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- 1. K i n g s u k S a r k a r , M D A s s t . P r o f . D e p t . o f C o m m u n i t y M e d i c i n e , D S M C H FUNDAMENTALS OF BIOSTATISTICS
- 2. statistics: - It refers to the subject of scientific activity dealing with the theories and methods of collection, compilation, analysis and interpretation of data. Bio-statistics: - An art & science of collection, compilation, analysis and interpretation of data. Data(sing. Datum): - A set of observations, usually obtained by
- 3. Classification of data- Qualitative/Attribute Quantitative/Variable: Continuous & Discreet Qualitative Data: - Can not be expressed in number - Not measurable - Can only be categorized under different categories & frequencies - E.g., Religion is an attribute; can be categorized into Hindu, Muslim, Christian - Human Blood Group: A,B,AB or O - Sex: M/F
- 4. Quantitative Data/variable: - In statistical language, any character, characteristic or quality that varies is called variable - It has got magnitude Continuous variable: - It is expressed in numbers & can be measured - Can take up infinite no. of values in a certain range - E.g., weight, height, blood sugar
- 5. Discreet variable: - Countable only - Takes only some isolated values - E.g., numbers of a family members, no. of workers in a factory, no. of persons suffering from a particular disease According to source- Primary Data Secondary Data
- 6. Primary Data: - Collected directly from the field of enquiry - original in nature - E.g., measurement of BP, weight, height, blood sugar Secondary Data: - Collected previously by some other agency/organization - Used afterwards by another - E.g., hospital records, census data
- 7. Nominal scales Ordinal Scales Interval Scales Ratio Nominal Scales: - Used when data are classified by major categories or subgroups of population - Religion can be assigned to following categories- Muslim, Hindu, Christian - Outcome of treatment: cured or not cured; died or survived
- 8. Ordinal Scales: - Assign rank order to categories placed in an order - E.g., students rank in a class; Grades A,B,C,D; - Literacy status: illiterate, just literate, primary, secondary, higher secondary, graduate, post graduate - Disease condition: mild, moderate, severe Interval Scale: - Distance between two measurement is defined, not their ratio - E.g., intelligence score in IQ tests, temperature in Centigrade
- 9. Ratio Scale: - Both the distance & ratio between two measurements are defined - E.g., length, weight, incidence of disease, no. of children in a family Dichotomy/ Binary Scale: - A scale with only two categories - E.g., disease→ present/absent; sex→male /female Population: - An aggregate of objects, animate or inanimate, under study - A group of units defined according to aims & objective of the study Sample: - a finite subset of or part of population - Every member of population should have equal chance to be included in sample
- 10. Parameter: - constant, describes the characteristics of population Statistic: - Function of observation, which describes a sample Statistic Parameter Mean x (x bar) µ(Mu) Standard Deviation s s (sigma) No. of Subject n N Proportion P P
- 11. • Main sources for collection of medical statistics are: 1. Experiments: - Performed in the laboratories of physiology, biochemistry, pharmacology,, clinical pathology - Hospital words→ for investigations & fundamental research - Used in preparation of thesis/dissertation, scientific paper for publication in scientific journals & books 2. Surveys: - Carried out for epidemiological studies in the field by trained teams to find out incidence or prevalence of health or disease situations in a community - Used in OR→ assessment of existing condition, how to follow a program, to study merits of different methods adopted to control of a disease - Provide trends in health status, morbidity, mortality, nutritional status, health practices, environmental hazards - Provide feedback needed to modify policy - Provide timely earning of public health hazards
- 12. 3. Records: - Maintained as a routine in registers or books over a long period of time - Used for keeping vital statistics: births, deaths, marriage, hospitalization following illness, - Used in demography & public health practices - Collected data are qualitative
- 13. DATA INFORMATION Statistical data is presented usually in tabular forms through different types of tables and in pictorial forms; diagrams, charts Method of presentation: A. Tabulation B. Drawing
- 14. Tabular presentation: - A form of presenting data from a mass of statistical data - at first frequency distribution table is prepared - Table can be simple or complex • Frequency distribution table or frequency table: - All frequencies considered together form “frequency distribution” - No of person in each group is called the frequency of that group - Frequency distribution table of most biological variables develop normal, binomial or Poisson distribution.
