BIOSTATISTICS AND RESEARCH METHODOLOGY

JNTUK 4th BPharm 2nd semester
UNIT-1
Introduction: Statistics, Biostatistics, Frequency distribution
Measures of central tendency: Mean, Median, Mode- Pharmaceutical examples
Measures of dispersion: Dispersion, Range, standard deviation, Pharmaceutical
problems
Correlation: Definition, Karl Pearson’s coefficient of correlation, Multiple correlation - Pharmaceuticals examples

1. BIOSTATISTICS AND RESEARCH METHODOLOGY UNIT - 1 Prepared by K . Venkata Chandana IV B Pharmacy- 8 th sem NRI College of Pharmacy Under the Guidance Agiripalli Dr G.Vamseekrishna M.pharm; Ph.D. Professor

2. STATISTICS : Statistics is the science which deals with the methods of collecting , classifying , presenting , comparing , and interpreting numerical data collected in any sphere if inquiry . Knowledge on statistical concepts is desired for the development , production , evaluation and marketing of various pharmaceutical dosage forms. statistics depends on measurement of contineous and discrete variables. BIOSTATISTICS : Is the application of statistical techniques to scientific research in health related fields , including medicine , biology and public health and the development of new tools to study these areas. Biostatistics use statistical techniques to : Design experiments to collect the right data. Collect and analyze data from experiments. Interpret the results of experiments. Account for biases , variables and missing data.

3. FREQUENCY DISTRIBUTION : A frequency distribution shows the repeated items in a graphical form. it gives display of the frequency of items or shows the number of times they occured. Frequency distribution is used to organize the collected data in table form . The data could be as marks scored by students, temperature of different towns, points scored in vollyball match etc.., After data collection we have to show data in a meaningfull manner for better understanding organise the data in such a way that all it’s features are summerized in a table this is known as frequency distribution. Ex-1 : scores of 10 students in the G.K quiz are 15,17,20,15,20,17,17,14,14,20. let’s represent this data in frequency distribution. S.NO QUIZ MARKS NUMBER 1. 14 2 2. 15 2 3. 17 3 4. 20 3

4. Ex-2 : Marks of final year B.pharm A-section students are 35,46,37,55,62,43,51,57,44,68,59,36,48,39,63,56,33,54,64,65 S.NO CLASS INTERVEL FREQUENCY 1. 30-40 5 2. 40-50 4 3. 50-60 6 4. 60-70 5

5. APPLICATIONS OF STATISTICS IN PHARMACY : 1. Analytical Statistics such as Correlation, Regression is used to establish the functional relation between variables like Concentration versus Absorbance, Time versus Amount of drug dissolved. 2. Discriptive statistical parameters such as Mean and Standard deviation are used to express the data generated from the replicated experiments to confirm reproducibility. 3. Inferential statistical tests such as T-test, ANOVA are used in bioavailability and bioequivalence studies. 4. Applied statistics is used in quality control. 5. Statistical treatment of data is required for validation of a process. 6. Statistical quality control charts are used to determine the quality of product. 7. Statistical knowledge is essential for validation of analytical technique. 8. A useful tool in the design of experiments like bioavailability studies. 9. Useful in interpretation of experimental results. 10. Statistical usage is recommended by the drug regulatory agencies. 11. Collection of true representative sample from the bulk needs the concept of statistics.

6. Most of the cases population mean advisable to measure is not due to problems in identidying all population suffering with disease more time requirement , highly expensive , ethical and impracticable. So Sample of ‘n’ objects is taken from a Population to estimate the properties of population Merits of Arthematic Mean :- Easy to understand and calculate. It takes all values into consideration. It is less affected by fluctuations of sampling. Different interpretations by different persons are not possible. Demerits of Arthematic Mean :- It cannot be determined by inspection nor by graphically. It is very much affected by extreme values (1,2,3,4,5,75,95) mean value doesnot furnish any information.

7. Mode (Z): The mode is the value that occurs most frequently in the dataset. Unlike the mean and median, The mode can be applied to both numerical and categorical data. It’s useful for identifying the most common value in a dataset. According to Croxton and Cowden “The mode of a distribution is the value at the Point around which the items tend to be most heavily Concentrated” The plasma Concentration values observed from iv injection is 14,13,16,12,17, 16, 14, 12, 18, 14, 16,14. The mode is “14”. The plasma conc observed after oral administration is 4,6,2,8,10,6,4,6,8,10,6,8. The mode is “6”. Advantages of Mode : It is readily understood and easily calculated. It is not affected by Extreme observations. Disadvantages of Mode : It is not based on all observations It is not Capable of further mathematical treatment. It is affected by sampling fluctuations

