This powerpoint presentation gives a brief explanation about the biostatic data .this is quite helpful to individuals to understand the basic research methodology terminologys

1. SCOPE & NEED OF
STATISTICAL APPLICATION
TO BIOLOGICAL DATA
DR. JYOTI SHARMA
MDS I
Dept of prosthodontics

2. CONTENTS
1. Definition
2. Use Of Biostatics
3. Basis Of Biostatics
4. Measures Of Statistical Averages Or Central Tendency
5. Measures Of Dispersion
6. Normal Distribution/Normal Curve/Gaussian Distribution
7. Standard Normal Deviation
8. Test Of Significance
9. Classification Of Tests Of Significance

3. 10.Standard Error Of Proportion
11.Standard Error Of Difference Between Two Means
12.Standard Error Of Difference Between Proportions
13.The Chi Square Test For Qualitative Data(X² Test)
14.z-test
15.Analysis Of Variance (Anova) Test
16.Correlation And Regression
17.Regression
18.Conclusion

4. 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.
DEFINATION

5. USES OF BIOSTATISTICS
1. Totest whether the difference between two populations is real or by chance occurrence.
2. Tostudy the correlation between attributes in the same population.
3. Toevaluate the efficacy of vaccines.
4. Tomeasure mortality and morbidity.
5. Toevaluate the achievements of public health programs
6. Tofix priorities in public health programs
7. Tohelp promote health legislation and create administrative standards for oral
health.

6. Basis Of Statistical Analysis
Based On Three Primary Entities :
 The Population (U)
 The Set Of Characteristic Variables (V)
 The Probability Distribution (P)

7. Measures of statistical averages or
central tendency
• Central value around which all the other observations are
distributed.
• Main objective is to condense the entire mass of data and to facilitate the
comparison.
• The most common measures of central tendency that are used in dental
sciences:
– Arithmetic mean
– Median
– Mode

8. • Refers to arithmetic 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.
Mean

9. • 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.
Median

10. • Most frequently occurring observation in a data is called mode.
• Not often used in medical statistics.
• EXAMPLE
Number of decayed teeth in 10 children
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 = 3 Median – 2 Mode
Mode

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
2. MEAN DEVIATION
3. STANDARD DEVIATION

13. • When the data is collected from a very large number of people and a
frequency distribution is made with narrow class intervals, the resulting
curve is smooth and symmetrical- NARROW CURVE.
• These limits on either side of measurement are called confidence limits .
Normal distribution/normal curve/
Gaussian distribution

14. STANDARD NORMAL DEVIATION
• There may be many normal curves but only one standard normal curve.
Characteristics
• Bell shaped
• Perfectly symmetrical
• Frequency increases from one side reaches its highest and decreases exactly
the way it had increased .
• Total area of the curve is one, its mean is zero and standard deviation is one.
• The highest point denotes mean, median and mode which coincide.

15. DISTRIBUTION CENTRAL TENDENCY
NORMAL/GAUSSIAN MEAN = MEDIAN = MODE
RIGHT/POSITIVE SKEWED MEAN > MEDIAN >MODE
LEFT/ NEGATIVE SKEWED MEAN < MEDIAN < MODE

16. Classification of tests of significance
The test which is done for testing the research hypothesis against the null hypothesis
For Qualitative data:-
1. Standard error of difference between 2 proportions (SEp1-p2)
2. Chi-square test or X2
For Quantitative data:-
1. Unpaired (student) ‘t’ test
2. Paired ‘t’ test
3. ANOVA
4. z test

17. • When different samples are drawn from the same population, the
estimates might differ - sampling variability.
• It deals with technique to know how far the difference between the
estimates of different samples is due to sampling variation.
a) Standard error of mean
b) Standard error of proportion
c) Standard error of difference between two means
d) Standard error of difference between two proportion.
Tests of significance

18. 1. Standard error of mean: Gives the standard deviation of
the means of several samples from the same population.
Example : Let us suppose, we obtained a random sample of 25
males, age 20-24 years whose mean temperature was 98.14
deg. F with a standard deviation of 0.6. What can we say of
the true mean of the universe from which the sample was
drawn?

19. Standard Error of Proportion
•Standard error of proportion may be defined as a unit that measures variation
which occurs by chance in the proportions of a character from sample to sample or
from sample to population or vice versa in a qualitative data.

20. Standard Error of Difference Between two Means
•The standard error of difference between the two means is 7 .5.
•The actual difference between the two means is (370 - 318) 52, which is more than twice the
standard error of difference between the two means, and therefore "significant".

21. Standard Error of Difference Between Proportions
•The standard error of difference is 6 whereas the observed difference (24.4 - 16.2) was 8.2.
• In other words the observed difference between the two groups is less than twice the S.E. of difference,
i.e., 2 x 6.
• There was no strong evidence of any difference between the efficacy of the two vaccines. Therefore, the
observed difference might be easily due to chance.

22. • Developed by Karl Pearson.
 Chi-square (x²) Test offers an alternate 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.
 Prerequisites for Chi square (X2) test to be applied:
– The sample must be a random sample
– None of the observed values must be zero.
– Adequate cell size
The CHI SQUARE TEST FOR QUALITATIVE DATA(X² TEST)

23. STEPS
 Test the null hypothesis .
 Then the x2 .
 Applying x2 test .
 Finding the degree of freedom (d.f)
 Finding probability .

