Research methodology and iostatistics ppt
- 1. Welcome Good morning to all
- 2. Biostatistics By, Dr Nithin N Bhaskar, Department of Community Dentistry.
- 3. “The most successful man is the man with the best information ”
- 4. Definition Biostatistics is that branch of statistics that deals with the mathematical facts and data related to biological events.
- 5. Elementary statistical methods Data: It consists of discrete observations of attributes or events. Information: The data collected is transformed into information by reducing them, summarizing them and adjusting them for variations.
- 6. Types of data: o Primary data : obtained directly from an individual Eg) Census 1991 o Secondary Data: Obtained from an outside source Eg) using census data for hospital records
- 7. Data o Raw Data o Discrete frequency data o Continuous frequency data
- 8. Uses of biostatistics o To measure the health status of the people, to quantify their health problems and treatment needs o For making comparisons- local, national, international o For planning health services o To assess the effectiveness of the health services o Help in research into particular problems
- 9. Scales of measurement o Nominal scale Characterized by named categories having no particular order Eg) Male /female or yes or no etc o Ordinal scale The data which possess a meaningful order Eg) The degree of malnutrition- mild, moderate, & severe, etc
- 10. o Interval scale Number between characters Eg) Heart rate per minute o Ratio scale Measurement of height / weight
- 11. Presentation of statistical data Methods o Tables o Charts o Diagrams o Graphs o Frequency polygon o Pictures o special curves
- 12. Tabulation o Tables are the devices for presenting data o It is the first step before data is used for interpretation 2 types of tables o Simple o Complex
- 13. Simple tables City Population 1981 Greater Bombay Calcutta Delhi Madras 8,227,332 9,165,654 5,713,581 4,276,635 Table 1 Population of some cities in India
- 14. Frequency distribution table o The data is split into convenient groups & then tabulated Age No of patients 0- 4 5- 9 10- 14 15- 19 20- 24 35 18 11 08 06 Age distribution of polio patients
- 15. Charts & diagrams Bar charts o Presenting a set of numbers by the length of the bar o Length of the bar is the magnitude to be presented
- 16. Types of bar charts o Simple o Multiple o component
- 17. 0 20 40 60 80 100 jan feb mar apr Simple bar graph Graph showing no of OP seen in community department in the foll months
- 18. Multiple type bar graph 0 10 20 30 40 50 60 70 Europe Africa USSR Asia Population Land
- 19. Component bar chart 0% 20% 40% 60% 80% 100% 2003 2005 growth population
- 20. Histogram It is a pictorial diagram of frequency distribution The area of each block or rectangle is proportional to the frequency
- 21. Frequency polygon It is obtained by joining the mid points of the histogram blocks
- 22. Line diagram These are used to show the trend of events with passage of time 0 1 2 3 4 5 6 7 1972 1973 1974 1975 World South East Asia Other regions A line diagram showing the trend of Malaria cases reported in the World
- 23. Pie charts o Instead of comparing the length of the bar, areas of segments of a circle are compared o The area of each segment depends upon the angle World 1972 16% 1973 21% 1974 29% 1975 34% Pie chart showing malaria trends in the world
- 24. Pictogram Small pictures or symbols are added to present the data
- 25. Measures of central tendency Definition: It is the measure of closeness of values to the central value o Mean o Median o Mode
- 26. Mean • It is defined as the sum of values divided by the number of values • Denoted as X bar Advantage o Easy to calculate & understand Disadvantage o Unduly influenced by abnormal values in the distribution
- 27. Median Definition: It is defined as the middle most number in the array of observations.
- 28. Mode Definition: It is the most commonly occurring value in a series of observations.
