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BIO_STATISTICS DR. N.C DAS
WHAT IS STATISTICS ,[object Object],[object Object]
ELEMENTS OF STATISTICS
APPLICATION OF STATISTICS STATISTICS POPULATION STUDY METHODS OF DATA REDUCTION/ CORRECTION VARIATION STUDY
BIO_STATISTICS Application of statistical methods for living organisms such as  medical, biological and public health related problems.  BIO-STATISTICS DESCRIPTIVE INFERENTIAL
BIO-STATISTICS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
COMPONENTS OF BIO-STATISTICS BIO- STATISTICS   RATES & RATIOS   STATISTICAL AVERAGE  DISPERSION  CO-RELATION  & REGRESSION   SAMPLING  INTERPRETATION
STATISTICAL AVERAGES ,[object Object],[object Object],[object Object],[object Object]
MEASURES OF CENTRAL TENDENCY CENTRAL TENDENCY Aggregate/ Sum of the multiple Observations divided by no. of observations is mean value. The mid point value of an arranged no. of observations The most frequently occurring  Value in the Observation.
BIO- STATISTICS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],c)  Mode: Mode is the frequently occurring variable in  the distribution. AVERAGES
MEAN (ARITHMETIC MEAN / AVERAGE) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Computation of the mean ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Advantages and disadvantages  of the mean ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The median is not sensitive to  extreme values Median Same median
ADVANTAGES AND DISADVANTAGES  OF THE MEDIAN ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
EXAMPLES OF MODE  ,[object Object],[object Object],[object Object],[object Object],a nnual salary  (in 10,000 rupees )
FREQUENCY DISTRIBUTION OF MODE 0 2 4 6 8 10 12 14 16 18 20 N MODE Mode
IDEAL CENTRAL TENDENCY ,[object Object],[object Object],[object Object]
0 2 4 6 8 10 12 14 N Mean  = 10.8 0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19 FREQUENCY GRAPH Median  = 10 Mode = 13.5
[object Object],DIFFERENCE Mean Median Mode Represents centre of gravity of data set Represents middle of data set (half below & half above) Represents most common value Sensitive to extreme values Not sensitive to extreme values Data set may have no mode, one or multiple mode Most useful when data is normally distributed Most useful when data set is skewed or has few extreme values in one direction Not popular  with  bio-scientists
1.  Measures  the scattering  / variability   of data  around a measure of CT.   2.  Gives an idea about the homogeneity or   heterogeneity of the distribution of data. : Range,  Mean Deviation (MD), Standard Deviation (SD),  Quartile Deviation (QD) Coefficients of range, Coefficient of Range: [L-S]/[L+S. Co-efficient of MD Coefficient of MD = MD/M (Where M = Mean/ Median) MEASURES OF DISPERSION/VARIATIONS  1 Absolute Measures  Relative Measures:
Position Dispersion CT
NORMAL STATISTICAL CURVE   68% 95% 99.7% Mean – 0 Total Area – 1 SD-1 SD-2 SD-3 In 95% confidence level there is probability of 5% of the data is outside SD-2  i.e. 1 in 20 samples therefore the probability P = 5/100 = 1/20 = 0.05 1 CT
NORMAL STATISTICAL DISTRIBUTION
DISPERSION  RANGE  MEASURES OF DISPERSION   MEAN  DEVIATION   STANDARD  DEVIATION
Measures of Dispersion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Range  =  71 - 95
INTERPRETATION  (STANDARD ERROR) Standard Error is a measure which enables to judge whether the mean of a given sample is within the set confidence level of population mean or not.  STANDARD  ERROR  STANDARD ERROR OF MEAN STANDARD ERROR BETWEEN TWO MEANS STANDARD ERROR OF PROPORTION STANDARD ERROR  OF DIFFERENCE BETWEEN  TWO PROPORTION CHI- SQUARE TEST
STANDARD ERROR OF MEAN   ,[object Object],[object Object],[object Object],[object Object],[object Object]
EXAMPLE  Take Random Sample of 25 males of age 12 years  Mean Height is 50” and SD of 0.6 S.E of mean = SD/  √ (n)  [n = Total Sample]   = 0.6/ √25    = 0.6/5    = 0.12 at 95% confidence level = 50” ± (2x 0.12)   = 50” ± 0.24   = 49.76 to 50.24 i.e. the population mean chance is 1 in 20 out side these limits.
Standard Error of proportion: p = Proportion of Male = 52 q = Proportion of Female = 48 n = Size of the sample  = 100 In random sample of 100 the proportion of Male is 40 while in the population male is 62 Relative Deviate – 52- 40 = 2.4 which is more than 2 hence the deviation is significant. SE (P) =  √ pq   n √  52 X 48 100 =  √ 2496 100 =  √ 24.96 = 5 52 + 2 (5) = 62 52- 2 (5) = 42 5
[object Object],Correlation  Correlation  Co-efficient of correlation  = r r  =  ∑   ( x- xi) (y- yi) ∑  √ (x- xi) 2  (y- yi) 2 The correlation co- efficient lies between -1 to +1. the value nearer to + 1 suggests degree of relation between variables but can not study the cause and effect relation.
