
Odds of Disease for Not Exposed = c/(c+d) d/(c+d) = c/dp ( ) ( )
OR = a/b c/d = ad / bc
Confidence Interval for an Confidence Interval for an
Odds Ratio Odds Ratio
The confidence interval for an Odds Ratio The confidence interval for an Odds Ratio
The confidence interval for an Odds Ratio The confidence interval for an Odds Ratio has the same general formula as the
has the same general formula as the
Confidence Interval for a population mean Confidence Interval for a population mean p p p p or population proportion
or population proportion
Error Standard
* t Coefficien Confidence
Estimate
Point
The difference is that the confidence The difference is that the confidence
interval for the Odds Ratio is calculated on interval for the Odds Ratio is calculated on the natural log (LN) scale and then
the natural log (LN) scale and then t d b k t th i i l l t d b k t th i i l l
converted back to the original scale.
converted back to the original scale.
Sampling Distribution of the Sampling Distribution of the
Odds Ratio Odds Ratio
The sampling distribution of the Odds Ratio is The sampling distribution of the Odds Ratio is
The sampling distribution of the Odds Ratio is The sampling distribution of the Odds Ratio is positively skewed.
positively skewed.
However It is approximately normally However It is approximately normally
However, It is approximately normally However, It is approximately normally distributed on the natural log scale.
distributed on the natural log scale.
Th fid i t l i l l t d th
Th fid i t l i l l t d th
The confidence interval is calculated on the The confidence interval is calculated on the natural log scale (LN)
natural log scale (LN)
After finding the limits on the LN scale, use the After finding the limits on the LN scale, use the EXP function to find the limits on the original EXP function to find the limits on the original scale.
scale.
95% Confidence Interval of OR:
95% Confidence Interval of OR:
h h
the steps the steps
1.
1. Calculate the Odds Ratio from the dataCalculate the Odds Ratio from the data
2.
2. Find the Natural log of the OR using the LN Find the Natural log of the OR using the LN function in Excel
function in Excel
3.
3. The confidence coefficient is from the standard The confidence coefficient is from the standard normal distribution: 1.96 for a 95% confidence normal distribution: 1.96 for a 95% confidence interval
interval interval interval
4.
4. Calculate the SE of LN(OR) Calculate the SE of LN(OR) –– see next slidesee next slide
5
5 The lower and upper limits on the log scale =The lower and upper limits on the log scale =
5.
5. The lower and upper limits on the log scale = The lower and upper limits on the log scale = LN(OR)
LN(OR) ±± 1.96* SE LN(OR) = (LL, UL)1.96* SE LN(OR) = (LL, UL)
6.
6. Use the EXP function to find the CI limits on Use the EXP function to find the CI limits on the original scale: EXP(LL), EXP(UL)
the original scale: EXP(LL), EXP(UL)
SE of LN(OR) SE of LN(OR) SE of LN(OR) SE of LN(OR)
The SE of LN(OR) is calculated from the The SE of LN(OR) is calculated from the cell counts in the 2 X 2 table:
cell counts in the 2 X 2 table:
Cases
Cases ControlsControls Cases
Cases ControlsControls Exposed
Exposed
a a b b
Not exposed
Not exposed
c c d d SE of LN(OR) =
SE of LN(OR) =
d 1 c
1 b
1 a
1 d c
b
a
95% Confidence Interval of Odds 95% Confidence Interval of Odds
R i R i Ratio Ratio
First calculate the upper and lower limits on First calculate the upper and lower limits on pppp the LN scale
the LN scale
d c
b
OR a1 1 1 1
* 96 . 1 )
ln(
After calculating the upper and lower limits After calculating the upper and lower limits d c
b a
on the LN scale, use the exponential on the LN scale, use the exponential
function (EXP) to find the lower and upper function (EXP) to find the lower and upper limits on the original scale
limits on the original scalegg
If the 95% Confidence Interval does not If the 95% Confidence Interval does not contain the value 1.0, the association is contain the value 1.0, the association is statistically significant at alpha = 0 05
statistically significant at alpha = 0 05 statistically significant at alpha = 0.05 statistically significant at alpha = 0.05
Example: Preterm delivery Example: Preterm delivery Example: Preterm delivery Example: Preterm delivery
and Mother’s SES level and Mother’s SES level
Study background: A case Study background: A case--control study of control study of
th id i l f t d li
th id i l f t d li
the epidemiology of preterm delivery was the epidemiology of preterm delivery was undertaken at Yale
undertaken at Yale--New Haven Hospital in New Haven Hospital in Connecticut during 1977 The table on the Connecticut during 1977 The table on the Connecticut during 1977. The table on the Connecticut during 1977. The table on the following slide contains data for Mother’s following slide contains data for Mother’s socioeconomic status (SES) for those with socioeconomic status (SES) for those with socioeconomic status (SES) for those with socioeconomic status (SES) for those with (cases) and without (controls) preterm
(cases) and without (controls) preterm delivery.
