2. PRESENTATION OF DATA TEXT FORM TABULATION DRAWINGS

3. TABULAR PRESENTATION A table is a systematic arrangement of data into vertical columns and horizontal rows. The process of arranging data into rows and columns is called tabulation.

4. TABULATION Simple table Complex table –Principles Table should be numbered Each table has a Title---brief & self explanatory Headings of column & rows should be clear Data must be presented a/c to size, importance, chronologically, alphabetically or geographically. No too large table Foot note may be given.

5. STATISTICAL TABLE THE TITLE THE STUB THE BOX-HEAD THE BODY

6. SIMPLE TABLE Table 1 Population of Pakistan yearPopulation (millions) 190116.6 191119.4 192121.1 193123.6 194128.3

7. COMPOUND TABLE Table III Sex wise fatality rate of untreated patients AttributeMenWomenTotal Attacked403070 Deaths12820 %age died3026.728.6

8. COMPOUND TABLE Table II Colour choices of medical students of shirts SexWhiteBlueYellowGreenPinkTotal Male60125201075290 Female55450255130 Total115170203580420

9. Compound table Table II Colour choices of medical students about shirt SexWhiteBlueGreenPinkYellowTotal Boys1060554522192 Girls55452550130 Total65105805022322

10. TABLE I Population of Punjab & Baluchistan (thousands) census PunjabBaluchistan MaleFemaleTotalMaleFemaleTotal 19611364311938255816405211161 1971199421756637508127211332405

11. DATA Arrangement of data is based on Classification Purpose of table Alphabetically Geographically According to magnitude Historically Customary classes Progressive arrangement.

12. FREQUENCY DISTRIBUTION Is a tabular arrangement of data in which various items are arranged into classes and the no. of items falling in each class (class frequency) is stated. Grouped data Class limits Class interval

13. FREQUENCY DISTRIBUTION Data is split into groups-called--- class intervals No. of items (frequency) is written in adjacent column

14. FREQUENCY DISTRIBUTION TABLE TABLE II Age distribution of patients on Monday AgeNumber of patients 0-423 5-921 10-1443 15-1910 20-246

15. FREQUENCY DISTRIBUTION TABLE TABLE II Weight of medical students of SZMC Weight (Kg)Number of students 35-3942 40-4435 45-4983 50-5470 55-5936 60 and above28

16. DESCRITIVE STATISTICS Descriptive statistics comprises those methods concerned with collecting and describing a set of data so as to yield meaningful information.

17. STATISTICAL INFERENCE Statistical inference comprises those methods concerning with the analysis of a subset of data leading to predictions or inferences about the entire set of data.

18. ANALYSIS OF DATA When characteristic and frequency are both variable Calculations are: Averages Percentiles Standard deviation, Standard error Correlation and Regression coefficients.

19. NORMAL Normal is not the mean or a central value but the accepted range of variation on either side of mean or average. –Normal BP is not the mean but is a range between 100and 140 (mean 120 ± 20). Chances of even higher or lower are there.

20. MEASURE OF CENTRAL LOCATION / TENDENCY Any measure indicating the centre of a set of data or observations, arranged in an increasing or decreasing order of magnitude. A single value which represents all the values of the distribution in a definite way. Most commonly used measures of central location are –Mean –Median –Mode

21. MEASURE OF CENTRAL TENDENCY “AVERAGE” What is the average or central value? How are the values dispersed around this value? Degree of scatter? Is the distribution normal ( shape of distribution)

22. AVERAGE Average value of a characteristic is the one central value around which all other observations are dispersed. 50% of observations lie above and 50% of values lie below the central value. It helps Most of normal observations lie close to central value Few of the too large or too small values lie far away at ends To find which group is better off by comparing the average of one group with that of other.