- 15. • Presentation of quantitative data is more cumbersome as - Characteristic has a measured magnitude as well as frequency - Table x: presentation of quantitative data of height in markingsHeight of groups in Cm Markings Frequency of each group 160-162 //// //// 10 162-164 //// //// //// 15 164-166 //// //// //// // 17 166-168 //// //// //// //// 19 168-170 //// //// //// //// 20 170-172 //// //// //// //// //// / 26 172-174 //// //// //// //// //// //// 29 174-176 //// //// //// //// //// //// 30 176-178 //// //// //// //// // 22 178-180 //// //// // 12 Total 200
- 16. - Data needs consolidation by way of tabulation to express some meaning - Tabulation → a process of summarizing raw data & displaying it in a compact form for further analysis - Orderly management of data in columns & rows
- 17. •General Principle in designing Table: - Table should be numbered - Brief & self-explanatory title should be there mentioning time, place, person - Headings of columns & rows should be clear & concise - Data to be presented according to size of importance chronologically, alphabetically, geographically - Data must be presented meaningfully - Table should not be too large - Foot notes given, if necessary - Total no of observations ; the denominator should be written - Information obtained should be summarized in the table
- 18. • Frequency distribution drawings: - After classwise or groupwise tabulation, the frequencies of a charecteristics can be presented by two kinds of drawings - Graphs & Diagrams - May be shown by either lines, dots, figures o Presentation of quantitative data is through graphs o Presentation of qualitative, discreet, counted data is through diagrams
- 19. 1. Histogram - Graphical presentation of frequency distribution - Variable characters of different groups are indicated in the horizontal line (x-axis) is called abscissa - No. of observations marked on the vertical line (y-axis) is called ordinate - Frequency of each group forms a triangle
- 20. 2. Frequency Polygon: - An area diagram of frequency distribution developed over a histogram - Mid points of the class intervals at the height of frequency are joined by straight lines - It gives a polygon, figure with many angles
- 21. 3. Frequency Curve: - If no. of observation are very large & group interval reduced - Frequency polygon tends to loose its angulation - Gives rise to a smooth curve → frequency curve
- 22. 4. Line Chart or Graph: - A frequency polygon presenting variation by lin - Shows trend of event occurring over a period of time - Shows rise, fall or periodic fluctuations vertical axis may not start from zero, but some point above frequency
- 23. 5. Cumulative Frequency Diagram or “Ogive” - Graph of the cumulative frequency distribution - An ordinary frequency distribution table→ relative frequency table - Cumulative frequency: total no. of persons in each particular range from lowest value of the characteristic up to & including any higher group value
- 24. 6. Scatter or Dot Diagram: - Prepared after tabulation in which frequencies of at least two variables have been cross classified - Shows nature of correlation between two variable character in same person(s)( e.g., height & weight) - Also called correlation diagram
- 25. 1. Bar Diagram: - Graphically present frequencies of different categories of qualitative data - Vertical/ horizontal - May be descending/ascending order - Widths should be equal - Spacing between bars should also be equal i. Simple Bar Diagram: - Each bar represents frequency of a single category with a distinct gap from one another
- 26. ii. Multiple bar diagram:- - Used to show comparison of two or more sets of related statistical data iii. Component/ proportional bar diagram: - Used to compare sizes of different component parts among themselves - Also shows relation between each part & the whole
- 27. 2. Pie/ sector Diagram: - A circle whose area is divided into different segments by different straight lines from cenre to circumference - Each segment express proportional components of the attributes - Angle ( ) of a sector is calculated by Class frequency X 3.6 or (Class frequency/total frequency)X 360
- 28. 3. Pictogram/ Picture Diagram: - A popular method to denote the frequency of the occurrence of events to common man such as attacks, deaths, number operated, admitted, discharged, accidents, etc. in a population.
