biostatistics
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BIOSTATISTICS
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- 1. BIOSTATISTICS
- 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