2. Contents Introduction Terminologies Sources &
Presentation of Data Measures of Central Tendency Measures of
Dispersion Normal curve Sampling Tests of significance Correlation
& regression Conclusion
3. Introduction Statistics Statista (Italian) Statistik
(German) John Graunt (1620-1674)
4. Introduction Why Statistics?
5. Epidemiology and Statistics Introduction
6. Variable X Constant , mean, standard deviation etc
Observation event +measurement Sample Parameter Summary value Mean
height, birth rate Statistic Terminologies
7. Terminologies Parametric test population constants are
described (mean, variances) Non parametric test- no population
constants - data do not follow specific distribution
8. Sources and presentation of data Collective recording of
observations either numerical or otherwise.
9. Sources and presentation of data By the investigator himself
Interviews, questionnare, oral health examination Primary Data
already present Records of OPD Secondar y Classification of
Data
10. Sources and presentation of data Nominal Qualitative data
Male / Female White / Black Socio- economic status Ordinal Arranged
in rank / order Ramu is taller than Ravi and Ravi is taller than
Ajay
11. Interval Placed in intervals or order - Uses a scale graded
in equal increments - Height, weight, blood pressure Ratio Interval
scale data is placed with meaningful ratio - Biomedically most
significant - Presented in frequency distribution
12. Qualitative Quantitative
13. Sources and presentation of data Methods of presentation
Tabulation Diagrams
14. Tabulation Most common way frequency distribution table
Important step in statistical analysis Presents a large amount of
data concisely Quantitative and qualitative data Sources and
presentation of data
15. Diagrams Through graphs Histogram, frequency polygon,
frequency curve, line graph, scatter or dot diagram Quantitative
Through diagrams Bar diagrams, pie diagram, picture diagram, map
diagram Qualitative Sources and presentation of data
16. Histogram Teeth Pocket depth Pocket depth in five teeth
Sources and presentation of data 2 4 6
17. Frequency polygon 0 1 2 3 4 5 6 7 8 1 2 3 4 5 6 Pocket
depth Number of teeth 0 1 2 3 4 5 6 7 8 1 2 3 4 5 6 Sources and
presentation of data
18. 0 2000 4000 6000 8000 10000 12000 14000 1999 2003 2007 2011
Numberofpeople Prevalence of periodontitis in Belgaum Sources and
presentation of data Line graph
19. Pie Chart Post graduate students Orthodontics Periodontics
Community dentistry Prosthodontic Sources and presentation of data
32% 32 % 23 %13 %
20. Bar diagram Teeth Pocket depth Pocket depth in five teeth
Sources and presentation of data 2 4 6
21. Measures of Central Tendency The single estimate of a
series of data that summarizes the data is known as parameter.
Objective : Condense the entire mass of data Facilitate comparison
3 types: Mean Median Mode
22. Measures of Central Tendency Mean Simplest Sum of all
observation s/number of observation s Median Middle value in a
distribution Mode Value of greatest frequency Number of flap
surgeries done by five doctors in a week are 7,5,4,9,5 Calculation
of Mean = (7+5+4+9+5)/5 Mean = 6 Number of flap surgeries done by
five doctors in a week are 7,5,4,9,5 Calculation of Median
4,5,5,7,9 Median = 5 Number of flap surgeries done by five doctors
in a week are 7,5,4,9,5 Calculation of Mode 4,5,5,7,9 Mode = 5
23. Measures of Dispersion Measures of central tendency single
value to represent data Dispersion - degree of spread or variation
of the variable about the central value. 3 types Range Standard
deviation Coefficien t of variation
24. Measures of Dispersion Range Simplest method Difference
between the value of the smallest item to the value of the largest
item
25. Standard deviation Most important and widely used Root mean
square deviation Summary measure of the differences of each
observation from mean of all observations Greater the deviation
greater the dispersion Lesser the deviation greater uniformity
Measures of Dispersion
26. Coefficient of variation Standard deviation deviation
within a series. Compare two or more series, with different units
of measurement Coefficient of variation = Standard deviation Mean
100 Measures of Dispersion
27. Normal curve Properties Bell shaped Symmetrical Height is
maximum at mean , Mean=Median=Mode Maximum number of observation at
mean and it decreases on either side Relation between mean and
standard deviation Forms basis of tests of significance Normal
distribution or Gaussian curve
28. Sampling Need for sampling ?? Two types of sample selection
Purposive Random
29. Sampling techniques Simple Random Systematic Random
Stratified Random Cluster sampling Multiphase sampling Pathfinder
survey Sampling
30. Sampling 1. Simple random sampling 2. Systematic random
sampling One unit is selected at random and all other at evenly
spaced intervals No periodicity of occurrence Lottery Table of
Random numbers
31. 3. Stratified Random sampling When the population is not
homogenous. Population is divided in homogenous groups, followed by
simple random selection Merits : Representative sample from each
strata is secured. Gives great accuracy Sampling
32. Disadvantage: Utmost care has to be taken while dividing
the population into strata (regarding homogeneity of the strata)
Sampling
33. Cluster sampling Natural clusters school, village etc. From
these clusters- the entire population is surveyed Advantages:
Simple Involves less time and cost Disadvantage : Higher standard
error Sampling
34. Multiphase sampling Part of information is collected from
whole sample and a part from sub-sample. Advantages : less
expensive less laborious more purposeful Sampling
35. All patients on OPD examined (first phase) Only those
suffering chronic periodontitis selected (second phase) Only those
within the age group of 35-45 years selected (third phase) Sample
size keeps on becoming smaller Sampling
36. Pathfinder survey A specified proportion of the population
Stratified cluster sampling Subjects in specific index age groups
are selected. Helps to assess 1. The variations in severity of
disease in different subgroups 2. Picture of age profiles of
various oral diseases. Sampling
37. Sample size Optimum size of sample based on following: 1.
Approximate idea of estimate of characteristics- Obtained from
previous studies or pilot studies prior to starting study. 2.