- 29. • 4. Map diagram/ spot Map: - These diagrams are prepared to visualize the geographic distribution of frequency of characteristics - One point denotes occurrence of one more events
- 30. • When a series of observations have been tabulated in the form of frequency distribution →→it is felt necessary to convert a series of observation in a single value, that describes the characteristics of that distribution,→ called Measure Of Central Tendency • All data or values are clustered round it • These values enable comparisons to be made between one series of observations and another • Individual values may overlap, two distributions have different central tendency • E.g., average incubation period of measles is 10 days and that of chicken pox is 15 days.
- 31. Measures of Central tendency Mean Mode Median Arithmetic Geometric Harmonic Mean(AM) Mean(GM) Mean(HM)
- 32. • Arithmetic mean: - Sum of all observations divided by number of observations - Mean(x)=Sx/n; x is a variable taking different observational values & n= no. of observations - Exmp. • ESR of 7 subjects are 8,7,9,10,7,7, & 6 mm for 1st hr. Calculate mean ESR. - Mean(x)= (8+7+9+10+7+7+6)/7=54/7=7.7 mm
- 33. • Median : when observations are arranged in ascending or descending order of magnitude, the middle most value is known as Median. • Problem: - From same example of ESR, observations are arranged first in ascending order: 6,7,7,7,8,9,10. - Median= {7+1}/2=8/2=4th observation I,e., 7 - When n is Odd no., Median={n+1}2 th observation - When n is Even no., Median={n/2th + (n/2+1)th}/2 th observation • Problem: suppose, there are 8 observations of ESR like 5,6,7,7,7,8,9,10 • Median={8/2th +(8/2+1)th}/2={4th+5th obs}/2=(7+7)/2=7
- 34. • Mode: - The observation, which occurs most frquently in series • Problem: ESR of 7 subjects are 8,7,9,10,7,7, & 6 mm for 1st hr. Calculate the Mode. - Mode is 7.
- 35. •
- 36. •
- 37. • Geometric mean: - Used when data contain a few extremely large or small values - It’s the nth root product of n observastions • GM=ⁿ√(x₁.x₂.x₃….xn) • Harmonic Mean: - Reciprocal of the arithmetic mean of reciprocals of observations arithmetic mean of reciprocals of observations=S(⅟x) - HM=n/S⅟x - got limited use - A.M>GM>HM
- 38. • Measures of central tendency do not provide information about spread or scatter values around them • Measures of dispersion helps us to find how individual observations are dispersed or scattered around the mean of a large series of data • Different measures of Dispersion are: i. Range ii. Mean deviation iii. Standard deviation iv. Variance v. Coefficient of variation
- 39. • Range: - Difference between highest & lowest value - Defines normal value of a biological characteristic • Problem: Systolic blood pressure (mm of Hg) of 10 medical students as follows: 140/70, 120/88, 160/90, 140/80, 110/70, 90/60, 124/64, 100/62, 110/70 & 154/90 • Range of Systolic BP of medical students = highest value- lowest value=160-90=70mm of Hg • Range of Diastolic BP= 90-60=30 mm of Hg
- 40. • Mean deviation: - Average deviations of observations from mean value - Mean Deviation(S) =(x-x)/n, where x=observation, x=Mean
- 41. •
- 42. • To estimate variability in population from values of a sample, degree of freedom is used in placed of no. of observations • Standard deviation is calculated by following stages: - Calculate the mean - Calculate the difference between each observation & mean - Square the difference - Sum the squared values - Divide the sum of squares by the no. of observations(n) to get mean square deviation or variances(s) - Find the square root of variance to get “Root-Mean- Square-Deviation” • Use: sample size calculation of any study - Summarizes deviation of a large series of observation around mean in a single value