delivery. y y
Preterm Delivery Preterm Deliveryyy Socio
Socio--
Economic Economic
Status
Status CasesCases ControlsControls Upper
Upper 1111 4040
Upper Middle Upper Middle Middle
Middle
L Middl L Middl
14 14 33 33 59 59
45 45 64 64 91 91 Lower Middle
Lower Middle Lower
Lower
Unknown Unknown
59 59 53 53 5 5
91 91 58 58 5 5 Unknown
Unknown 55 55
Construct a 95% Confidence Interval for the odds ratio for Preterm delivery comparing Lower to Upper SES
Data table for Confidence Interval of Data table for Confidence Interval of
Odds Ratio of preterm delivery Odds Ratio of preterm delivery comparing lower to upper SES comparing lower to upper SES
Preterm Delivery Preterm Delivery SES
SES
Yes: CasesYes: Cases No: ControlsNo: ControlsLower
Lower 53 53 58 58
Upper
Upper 11 11 40 40
Upper
Upper 11 11 40 40
1. Calculate the OR for Preterm Delivery:
1. Calculate the OR for Preterm Delivery:
L SES d t U SES
L SES d t U SES
Lower SES compared to Upper SES Lower SES compared to Upper SES
Preterm Delivery Preterm Delivery Preterm Delivery Preterm Delivery SES
SES
Yes: CasesYes: Cases No: ControlsNo: ControlsLower
Lower 53 53 58 58
Upper
Upper 11 11 40 40
Odds Ratio = (53/58) / (11/40) = 3.32
2. Calculate the LN (OR) and 2. Calculate the LN (OR) and
3 Fi d h fid ffi i
3 Fi d h fid ffi i
3. Find the confidence coefficient 3. Find the confidence coefficient
2 Calculate the LN(OR) 2 Calculate the LN(OR) 2. Calculate the LN(OR) 2. Calculate the LN(OR)
LN(3.32) = 1.20 LN(3.32) = 1.20
Thi i th i t ti t f th Thi i th i t ti t f th This is the point estimate for the This is the point estimate for the confidence interval
confidence interval
3. The confidence coefficient for the LN(OR) 3. The confidence coefficient for the LN(OR)
is from the standard normal distribution.
is from the standard normal distribution.
For a 95% confidence interval, the For a 95% confidence interval, the coefficient = 1.96
coefficient = 1.96
4. Calculate the SE of LN(OR) 4. Calculate the SE of LN(OR) 4. Calculate the SE of LN(OR) 4. Calculate the SE of LN(OR)
Preterm Delivery Preterm Delivery Preterm Delivery Preterm Delivery SES
SES
Yes: CasesYes: Cases No: ControlsNo: ControlsL
L 53 53 58 58
Lower
Lower 53 53 58 58
Upper
Upper pp pp 11 11 40 40
1 1
1
1 0 . 39
40 1 11
1 58
1 53
ln(OR) 1
SE
5. & 6. Find the Lower and Upper 5. & 6. Find the Lower and Upper
limits on the LN scale and the limits on the LN scale and the limits on the LN scale and the limits on the LN scale and the
original scale original scale
) 97 .
1 , 44 .
0 ( 39
. 0
* 96 .
1 20
.