Knowledge about the estimate of precision probability level for
precision. Sampling precision= n / s (s=SD)
38. Sample size n = Sample size, p = Approx prevalence rate, L
= Permissible error in p estimation, Z = Normal value for
probability level. Sampling Z 2 * p * (1-p) L2 n =
39. If p = 10% , investigator allows an error of prevalence
rate of 20%, n =900 Sampling 4* 0.1*(0.9) (0.01)2 n =
40. Tests of significance Sampling variability Tests of
hypothesis
41. Tests of significance Null Hypothesis and Alternative
Hypothesis Null hypothesis No real difference Difference found -
accidental Alternative hypothesis Real difference present
42. Level of significance Probability level P Small P value
Tests of significance Null Hypothesis rejected P-value 0.05-0.01
Statistically significant < 0.01 Highly statistically
significant < 0.001 or 0.005 Very highly statistically
significant
43. Degree of freedom Number of independent members in a sample
Degree of freedom = (n 1)
44. Tests of significance Standard error Standard error of mean
Gives the standard deviation of means of various samples from the
same population Measure of chance variation Mean error or mistake
Standard error of mean = Standard deviation n
45. Types of error Hypothesis Accept Reject True Right Type I
error False Type II error Right Decision Tests of significance
46. Steps involved in testing of hypothesis 1. State Null and
Alternative hypothesis 2. Calculate t, F, 2 3. Determine degree of
freedom 4. Find probability P using appropriate data 5. Null
hypothesis rejected p < 0.05 Null hypothesis accepted p >
0.05 Tests of significance
47. t-test- paired/unpaired ANOVA Test of significance b/w
means Pearsons Correlation Coefficient Mann Whitney Wilcoxons
signed rank test Mc nemars Kruskal Wallis Freidman Kendalls S
Chi-Square Fischers exact Spearmans Rank Correlation Parametric
tests Non-parametric tests Tests of significance Classification of
tests
48. These are mathematical tests They assess the probability of
an observed difference, occurring by chance Most commonly used
tests are - Z test, t test, 2 test Tests of significance
49. Students t test Designed by W.S. Gossett Applied to find
the difference between two means Criteria for applying t test 1.
Random samples 2. Quantitative data 3. Sample size < 30 4.
Variable normally distributed Tests of significance
50. Unpaired t test Data of independent observations made on
individuals of two different groups or samples Checks sampling
variability between experimental and control groups e.g. checking
sampling variability between SRP+ subgingival irrigation
(experimental group) and SRP alone (control group) Tests of
significance
51. Paired t test Paired data of independent observations from
one sample only who gives a pair of observations. E.g. sampling
variability in the decrease in the microbial load before and after
administration of antimicrobial therapy. Tests of significance
52. Wilcoxons signed rank test Developed by Frank Wilcoxon
Alternative to the Students paired t test Tests of
significance
53. Analysis of Variance (ANOVA) test Compares more than two
samples drawn from corresponding normal population E.g : to check
if different agents used for subgingival irrigation have an effect
on the decrease in microbial load. Use 3 groups (chlorhexidine ,
saline, povidone iodine) Tests of significance
54. If the difference between their means is significant -
different agents used do have different effect on the decrease in
microbial load. To assess this difference in means- ANOVA test is
important Tests of significance
55. Chi square test Developed by Karl Pearson Data measured -
terms of attributes/qualities- intended to test if difference is
due to sampling variation Involves calculation of a quantity 3
important applications: 1. Proportion 2. Association 3. Goodness of
fit Tests of significance
56. E.g. : Two groups are present Oral hygiene Oral hygiene
instructions given instructions not given To assess if there is an
association between gingivitis and oral hygiene instructions. Tests
of significance
57. Correlation and Regression Correlation The relationship
between two quantitatively measured variables Change in the value
of one variable, results in a change in the other Magnitude or
degree of relationship between two variables is called correlation
coefficient (r)
58. Correlation and Regression Pearsons correlation coefficient
Pearsons correlation coefficient Variables are normally distributed
(height and weight) Variables are not normally distributed (IQ,
income) Pearsons correlation coefficient
59. Correlation and Regression Types of correlation 1. r = +1
2. r = - 1 0 < r < 1 4. -1 < r < 0 5. r = 0 1 65 43
2
60. Regression Regression coefficient measure of change in one
character (dependent variable - Y) , with one unit change in the
independent character (X) Denoted by b Regression line Correlation
and Regression
61. Change of dependent variable in linear way Y = a+bX Y =
dependent variable a = Y value b = regression coefficient X =
independent variable Correlation and Regression
62. Conclusion Clinician Facts Figures Statistics
63. References B K Mahajan ; Methods in Biostatistics, 6th
edition Soben Peter ; Essentials of Preventive and Community
dentistry , 2nd edition K. Park ; Parks Textbook of Preventive And
Social medicine , 19th edition