- 43. • Coefficient of Variation: - Used to denote the comparability of variances of two or more different sets of observations - Coefficient of Variation=(Sd/Mean)X100 - Coefficient of Variation indicates relative variability
- 44. NORMAL DISTRIBUTION • Most important useful distribution in theoretical statistics • Quantitative data can be represented by a histogram & by joining midpoints of each rectangle in the histogram we can get a frequency polygon • when no. of observations become very large & class intervals get very much reduced→ frequency polygon loses its angulation →gives rise to a smooth curve known as frequency curve, • Most biological variables , e.g., height, weight, blood cholesterol etc, follows normal distribution can be graphically represented by “normal curve”
- 45. • If a large no. of observations of any variables such as height, weight, blood pressure, pulse rate etc. are taken at random to make a representative sample of the world and if a frequency distribution table is made, it will show following characteristics: - Exactly half the observations will lie above & half below the mean and all observations are symmetrically distributed on either side of mean - Maximum no. of frequencies will be seen in the middle around the mean and fewer at extremities, decreasing smoothly on both sides
- 46. •
- 47. • Normal Curve: - Observations of a variable, which are normally distributed in a population, when plotted as a frequency curve will give rise to Normal Curve • Characteristics of a Normal Curve: - Smooth - Bell shaped - Bilaterally symmetrical - Mean, Median, Mode coincide - Distribution of observation under normal curve follows the same pattern of normal distribution as already mentioned
- 48. •
- 49. •
- 50. SAMPLING TECHNIQUE Universe/population: - Aggregate of units of observation about which certain information is required - Population is a set of persons (or objects) having a common observable characteristics - E.g., while recording pulse rate of boys in a school, all boys in the school constitute the population/universe Sample: - A portion or part of total population selected in some manner Sapling Frame: - A complete, non-overlapping list of all the sampling units (persons or objects) of the population from which the sample is to be drawn - E.g., telephone directory acts as a frame for conducting opinion
- 51. • Statistic: - A characteristic of a sample, whereas a • parameter - a character of a population Types of sampling: non-probability & probability/random sampling • Non-probability sampling: - Easier, less expensive o perform - Sampling is done by choice & not by chance - Information collected cannot be presumed to be representative of the whole universe - E.g, Quota Sampling, convenience sampling, Purposive sampling, Snowball Sampling, Case Study
- 52. • Probability/Random Sampling: - Sample are selected from universe by proper sampling technique - Each member of the universe has equal opportunity to get selected - Composition of sample from universe occurs only by chance Types: oSimple Random Sampling:
- 53. oStratified Random Sampling: oSystemic Random Sampling: oCluster Sampling: oMultistage sampling: oMultiphase Sampling:
- 54. • Exercise no. 1 Following are the diastolic blood pressure values (in mmHg) of 10 male adults. 80, 60, 70, 80,65, 74, 66, 80, 70, 55 Solution: Mode= 80 Arranging in ascending order: 55,60,65,66,70,70,74,80,80,80 Median={10/2th+(10/2+1)th}/2={5th + 6th}/2={70+70}/2=70 Mean=700/10=70
- 55. Exercise No. 5. The following table shows the number of children per family in a village Calculate the measure of central tendency: No of children per family No of families 0 30 1 40 2 70 3 30 4 20 5 10
- 56. Solution: Table 1.1 showing number of children in families • Average (x)no. of children=400/200=2 No. of children in a family(x) No. of families(f) Total no. of children(fx) 0 30 0x30=0 1 40 1x40=40 2 70 2x70=140 3 30 3x30=90 4 20 4x20=80 5 10 5x10=50 Total 200 400
- 57. Exercise no. 8 Marks obtained by 50 students in community medicine in final MBBS Part-I Exam as follows: Calculate central tendency. Marks No. of students 41-50 5 51-60 18 61-70 15 71-80 7 81-90 5
- 58. • Solution: Average marks obtained by students=3165/50=63.3 Marks obtained No. of students(f) Mid value of marks group(x) of students Total marks obtained by each group(fx) 41-50 5 45.5 227.5 51-60 18 55.5 999 61-70 15 65.5 982.5 71-80 7 75.5 528.5 81-90 5 85.5 427.5 Total 50 3165
- 59. Calculation of Median: N/2=3165/2=1582.5 Median class=60.5-70.5 Median=L+{(N/2 –cf) xh}/f • where: • L = lower boundary of the median class h= class width N = total frequency cf = cumulative frequency of the class previous to the median class f = frequency in the median class Class boundary frequency Cumulative frequency 40.5-50.5 227.5 227.5 <N/2 50.5-60.5 999 Cf=1226.5 <N/2 60.5-70.5 f=982.5 2209 >N/2 70.5-80.5 528.5 2737.5 80.5-90.5 427.5 3165 Total 3165
- 60. • Median= 60.5+ (1582.5 - 1226.5)x10/982.5 = 60.5 + 3560/982.5 = 60.5 + 3.62 = 64.12 *Modal class: the class having maximum frequency Class boundary frequency 40.5-50.5 f1=227.5 50.5-60.5 fm=999 Modal Class 60.5-70.5 f2=982.5 70.5-80.5 528.5 80.5-90.5 427.5 Total 3165
- 61. • Mode=L + (fm –f1)/(2fm- f1 – f2)x h Where, L= lower boundary of modal class fm =Frequency of modal class f1= frequency of pre-modal class f2= Frequency of post-modal class h= width of modal class Median= 60.5 +(999 –227.5 )/(2x 999- 227.5- 982.5 )x10 =60.5 -771.5/(1998-1210)x10 =60.5 – 771.5/788x10 =60.5 – 9.79 =50.71
- 62. • Exercise no. 11 Calculate measures of dispersion from following data: 15,17,19,25,30,35,48 Solution: Range=48- 15= 33 Mean deviation= Σ(x- x)/n Observation(x) Mean(x) (x-x) 15 X=Σx/n=189/7=27 -12 17 -10 19 -8 25 -2 30 3 35 8 48 11 Σx=189 Σ(x-x)=54, ignoring- or + signs
- 63. X • Standard deviation: SD=√(506/10)=√50.6= Observatio n(x) Mean(x) Deviation (x-x) (x-x)2 15 X=Σx/n=189 /7=27 -12 144 17 -10 100 19 -8 64 25 -2 4 30 3 9 35 8 64 48 11 121 Σx=189 Σ(x-x)=54, Σ(x-x)=506
- 64. • Coefficient of variation=(SD/Mean)x 100 =√50.6/27 x 100 =
- 65. • Exercise no. 20 In the following data A & B are given below: Calculate mean deviation & standard deviation. A-item B-frequency 10-20 4 20-30 8 30-40 8 40-50 16 50-60 12 60-70 6 70-80 4
- 66. • Solution: a=assumed mean SD=√{(sumfd1)2 – (sum fd1)/N}2/√(N-1) x h • x= sumfd1 x h + a Data A - Class interval Data B- frequency (f) Mid value (x) d1=(x-a)/h fd1 fd1 2 10-20 4 15 (15-35)/10=- 2 -8 64 20-30 8 25 -1 -8 64 30-40 8 a=35 0 0 0 40-50 16 45 1 16 256 50-60 12 55 2 24 576 60-70 6 65 3 18 324 total 54 Σfd1=74 Σfd1 2=1284
- 67. • SD=√{1284- 74/54}/√(54-1) x 10 = √{1284- 1.37}/√53 x 10 = √( 1282.63/53) x 10 = √24.2 x 10

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