- 29. Measures of Dispersion Definition: Dispersion is the measure of scattered ness of values away from the central value o Range o Mean deviation o Standard deviation
- 30. Range Definition: It is defined as the difference between the highest & lowest figures in a given sample. Eg) 83, 75, 81,79, 90, 71, 95, 77, 94 Here range is 71 to 95
- 31. Mean deviation It is the average of the deviations from the arithmetic mean. It is given by the formula M. D= ∑(x- x) n
- 32. Standard Deviation Definition: It is defined as the root means square deviation. It is denoted as sigma or S.D
- 33. Steps • X = ∑ X/n -calculate the mean of the group • (X-X ) -subtract the mean from each value • (X-X )2 -square each deviation from the mean • ∑ (X-X)2-add the squared deviation from the mean • ∑ (X-X)2 /(n-1) - divide the sums of the square (n-1) • √ ∑ (X-X)2 /(n-1) -Find the square root of variance
- 34. 68.3% 95.4% 99.7% -3 -2 -1 1 2 3 Normal distribution curve
- 35. Characteristics of a normal curve • It is bell shaped • It is symmetrical • Mean median and mode coincide
- 36. • In a normal curve the area b/w one SD on either side of the mean (x +1) will include approximately 68.3%of the values of distribution • The area b/w 2 standard deviation on either side of the mean (x +2) will cover most of the values i.e. 95.4%of 2 values
- 37. • The area b/w (x +3) will include 99.7% of the values. • These limits on either side of the mean is called “confidence limits”. • The total area of the curve is 1, its mean is zero and its SD is 1
- 38. Sampling DEFINITION • Sampling can be defined as the investigation of part of a population, in order to provide information, which can then be generalized to cover the whole population.
- 39. Sampling Methods Simple random sampling Systemic random sampling Stratified random sampling
- 40. Sampling errors • If we take repeated samples from the same population, the results will differ this is called sampling error • This is because data is gathered from the sample and not the entire population
- 41. Non sampling errors These include errors that occur due to improper calibration of instruments, observer variation and incomplete coverage of examining of subjects
- 42. Standard error of mean It is given by the formula S.E. x= SD/ √n where S.E. x= Std error of mean S.D = Std Deviation n = No of values
- 43. Standard error of proportion Used when means are not given but proportions are given Given by the formula S.E (proportion)= √pq n p & q = proportions n = size of the sample
- 44. Standard error of difference between two means Used when comparing the results b/w 2 groups Its given by the formula S.E (d) = √ SD1 2 + SD2 2 b/w means n1 n2
- 45. Standard error of difference between two proportions It is given by the formula SE (d) = √ p1q1 + p2q2 B/w proportions n1 n2
- 47. Chi square test A method used to test the significance of difference between two proportions Used when more than 2 groups are compared Given by the formula x2= ∑(O- E)2 E
- 48. • Test null hypothesis • Apply the chi square test • Finding degree of freedom d.f = (c- 1)(r- 1) where c= no of columns r= no of rows • Probability tables Procedure
- 49. Interpretation of the results • After the chi square value is found it is compared with the standard table of chi square value to determine the ‘p’ value. The ’p’ value indicates the probability that a chi square value that large would have resulted from chance alone
- 50. Uses of chi square test • It is used to find the significance of difference of 2 or more than 2 proportions • It is used to test association b/w 2 events in binomial or multinomial samples.
- 51. Correlation and regression Correlation is the linear relation between two variables Co- efficient of correlation: Used to find out if there is a significant association or not between two variables r= ∑(x- x) (y- y) x & y are variables √ ∑(x- x)2 ∑ (y- y )2
- 52. • If the chi square value is too small the fit is good and null hypothesis is not rejected. • If chi square value is large the data do not fit the hypothesis well.
- 53. Co- efficient of regression: It is used to find out the value of one variable using the values of another variable b= ∑(x- x) (y- y) ∑(x- x)2 b is called the regression co- efficient of y upon x Similarly b= ∑(x- x) (y- y) ∑(y- y )2 b is called the regression co- efficient of x upon y
- 54. T test A method used to test the significance of difference between two means.