8. Median :- Median is the value of middle item of series arranged magnitudes in an ascending or desending order of magnitudes The Median is the center point of distribution it divides data into two equal parts. It is calculated with the following steps : 1. Collect the data. 2. Arrange the data in rank order. 3.Observe the central value in case of odd number of observations. 4. The mean of two central values in case of even observations and express it is the median value. Ex-1: Calculate the median plasma concentration of different patients by oral route 5,6,7,8,7,5,7,6 and 7. Arranged in ascending order 5,5,6,6,7,7,7 and 8 Central value median is “7” Ex-2 : If number of observations in a series is even take the average of two middle values as median . Calculate median for the data 2,4,5,6, 2,4,5,7,5 and 2 Arranged in ascending order 2,2,2,4,4,5,5,5,6 and 7 Central values are the average of 4,5 and the median is  4+5/2 = “4.5”

9. Percentile ×100 Ex: 12,000 students appeared for GPAT Examination 11.900 students got less than marks than sri hari then the percentile score of Sri hari is 11900/12000 = 0.9916 ; usually it is mulltiplied with 100 then the values becomes 99.16. percentile X100 = 99.16 Advantages of Median : It is easy to calculate and is readily understood. It is not at all affected by extreme values. The median value can be located graphically. It is only average that can be used in qualitative analysis. Disadvantages of Median : It cannot be exactly determined in case of even no.of observations. It is much affected by Fluctuations of Sampling.  

10. Measures of Central dispersion : Disperson is useful to know variability in the data. It finds how individual value are spread around the Central value or mean value or Average value. Brooks and Dick define “dispersion is the degree of the scatter or variation of the variable about central value” Objectives : To judge the reliability of measures of central tendency. To Compare different sets of data with respect to variability. To control the variability in data. Methods of measuring dispersion - 1. Range 2. Mean deviation 3. Variance and standard deviation. I.Range :- It is a simple method to study the dispersion Range = Heighest value - Lowest value.

11. Ex : Range of 5,10,18,19,23,27. Range = Heighest value  －  Lowest value. = 27 － 5 = 22 Coefficient of Range = 0.6875 Merits of Range : Easy to calculate Demerits of Range : Not based on all observations. Much affected by fluctuations of sampling. Not suitable for mathematical treatment.  

12. 2. Mean deviation (or) Average deviation :- Mean deviation is a measure of dispersion based on all observations. The Mean deviation is the arthimatic mean of the deviation of the individual values from the average of given data. Mean deviation Can be computed from any average i.e.., Mean, Median and Mode, but Mean is preferable because it is a more appropriate measure of central value. Mean deviation Where , x = Individual values = Mean ︱︱= Modulus (-ves into +ves)    

13. Ex : Absorbance values from spectrophotometer are 0.104,0.108,0.112,0.117,0.106, and 0.114 calculate mean deviation. 0.1101 n=6 Mean deviation Mean deviation = 0.00416  

14. Coefficient of mean deviation : coefficient of relative Mean deviation will give a relative measure of dispersion , Suitable to compare two or more series. Coefficient of mean deviation Ex : Absorbance of same solution by two different spectrophotometers are 0.104,0.108,0.112,0.117,0.106 and 0.114 . Coefficient of mean deviation = 0.0372  

15. Advantages of Mean Deviation : It is easy to calculate when compare with other methods of dispersion. Calculation involves all observations. It is less affected by Extreme values when Compared with Standard Deviation. Disadvantages of Mean Deviation : It ignores -ve signs of deviation.

16. 3 . Standard deviation : It is the most appropriate method of dispersion It is first introduced by karl pearson in 1993. It is defined as the positive square root of the arthimatic mean of squares of the deviations of given observations from their arthimatic mean. Standard deviation (s) = √ = n-1 (n ≤ 30) For sample(s) Standard deviation (σ) = √ = n (n > 30) For population( σ) It is difficult to calculate population standard deviation. Standard deviation tells you how much data points vary from the average. High standard deviation means greater variation between the data points of dispersion (Scattered). Low standard deviation all the values close together.  

17. Variance : It is the square of Standard deviation. It shows how much data points deviates from the mean. It is also known as mean Square deviation. It is Important measure in the quantitative analysis of data,In biological, agricultural and medical sciences. Comparing two data sets with similar averages but one has higher variants indicating more fluctuations. Standard Variance ( ) = = (n ≤ 30) For sample Standard Variance ( ) = = (n > 30) For population  

18. Advantages of Variance : All the data points are involved in calculation. Least effected by Sampling fluctuations. Useful to know reliability of means of two or more different series. Disadvantages of Variance : Difficult to calculate. Affected by extreme values.

