slides contains definitions, explanation and examples of odds ratio and confidence interval.

1. Presented by: Nang Uttama Tungkhang
Roll. No. 20/BIOT/017
2nd semester
Department of biotechnology
MZU

2. ODDS
It is defined as the probability that the event will occur divided
by the probability that the event will not occur.
ODDS RATIO
An odds ratio is a measure of association between a certain
events ‘’a’’ and a second event ‘’b’’.

3. Ratio of
these odds
Ratio of
these
odds

4. How to calculate the odds ratio
General steps:
• Calculate the odds that a member of the population has event
‘‘a’’. assume the person already has ‘’b’’.
E.g., ‘’a’’= cancer, ‘’b’’= mutated gene
• Calculate the odds that a member of the population has event
‘’a’’. assume the person does not have ‘’b’’.
• Divide step1 by step 2 to get the odds ratio.

5. example
23 117
6 210
Has cancer
yes no
yes
no
Has the
mutated
gene
If someone has the mutated
genes are the odds higher that
they will get cancer?
23/117
6/210
=0.2/0.03
=6.88

6. Interpretation
What do the results mean?
• odds ratio= 1, means that exposure to event ‘’a’’
does not affect the odds of event ‘’b’’.
• Odds ratio>1, means that there is higher odds of
event ‘’b’’ happening with exposure to event ‘’a’’.
• Odds ratio<1, is associated with lower odds.

7. Importance
• Odds ratio tells us if there is a strong or weak
relationship between two things, like whether
or not having a mutated gene increases the
odds of having cancer.
• The great value of the odds ratio is it is simple
to calculate , very easy to interpret, and
provide results upon which clinical decisions
can be made.

8. Confidence interval
• A confidence interval is how much uncertainty there
is with any particular statistic.
• It tells you how confident you can be that the results
from a poll or survey reflect what you would expect
to find if it were possible to survey the entire
population.
population
sample

9. Confidence level vs. confidence
interval
• Cl are expressed in percentage
• For example, a 95% confidence level.
• Ci are expressed in numbers
• In order to calculate confidence interval we must decide our
confidence level.
• Confidence interval is the range of values that contains the
true value
• larger the confidence level larger will be confidence interval
and vice-versa

10. Confidence interval
• Confidence, in statistics , is another way to describe
probability.
• E.g., probability of the population mean value being between
-1.96 and +1.96 (z-score) from the sample mean is 95%.
• Accordingly, there is a 5% chance that the population
mean lies outside of the upper and lower confidence
interval.

11. Formula for calculating confidence
interval
• Most commonly used confidence level is 95%.
• Formula:
where:
• x̅ is the mean
• Z is the chosen z value
• S is standard deviation
• N is the sample size

12. example
• We measure the height of 40 randomly chosen men, and get a
mean of 175cm, standard deviation of men’s height is 20cm.
• Confidence level 95%.
• N=40
• x̅= 175
• S=20
• Z=1.96
• Using the values in
Formula;
175±1.96* 20/40
which is 175cm±6.20cm
Means from 168.8cm to 181.2 cm.

13. conclusion
• confidence intervals permit a flexible
approach to analysis of research data.
• Confidence interval are also useful in the
interpretation of studies with small sample
size , allowing the researchers and consumers
of scientific literature to draw more
meaningful conclusions about clinical
significance of such studies.

14. references
https://en.wikipedia.org/wiki/Odds_ratio
https://www.biochemia-
medica.com/en/journal/19/2/10.11613/BM.2009.011/
fullArticle
https://www.statisticshowto.com/probability-and-
statistics/probability-main-index/odds-ratio/
https://en.wikipedia.org/wiki/Confidence_interval
https://www.mathsisfun.com/data/confidence-
interval.html
https://www.statisticshowto.com/probability-and-
statistics/confidence-interval/