Regression: It measures back wards and study of relation in cause and effect is possible between two dependable or independent variables. Given the value of independent variable, value of the dependent variable can be obtained by the formula y =  y  + b (x- x) Regression co- efficient (b) can be calculated as for Y upon ‘X’  b =  ∑  (x- xi) (y- yi)     ∑  (x-xi) 2
SAMPLING ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
SAMPLING METHODS Random Sampling  Non Random Sampling Simple  Restricted  Judgment  Convenience   (When no of unit are less)  (Easy to approach) Systematic  Stratified  Multistage
Samplings Error: If repeated samples are taken from the same population the result obtained from one sample will differ from the other because of   ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],p = Proportion of Male = 52 q = Proportion of Female = 48 n = Size of the sample  = 100 In random sample of 100 the proportion of Male is 40 while in the population male is 62 Relative Deviate – 52-40  5 = 2.4 which is more than 2 hence the deviation is significant And not acceptable.
Hospital Administration Made Easy http//hospiad.blogspot.com An effort solely to help students and aspirants in their attempt to become a successful Hospital Administrator. hospi ad DR. N. C. DAS

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Bio statistics

  • 2.
  • 4. APPLICATION OF STATISTICS STATISTICS POPULATION STUDY METHODS OF DATA REDUCTION/ CORRECTION VARIATION STUDY
  • 5. BIO_STATISTICS Application of statistical methods for living organisms such as medical, biological and public health related problems. BIO-STATISTICS DESCRIPTIVE INFERENTIAL
  • 6.
  • 7. COMPONENTS OF BIO-STATISTICS BIO- STATISTICS RATES & RATIOS STATISTICAL AVERAGE DISPERSION CO-RELATION & REGRESSION SAMPLING INTERPRETATION
  • 8.
  • 9. MEASURES OF CENTRAL TENDENCY CENTRAL TENDENCY Aggregate/ Sum of the multiple Observations divided by no. of observations is mean value. The mid point value of an arranged no. of observations The most frequently occurring Value in the Observation.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17. The median is not sensitive to extreme values Median Same median
  • 18.
  • 19.
  • 20.
  • 21. FREQUENCY DISTRIBUTION OF MODE 0 2 4 6 8 10 12 14 16 18 20 N MODE Mode
  • 22.
  • 23. 0 2 4 6 8 10 12 14 N Mean = 10.8 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 FREQUENCY GRAPH Median = 10 Mode = 13.5
  • 24.
  • 25. 1. Measures the scattering / variability of data around a measure of CT. 2. Gives an idea about the homogeneity or heterogeneity of the distribution of data. : Range, Mean Deviation (MD), Standard Deviation (SD), Quartile Deviation (QD) Coefficients of range, Coefficient of Range: [L-S]/[L+S. Co-efficient of MD Coefficient of MD = MD/M (Where M = Mean/ Median) MEASURES OF DISPERSION/VARIATIONS 1 Absolute Measures Relative Measures:
  • 27. NORMAL STATISTICAL CURVE 68% 95% 99.7% Mean – 0 Total Area – 1 SD-1 SD-2 SD-3 In 95% confidence level there is probability of 5% of the data is outside SD-2 i.e. 1 in 20 samples therefore the probability P = 5/100 = 1/20 = 0.05 1 CT
  • 29. DISPERSION RANGE MEASURES OF DISPERSION MEAN DEVIATION STANDARD DEVIATION
  • 30.
  • 31. INTERPRETATION (STANDARD ERROR) Standard Error is a measure which enables to judge whether the mean of a given sample is within the set confidence level of population mean or not. STANDARD ERROR STANDARD ERROR OF MEAN STANDARD ERROR BETWEEN TWO MEANS STANDARD ERROR OF PROPORTION STANDARD ERROR OF DIFFERENCE BETWEEN TWO PROPORTION CHI- SQUARE TEST
  • 32.
  • 33. EXAMPLE Take Random Sample of 25 males of age 12 years Mean Height is 50” and SD of 0.6 S.E of mean = SD/ √ (n) [n = Total Sample] = 0.6/ √25 = 0.6/5 = 0.12 at 95% confidence level = 50” ± (2x 0.12) = 50” ± 0.24 = 49.76 to 50.24 i.e. the population mean chance is 1 in 20 out side these limits.
  • 34. Standard Error of proportion: p = Proportion of Male = 52 q = Proportion of Female = 48 n = Size of the sample = 100 In random sample of 100 the proportion of Male is 40 while in the population male is 62 Relative Deviate – 52- 40 = 2.4 which is more than 2 hence the deviation is significant. SE (P) = √ pq n √ 52 X 48 100 = √ 2496 100 = √ 24.96 = 5 52 + 2 (5) = 62 52- 2 (5) = 42 5
  • 35.
  • 36. Regression: It measures back wards and study of relation in cause and effect is possible between two dependable or independent variables. Given the value of independent variable, value of the dependent variable can be obtained by the formula y = y + b (x- x) Regression co- efficient (b) can be calculated as for Y upon ‘X’ b = ∑ (x- xi) (y- yi) ∑ (x-xi) 2
  • 37.
  • 38. SAMPLING METHODS Random Sampling Non Random Sampling Simple Restricted Judgment Convenience (When no of unit are less) (Easy to approach) Systematic Stratified Multistage
  • 39.
  • 40. Hospital Administration Made Easy http//hospiad.blogspot.com An effort solely to help students and aspirants in their attempt to become a successful Hospital Administrator. hospi ad DR. N. C. DAS