1
5. The upper and lower limits of the 5. The upper and lower limits of the
confidence interval on the LN scale are confidence interval on the LN scale are confidence interval on the LN scale are confidence interval on the LN scale are (0.44, 1.97)
(0.44, 1.97)
6. Use the EXP function in Excel to find 6. Use the EXP function in Excel to find
the interval limits of the 95% CI of the the interval limits of the 95% CI of the OR:
OR: (1.55, 7.14) (1.55, 7.14)
Interpretation of the CI for Preterm Interpretation of the CI for Preterm
Delivery and SES Delivery and SES
State the conclusion in the original scale State the conclusion in the original scale g g
The odds ratio for preThe odds ratio for pre--term delivery for Lower SES term delivery for Lower SES compared to the Upper SES is 3.32 indicating
compared to the Upper SES is 3.32 indicating increased odds of pre
increased odds of pre--term delivery for mothers in term delivery for mothers in Lower SES
Lower SES
The 95% Confidence Interval of the Odds Ratio The 95% Confidence Interval of the Odds Ratio (1.55 , 7.14) indicates that odds of pre
(1.55 , 7.14) indicates that odds of pre--term delivery term delivery i ifi tl
i ifi tl hi hhi h ff th Lth L SESSES are
are significantlysignificantly higher for the Lower SES group higher for the Lower SES group compared to the Upper SES group (at 0.05
compared to the Upper SES group (at 0.05
significance level) because the CI does not contain 1 significance level) because the CI does not contain 1 significance level) because the CI does not contain 1.
significance level) because the CI does not contain 1.
Interpretation of 95%
Interpretation of 95% te p etat o o 95% te p etat o o 95%
Confidence Interval of OR Confidence Interval of OR
An Odds Ratio = 1 indicates ‘no association’ An Odds Ratio = 1 indicates ‘no association’
between the exposure and the disease.
between the exposure and the disease.
If the 95% confidence interval for the OR does If the 95% confidence interval for the OR does not contain 1.0 we can conclude that there is a not contain 1.0 we can conclude that there is a statisticall significant* association bet een the statisticall significant* association bet een the statistically significant* association between the statistically significant* association between the exposure and the disease.
exposure and the disease.
* at the 0 05 significance level
* at the 0 05 significance level at the 0.05 significance level at the 0.05 significance level
If the 95% confidence interval for the OR If the 95% confidence interval for the OR contains 1.0, the association is
contains 1.0, the association is not not significant at significant at gg the 0.05 level.
the 0.05 level.
Confidence Interval Confidence Interval
f R l ti Ri k
f R l ti Ri k
of Relative Risk
of Relative Risk
Review: Relative Risk Review: Relative Risk Review: Relative Risk Review: Relative Risk
Risk of an event = Risk of an event =
Risk of an event = Risk of an event =
probability that the event occurs probability that the event occurs
Relative Risk Relative Risk
probability that event occurs for group 1
probability that event occurs for group 1
probability that event occurs for group 2
probability that event occurs for group 2
probability that event occurs for group 2
probability that event occurs for group 2
Review: RR Calculated from a Review: RR Calculated from a
table table
Disease
Disease No DiseaseNo Disease TotalTotal Disease
Disease No DiseaseNo Disease TotalTotal
Exposed Group
Exposed Group
a a b b a+b a+b
Not Exposed Not Exposed Group
Group
c c d d c+d c+d
Risk of Disease for Exposed = a/(a+b) Risk of Disease for Not exposed = c/(c+d) Risk of Disease for Not exposed = c/(c+d)
RR = a/(a+b) c/(c+d)
RR a/(a+b) c/(c+d)
Confidence Interval for Confidence Interval for
Relative Risk Relative Risk
Like the Odds Ratio, the sampling Like the Odds Ratio, the sampling distribution of the Relative Risk is distribution of the Relative Risk is
positively skewed but is approximately positively skewed but is approximately normally distributed on the natural log normally distributed on the natural log scale
scale scale.
scale.
Constructing a Confidence Interval for the Constructing a Confidence Interval for the Relative Risk is similar to constructing a CI Relative Risk is similar to constructing a CI Relative Risk is similar to constructing a CI Relative Risk is similar to constructing a CI for the Odds Ratio except that there is a
for the Odds Ratio except that there is a different formula for the SE
different formula for the SE different formula for the SE.
different formula for the SE.
