2. Contents
Definition
Use Of Biostatics
Basis Of Biostatics
Measures Of Statistical Averages Or
Central Tendency
Measures Of Dispersion
Normal Distribution/Normal
Curve/Gaussian Distribution
Standard Normal Deviation
3. Test Of Significance
Classification Of Tests Of Significance
The Chi Square Test (X² Test)
z-test
Analysis Of Variance (Anova) Test
Correlation And Regression
Conclusion
4. Definition
STATISTICS - is a science of compiling,
classifying, and tabulating numerical
data and expressing the results in a
mathematical and graphical form
BIOSTATISTICS - is that branch of
statistics concerned with the
mathematical facts and data related to
biological events
5. USES OF BIOSTATISTICS
To test whether the difference between
two populations is real or by chance
occurrence.
To study the correlation between
attributes in the same population.
To evaluate the efficacy of vaccines.
To measure mortality and morbidity.
6. To evaluate the achievements of public
health programs
To fix priorities in public health programs
To help promote health legislation and
create administrative standards for oral
health.
7. Measures of statistical
averages or central tendency
Central value around which all the other
observations are
Main objective is to condense the entire
mass of data and to facilitate the
comparison distributed
The most common measures of central
tendency that are used in BioStats are :
– Mean – Median – Mode
8. Mean
It is obtained by adding the individual
observations divided by the total number
of observations.
Advantages –
It is easy to calculate.
Most useful of all the averages.
Disadvantages –
Influenced by abnormal values.
9. Median
When all the observation are arranged
either in ascending order or descending
order, the middle observation is known
as median.
In case of even number the average of
the two middle values is taken.
Median is better indicator of central value as
it is not affected by the extreme values.
10. Mode
Most frequently occurring observation in
a data is called mode.
EXAMPLE Number of broken bones in
10 person from car accident.
(2,2,4,1,3,0,10,2,3,8 )
Mean = 34 / 10 = 3.4
Median= (0,1,2,2,2,3,3,4,8,10)
= 2+3 /2 = 2.5
Mode = 2 (occurs thrice)
11. MEASURES OF
DISPERSION
Dispersion is the degree of spread or
variation of the variable about a central
value.
Helps to know how widely the observations
are spread on either side of the average.
Most common measures of dispersion are:
1. RANGE (spread)
2. MEAN DEVIATION (set to disuse)
3. STANDARD DEVIATION (squared deviations)
12. Range
Difference between the value of the
largest and the value of the smallest
item in the data set
EXAMPLE Number of broken bones in 10
person from car accident.
(2,2,4,1,3,0,10,2,3,8 )
Convert In ascending order
(0,1,2,2,2,3,3,4,8,10)
Range = 10 – 0 = 10
13. Mean Deviation - Average of deviation
from the arithmetic mean
Standard Deviation – Considers the
squared deviation and thus a better
measure of dispersion
14. tests of significance
The test which is done for testing the
research hypothesis against the null
hypothesis
Chi-square test or X 2
Unpaired/Independent/student’s ‘t’ test
Paired sample t-test
ANOVA (Analysis of Variance)
15. CHI SQUARE TEST
Developed by Karl Pearson.
Chi-square (X 2) Test offers a method of testing
the significance of difference between two
proportions.
It has the advantage that it can also be used when
more than two groups are to be compared.
It is most commonly used when data are in
frequencies such as in the number of responses in
two or more categories.
16. Example: Effectiveness of
vaccination
Vaccinated Placebo Not Vaccinated
Caught flu 8 19 21
Did not
catch flu
142 161 79
H0: There is no relationship between people getting vaccinated and their
probability of getting infected with flu
17.
18. Expected Vaccinated Placebo Not Vaccinated
Caught flu
48*150/430
=16.7
48*180/430
= 20.1
48*100/430
= 11.2
48
Did not
catch flu
382*150/430
= 133.3
382*150/430
= 159.9
382*100/430
= 88.8
382
150 180 100 430
Observed Vaccinated Placebo Not Vaccinated
Caught flu 8 19 21 48
Did not
catch flu
142 161 79 382
150 180 100 430
19. Expected Vaccinated Placebo Not Vaccinated
Caught flu
(8-16.7)2
16.7
(19-20.1) 2
20.1
(21-11.2) 2
11.2
Did not
catch flu
(142-133.3) 2
133.3
(161-159.9) 2
159.39
(79-88.8) 2
88.8
14.97
Observed Vaccinated Placebo Not Vaccinated
Caught flu
8
(16.7)
19
(20.1)
21
(11.2)
48
Did not
catch flu
142
(133.3)
161
(159.9)
79
(88.8)
382
150 180 100 430
20. df = (r-1)(c-1) = 2 at 5% p-value
5.99 (critical value)
14.97 (calculated value)
Find out the critical value from chi-square
table by comparing the df and probability
(p-value)
If your chi-square calculated value is
greater than the chi-square critical value,
then you reject your null hypothesis.