23. MEAN Most commonly used average. It is the value obtained by dividing the sum of the values by their number i.e., summarizing up of all observations and dividing total by no. of observations

24. MEAN It implies arithmetic average or arithmetic mean which is obtained by summing up all the observations and dividing by the total number of observations.e.g. ESRs of 7 patients are 7,5,4,6,4,5,9 Mean =7+5+4+6+4+5+9 =40/7=5.71 7

25. MEDIAN When all observations are arranged in either ascending or descending order, the middle observation is called as median. i.e. mid value of series Median is better indicator of central value when one or more of the lowest or highest observations are wide apart or not so evenly distributed.

26. MEDIAN 83, 75, 81, 79, 71, 95, 75, 77, 84, 79, 75, 71, 73, 91, 93. 71, 71, 73, 75, 75, 75, 77, 79, 79, 81, 83, 84, 91, 93, 95. Median = 79

27. MODE Most frequently occurring value or observation in a series i.e. the most common or most fashionable value. 85, 75, 81, 79, 71, 95, 75, 77, 75, 90, 71, 75, 79, 95, 75, 77, 84, 75, 81, 75.

28. MODE Most frequently occurring observation in a series I.e. the most common or most fashionable value. 85, 75, 81, 79, 71, 95, 75, 77, 75, 90, 71, 75, 79, 95, 75, 77, 84, 75, 81, 75. Mode = 75.

29. NORMAL DISTRIBUTION Normal curve Smooth, Bell shaped, bilaterally symmetrical curve Total area is =1 Mean, Median and mode are equal. Standard deviation=1 Mean, median, mode coincide. Area between ¯X±1 SD=68.3% X±2SD=95.5% X±3SD=99.9%

30. NORMAL DISTRIBUTION

31. POSITIVELY SKEWED

32. NEGATIVELY SKEWED

33. Normal distribution

34. NORMAL DISTRIBUTION

35. POSITIVELY SKEWED

36. NEGATIVELY SKEWED

37. VARIABILITY Biological data are variable Two measurements in man are variable Cure rate are not equal but variable Height of students in same age group is not same but variable Height of students in one area is not same as compared to other place but variable Variability is essentially a normal character It is a biological phenomenon.

38. TYPES OF VARIABILITY Biological variability That occurs within certain accepted biological limits. It occurs by chance. –Individual variability –Periodical variability –Class, group or category variability –Sampling variability or sampling error

39. REAL VARIABILITY –When the difference between two readings or observations or values of classes or samples is more than the defined limits in the universe, it is said to be real variability. The cause is external factors. e.g. significant difference in cure rates may be due to a better drug but not due to a chance.

40. Experimental variability Errors or differences due to materials, methods, procedures employed in the study or defects in the techniques involved in the experiment. –Observer error –Instrumental error –Sampling error.

41. MEASURES OF VARIABILITY How individual observations are dispersed around the mean of a large series. Measures of variability of individual observations. –Range –Mean deviation –Standard deviation –Coefficient of variation Measures of variability of samples –Standard error of mean –Standard error of difference between two means –Standard error of proportion –Standard error of difference between two proportions –Standard error of correlation coefficient –Standard error of regression coefficient.

42. RANGE It is the difference between the highest and lowest values or figures in a given sample. Example: 83,75,81,79,71,90,75,95,77,94. Range =71 to 95.

43. RANGE Range defines the normal limits of a biological characteristic. It is the simplest measure of dispersion Usually employed as a measure of variability in medical practice It indicates the distance between the lowest and highest. It ignores all observations except two extreme values on which it is based. Normal range covers observations falling in 95% confidence limits.

44. MEAN DEVIATION It the average of the deviations from the arithmetic mean. M.D=∑ (X-¯X) n Example: 83,75,81,79,71,90,75,95,77,94.