24. Steps in Calculating (X2) value
1. Make a contingency table mentioning the frequencies in all cells.
2. Determine the expected value (E) in each cell.
3. Calculate the difference between observed and expected values in each cell (O-E).
4. Calculate X2 value for each cell
5. Sum up X2 value of each cell to get X2 value of the table.

25. Z-TEST
• Used to test the significance of difference in means for large samples.
• Criteria:
1. Sample must be randomly selected.
2. Data must be quantitative.
3. The variable is assumed to follow a normal distribution in the
population.
4. Samples should be larger than 30.

26. ‘t’ test
Very common test used in biomedical research.
Applied to test the significance of difference between two means.
It has the advantage that it can be used for small samples.
Types of ‘t’ tests
—Unpaired ‘t’ test
—Paired ‘t’ test.
• In case of small samples, t-test is applied instead of Z-test.
• It was designed by W.S.Gossett whose pen name was Student. Hence, this test is also called Student’s
t-test.

27. Criteria for applying t-test
1. Random samples
2. Quantitative data
3. Variable normally distributed
4. Sample size less than 30.

28. • This test is applied to unpaired data of independent observations
made on individuals of two different or separate groups or samples
drawn from two populations, to test if the difference between the two
means is real or it can be attributed to sampling variability .
• EXAMPLE: between means of the control and experimental
groups.
Unpaired t test
Where S is Standard error of difference between two means

29. • It is applied to paired data of dependent observation from one
sample only when each individual given a pair of observations.
• The individual gives a pair of observation i.e. observation
before and after taking a drug.
Paired t test

30. Analysis of Variance (ANOVA) Test
• Not confined to comparing two sample means, but more than two
samples drawn from corresponding normal populations.
• Eg. In experimental situations where several different treatments
(various therapeutic approaches to a specific problem or various
drug levels of a particular drug) are under comparison.
• It is the best way to test the equality of three or more means of
more than two groups.

31. • Requirements
– Data for each group are assumed to be independent and normally
distributed
– Sampling should be at random
• One way ANOVA
– Where only one factor will effect the result between 2 groups
• Two way ANOVA
– Where we have 2 factors that affect the result or outcome
• Multi way ANOVA
– Three or more factors affect the result or outcomes between groups .

32. CORRELATION AND REGRESSION
• Correlation: When dealing with measurement on 2 sets of variable
in a same person, one variable may be related to the other in same
way. (i.e change in one variable may result in change in the value
of other variable.)
• Correlation is the relationship between two sets of variable.
• Correlation coefficient is the magnitude or degree of relationship
between 2 variables. (varies from -1 to +1).

33. • Obtained by plotting scatter diagram (i.e one variable on x-axis and
other on y-axis).
• Perfect Positive Correlation
• In this, the two variables denoted by letter X and Y are directly
proportional and fully correlated with each other.
• The correlation coefficent (r) = + 1, i.e. both variables rise or fall in the
same proportion.
• Perfect Negative Correlation
• Values are inversely proportional to each other, i.e. when one rises, the
other falls in the same proportion,
i.e. the correlation coefficient (r) = –1.

34. TYPES OF CORRELATION

35. Regression
• Toknow in an individual case the value of one variable, knowing the value of
the other, we calculate what is known as the regression coefficient of one
measurement to the other.
• It is customary to denote the independent variate by x and the dependent
variate by y.
• The value of b is called the regression coefficient of y upon
x. Similarly, we can obtain the regression of x upon y.

36. 1. Categorical Vs Categorical
Unrelated Related
-Chi square test McNemar test
- Fishers Exact test
X=2 group, Y=2group X>2, Y>2 group
Unrelated
- Chi square test
- Fishers Exact test
X :Group variable
Y :Outcome variable

37. 2. Categorical Vs Quantitative
X=2 & Y: Normal
Unrelated Related
Student’s t test Paired ‘t’ test
X=2 group & Y: Non Normal
Unrelated Related
Wilcoxon ranksum Wilcoxon
signrank
X>2 group & Y: Non-Normal
X> 2group & Y: Normal
Unrelated Related
One way Repeated
ANOVA measures ANOVA
Unrelated Related
Kruskal Wallis Freidmans test
Parametric Non-Parametric

38. Conclusion
1.For generation of evidence , we do studies taking sample from population.
2.We apply different statistical tests on selected sample to detect whether there is
actual difference is there or not between new and old method.
3.Based on result of sample we apply findings of study on population for betterment.
4.So for drawing correct conclusion and extra polting findings of study on population
we must understand which statistical test to use on which type of data.

39. REFERENCES
• Essentials Of Preventive Community Dentistry –
Dr.Soben Peter. Third Edition
• Essentials Of Preventive Community Dentistry –
Dr.Soben Peter. Fourth Edition
• Mahajan's Methods in Biostatistics for Medical Students and
Research Workers. 8th edition.
• Parks textbook of preventive and social medicine. 18th edition.

40. Thank you