95% Confidence Interval of RR 95% Confidence Interval of RR 95% Confidence Interval of RR 95% Confidence Interval of RR
1. Estimate the RR from the data 1. Estimate the RR from the data
2. Find the natural log of RR: LN(RR) 2. Find the natural log of RR: LN(RR)
3. The confidence coefficient is from the standard 3. The confidence coefficient is from the standard
normal distribution: 1.96 for a 95% confidence normal distribution: 1.96 for a 95% confidence interval
interval
4 C l l t th SE f LN(RR)
4 C l l t th SE f LN(RR) t lidt lid 4. Calculate the SE of LN(RR)
4. Calculate the SE of LN(RR) –– see next slidesee next slide
5. Calculate the lower and upper limits on the LN 5. Calculate the lower and upper limits on the LN
scale: LN(RR)
scale: LN(RR) ±± 1 96* SE LN(RR)1 96* SE LN(RR) scale: LN(RR)
scale: LN(RR) ±± 1.96 SE LN(RR)1.96 SE LN(RR)
6. Use the EXP function to find the limits on the 6. Use the EXP function to find the limits on the
original scale: EXP(LL), EXP (UL) original scale: EXP(LL), EXP (UL)gg (( ),), (( ))
SE of LN(RR) SE of LN(RR) SE of LN(RR) SE of LN(RR)
The SE of LN(RR) is calculated from the cell The SE of LN(RR) is calculated from the cell t i th 2 X 2 t bl
t i th 2 X 2 t bl counts in the 2 X 2 table:
counts in the 2 X 2 table:
Disease
Disease No DiseaseNo Disease TotalTotal
Exposed Group
Exposed Group
a a b b a+b a+b
Not Exposed
Not Exposed
c c d d c+d c+d
Group
Group
c c d d c d c d
d b
d) c(c
d b)
a(a ln(RR) b
SE
95% Confidence Interval of 95% Confidence Interval of
R l i Ri k R l i Ri k Relative Risk Relative Risk
First calculate the upper and lower limits on the First calculate the upper and lower limits on the pppp LN scale
LN scale
* 96 1
)
l ( b d
RR
) (
)
* ( 96 . 1 )
ln( RR a a b c c d
After calculating the upper and lower limits on After calculating the upper and lower limits on
the LN scale, use the exponential function to find the LN scale, use the exponential function to find the limits on the original scale
the limits on the original scale the limits on the original scale the limits on the original scale
If the 95% Confidence Interval does not contain If the 95% Confidence Interval does not contain the value 1.0, the association is statistically
the value 1.0, the association is statistically significant at alpha = 0 05
significant at alpha = 0 05 significant at alpha = 0.05 significant at alpha = 0.05
Example: 95% CI for RR of Example: 95% CI for RR of
Myocardial Infarction (MI) Myocardial Infarction (MI)
Background: Physicians enrolled in the Physician’s Health Background: Physicians enrolled in the Physician’s Health gg yy yy Study were randomly assigned to take a daily aspirin or Study were randomly assigned to take a daily aspirin or placebo. The table provides the number with MI in each placebo. The table provides the number with MI in each group.
group.
g p
g p
Group Yes No
Myocardial Infarction (MI)
Group Yes No
Aspirin 139 10898 11037 Placebo 239 10795 11034 378 21693 22071
Calculate the RR and 95% CI for the RR for MI (aspirin Calculate the RR and 95% CI for the RR for MI (aspirin
378 21693 22071
( p ( p group compared to placebo group)
group compared to placebo group)
1.
1. Calculate the RR for MI: Calculate the RR for MI:
aspirin group compared to aspirin group compared to
placebo placebo placebo placebo
Myocardial Infarction (MI)
Group Yes No
Aspirin 139 10898 11037 Placebo 239 10795 11034
Infarction (MI)
Placebo 239 10795 11034 378 21693 22071
RR = (139/11037) / (239/11034) = 0.581
2. Calculate the LN (RR) and 2. Calculate the LN (RR) and
3 Fi d h fid ffi i
3 Fi d h fid ffi i
3. Find the confidence coefficient 3. Find the confidence coefficient
2 Calculate the LN(RR) 2 Calculate the LN(RR) 2. Calculate the LN(RR) 2. Calculate the LN(RR)
LN(0.581) =
LN(0.581) = --0.543 0.543
Thi i th i t ti t f th Thi i th i t ti t f th This is the point estimate for the This is the point estimate for the confidence interval
confidence interval
3. The confidence coefficient for the LN(RR) 3. The confidence coefficient for the LN(RR)
is from the standard normal distribution.
is from the standard normal distribution.
For a 95% confidence interval, the For a 95% confidence interval, the coefficient = 1.96
coefficient = 1.96
4. Calculate the SE LN(RR) 4. Calculate the SE LN(RR) 4. Calculate the SE LN(RR) 4. Calculate the SE LN(RR)
Group Yes No
Myocardial Infarction (MI)
Group Yes No
Aspirin 139 10898 11037 Placebo 239 10795 11034 378 21693 22071 378 21693 22071
10795 10898
106 .
11034 0
* 239
10795 11037
* 139
10898 ln(RR)
SE
5. & 6. Find the Lower and 5. & 6. Find the Lower and
Upper limits on the LN scale and Upper limits on the LN scale and
the original scale the original scale the original scale the original scale
) 336 .