45. MEAN DEVIATION D BPMeanDeviation from mean=X-X 83812 7581-6 81 0 7981-2 7181-10 958114 7581-6 7781-4 84813 90819 81056 M.D=5.6

46. STANDARD DEVIATION Most frequently used measure of deviation “Root – means—square--deviation”

47. SD 142.53162.5136 145816593 147.515167.542 1504517016 152.590172.56 1551551752 157.5194M=160 160 (M)195SD=5

48. SD

49. NORMAL DISTRIBUTION Range, mean±1SD=160±5=155 to 165cm –68.27% of the observations Range, mean±2SD=160±2x5=150 to 170cm –95.45% of the observations Range, mean±3SD=160±3x5=145 to 175cm –99.5% of the observations 3 observations +3 SD fall in 0.05% group.

50. RELATIVE VARIATE ( Z ) Deviation from the mean in a normal distribution or curve is called relative or standard normal deviate. It is measured in terms of SD & it tells us how much an observation is higher or smaller than mean in terms of SD. Z=observation-mean=X-X¯ SD SD

51. RANGE Easy to understand Easy to calculate Useful as a rough measure of variation Value may be greatly changed by an extreme value Highly unstable measure of variation.

52. MEAN DEVIATION Simple to understand and interpret. Affected by the value of every observation Less affected by absolute variation Not suited for any mathematical treatment.

53. SD Affected by value of every observation It avoids algebraic fallacy Less affected by fluctuations of sampling than other measures of dispersion Has a definite mathematical meaning Has a great practical utility in sampling and statistical inferences.

54. QUESTION Average weight of baby at birth is 3.05Kg with SD of 0.39Kg. In a normal distribution a) wt. of 4 Kg as abnormal? b)wt. of 2.5 Kg as normal?

55. Percentage Is the number of units with a certain characteristic divided by total no. of units multiplied by 100.

56. Proportion It is a numerical expression that compares one part of the study unit to the whole.

57. RATIO It is a numerical expression, which indicates the relationship in quantity, amount or size between two or more parts.

58. SAMPLING Not possible to include each & every member Not possible to examine all people of country To test efficacy of drug to all patients Cooking of rice Costly collection & Time consuming Blood test

59. POPULATION Population Sample Parameter: a value calculated from a population –Mean (μ) –Standard Deviation(σ) Sample –Mean (X) –Standard deviation ( s)

60. SAMPLING Sample is a part of population Estimation of population parameters To test the hypothesis about the population from which the sample was drawn. Inferences are applied to the whole population but generalization are valid if sample size is sufficiently large & must be representative of the population-unbiased.

61. SAMPLING Sampling units are break down of population into smaller parts which are distinct and non overlapping so that each member / element of the population belongs to one and only one sampling unit. When a list of all individuals, households, schools and industries are drawn, it is called sampling frame.

62. Sample A representative sample is the one with which we can draw valid inference regarding the population parameters. It is representative of the population under study Is large enough but not too large The selected elements must be properly approached, included and interviewed.

63. CONFIDENCE INTERVAL It is the interval or range of values which most likely encompasses the true population value. It is the extent that a particular sample value deviates from the population A range or an interval around the sample value Range or interval is called confidence interval. Upper & lower limits are called confidence limits.

64. C.I Random sample of 11 three years children were taken, sample mean was 16 Kg and standard deviation is 2 Kg. standard error is 0.6 Kg. find C.I.

65. STANDARD ERROR Standard error is the standard deviation of the means of different samples of population. Standard error of the mean S.E. is a measure which enables to judge whether a mean of a given sample is within the set of confidence limits or not, in a population. S.E= SD/√n

66. SAMPLING TECHNIQUES SIMPLE RANDOM SAMPLING SYSTEMATIC SAMPLING STRATIFIED SAMPLING MULTISTAGE SAMPLING CLUSTER SAMPLING MULTIPHASE SAMPLING CONVENIENT SAMPLING QUOTA SAMPLING SNOW BALL SAMPLIG

67. Sample size L= 2 σ √n √n= 2 σ L n= 4 σ² L² Example: 1.mean pulse rate=70 Pop. Standard deviation(σ)=8 beats Calculate sample size? 2. Mean SBP=120,SD=10, calculate n?

68. Sample size Qualitative data N=4pq L² e.g.