19. Coefficient of variation / Relative standard deviation (RSD) : It is clear that standard deviation of height of plants cannot compare with the standard deviation of weight of plants because they are exprested in different units. i.e.., Height in (cm) and weight in (gm). So the meature Standard deviation must be converted into a relative measure for the purpose of Comparision. % Relative Standard Deviation (or) C.V = 100 Where , S = Sample Standard deviation. = sample mean. RSD always expressed in terms of % . RSD should be < 2%  

20. Ex :1- Calculate the mean,mean deviation, Standard deviation, %RSD for the peak areas of Chromatograph 14400, 14980, 15046, 13975, 14295, 15200. Mean =14,619 Mean deviation = 426 Standard deviation = 492.41 %RSD = 3.36 Ex :2 - Calculate mean,mean deviation,standard deviation,%RSD plasma concentrations of 2.4,2.8,3.1,2.7,2.2,2.9. Mean = 2.683 Standard deviation = 0.3435 Mean deviation = 0.283 %RSD = 12.802

21. Correlation : It measures the closeness of the relationship between two variables (independent and dependent variables) The word relationship indicates that there is some Connection to measure the closeness of the relationship between the variables. Ex: 1. concentration (independent variable) vs absorbance (dependent variable) 2.dose of drug ( independent variable) vs response (dependent variable) 3.Time ( independent variable) vs drug disolved (dependent variable) Mathematical formula established by - Karl pearson Graphically represented by - Sir francis galton Corelation analysis helps to determining the degree of relationship between two or more variables but it doesnot indicate a cause and effect of relationship between two variables.

22. Types of correlation : Based on nature of relationship 1. positive (or) negative Correlation 2. Linear (or) non-linear correlation 3. Simple (or) multiple correlation 4. partial (or) total correlation 1.Positive Correlation : Increase in the value of one variable is associated with an increase in the value of other variable or decrease in the value of one variable is associated with an decrease in the value of other variable. concentration g/ml Absorbance 2 0.204 4 0.408 6 0.612 8 0.816 10 1.02

23. Negative Correlation : As the one variable increases second variable decreases and vice versa. 2. Linear Correlation : If the variation in the values of two variables has a constant ratio. Ex :- Variables (x) = 10 20 30 40 50 Variables(y) = 20 40 60 80 100 Time (months) Potency 0 100 3 98 6 96 8 94 10 92 12 90

24. Non- linear correlation : If the variation in the values of two variables doesnot show constant variation. Simple correlation : It involves two variables or can include relationship between two variables. Ex :- Amount of drug dissolved and hardness Multiple correlation : It involves a dependent variable and two or more independent variables. Ex :- Relationship between amount of drug release (dependent variable) and Hardness , granule size (independent variable) Partial correlation : In the study of relationship between two variables , excluding some other variables. Ex :- Potency of the drug is influenced by humidity and temperature .but potency of drug effect of temperature is only studied , neglect the effect of humidity.

25. Total correlation : It involves study of effect of all independent variables or dependent variables. Ex : Relationship between potency of drug is dependent variable temp & humidity. Methods of studying correlation : 1. scatter or dot diagram method. 2. Graphical method 3. karl pearsons coefficient of correlation method. 1. Scatter or dot diagram method :- The diagram of dots or points Obtained is called a scattered diagram or dot diagram with the help of this diagram we get an idea about the relationship between two variables x and y. strong positive correlation : As the value of 1 increases, y also increases proportionately. b) strong negative correlation : As the value of x increases, y increases proportionately.

26. c) Weak positive Correlation : As the value of x increases , y Increases but not proportionately. d) Weak Negative Correlation : As the value of x increases , y decreases but not proportionately. e) Complex correlation : y seems to be related to x , but complex. f) No correlation : No relationship between x and y.  

27. a) Strong positive correlation b) Strong negative correlation c) Weak positive correlation d) Weak negative correlation f) No correlation

28. 2.Graphical method : Using graph paper can establish relationship between x and y Variables. X increases, Y also increases then it is said to be positive correletion. If X and Y it is ve move in opposite direction then Correlation. This type of graphical method is used in environmental biology and general studies. 3 . Correlation coefficient : The above two methods are usedul to establish qualitative relationship only without giving quantitative relation blw two vanables, the data is not valid

29. Positive , negative correlation, the correlation coefficient value should be more than 0.99 in process validation of pharmaceutical industry. The rough guide for correlation is follows : < 0.2 = Slight or almost negligible relationship 0.2 - 0.4 = Low correlation 0.4 - 0.7 = Moderate correlation 0.7 - 0.9 = High correlation > 0.9 = Very high correlation Based on ‘r’ values we can define relationship between two variables to give more justification about the relation correlation coefficient subjected to “ t- Test “ t Where , r = correlation coefficient n = number of observations n-2 = degrees of freedom  

30. Now ‘t’ calculated value compare with ‘t’ table value . To record the ‘t’ table value , fix probability either 0.05 (5% bias , 95% confidence) or 0.01 (1% bias , 99% confidence) If calculated t value is > table t value indicates Real correlation. If calculated t value is < table y value indicates No correlation. Time Amount of drug release % drug release 0 0 0 1 20 20 2 36 36 3 48 48 4 56 56 5 66 66 6 76 76 7 85 85