0 ,
75 .
0 (
106 .
0
* 96 .
1 543
.
0
5. The upper and lower limits of the 5. The upper and lower limits of the
confidence interval on the LN scale are confidence interval on the LN scale are
) (
confidence interval on the LN scale are confidence interval on the LN scale are ((--0.750, 0.750, --0.336) 0.336)
6. Use the EXP function in Excel to find 6. Use the EXP function in Excel to find
the interval limits of the 95% CI of the the interval limits of the 95% CI of the RR:
RR: (0.472, 0.715) (0.472, 0.715)
Interpretation of 95% CI of RR Interpretation of 95% CI of RR
for MI for MI
The Relative Risk estimate = 0.58 which The Relative Risk estimate = 0.58 which indicates that physicians in the aspirin indicates that physicians in the aspirin
h d l i k f MI th h d l i k f MI th
group had a lower risk of MI than group had a lower risk of MI than physicians in the placebo group.
physicians in the placebo group.
Th 95% fid i t l i di t th t Th 95% fid i t l i di t th t
The 95% confidence interval indicates that The 95% confidence interval indicates that the decreased risk related to daily aspirin the decreased risk related to daily aspirin use is
use is significant significant (at alpha = 0 05) since (at alpha = 0 05) since use is
use is significant significant (at alpha = 0.05) since (at alpha = 0.05) since the interval (0.472, 0.715) does not
the interval (0.472, 0.715) does not contain 1.
contain 1.
contain 1.
contain 1.
General Interpretation of 95%
General Interpretation of 95%
Ge e a te p etat o o 95%
Ge e a te p etat o o 95%
Confidence Interval of RR Confidence Interval of RR
A Relative Risk = 1.0 indicates ‘no association’ A Relative Risk = 1.0 indicates ‘no association’
between the exposure and the disease.
between the exposure and the disease.
If the 95% confidence interval for the RR does If the 95% confidence interval for the RR does not contain 1.0 we can conclude that there is a not contain 1.0 we can conclude that there is a statisticall significant* association bet een the statisticall significant* association bet een the statistically significant* association between the statistically significant* association between the exposure and the disease.
exposure and the disease.
* at the 0 05 significance level
* at the 0 05 significance level at the 0.05 significance level at the 0.05 significance level
If the 95% confidence interval for the RR If the 95% confidence interval for the RR contains 1.0, the association is
contains 1.0, the association is notnot significant at significant at gg the 0.05 level.
the 0.05 level.
Notes on the OR and RR CI:
Notes on the OR and RR CI:
Notes on the OR and RR CI:
Notes on the OR and RR CI:
The RR estimate will not be exactly in the middle The RR estimate will not be exactly in the middle yy of the confidence interval on the original scale
of the confidence interval on the original scale
The LN(RR) is exactly in the middle of the interval on The LN(RR) is exactly in the middle of the interval on the LN scale
the LN scale the LN scale the LN scale
The OR estimate will not be exactly in the middle The OR estimate will not be exactly in the middle of the confidence interval on the original scale
of the confidence interval on the original scale of the confidence interval on the original scale of the confidence interval on the original scale
The LN(OR) is exactly in the middle of the interval on The LN(OR) is exactly in the middle of the interval on the LN scale
the LN scale
Ch k th t th RR OR ti t i t i d Ch k th t th RR OR ti t i t i d
Check that the RR or OR estimate is contained Check that the RR or OR estimate is contained in the final interval
in the final interval –– it’s easy to forget the EXP it’s easy to forget the EXP step
step step step
Readings and Assignments Readings and Assignments Readings and Assignments Readings and Assignments
Reading: Chapter 8 pgs 200Reading: Chapter 8 pgs 200--201201
Reading: Chapter 8 pgs 200Reading: Chapter 8 pgs 200 201 201
Work through the Lesson 14 practice exercisesWork through the Lesson 14 practice exercises
Excel Module 14 works through the examples inExcel Module 14 works through the examples in
Excel Module 14 works through the examples in Excel Module 14 works through the examples in this lesson for the confidence intervals of OR and this lesson for the confidence intervals of OR and RR
RR
Excel functions: LN and EXPExcel functions: LN and EXP
There is no CI function for the RR and OR There is no CI function for the RR and OR –– you just you just work through the steps
work through the steps
Complete Homework 10Complete Homework 10
