A SEMINAR ON STATISTICAL ANALYSIS IN MODERN PHARMACEUTICAL ANALYSIS FACILITATED BY: Dr. NAGRAJ HOD , Department of Pharmaceutical analysis, PESCP,Bangalore-560050 PRESENTED BY: Shiva shanker rai 1 st M. Pharma Department of Pharmacology 3/24/2013 1

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CONTENTS Introduction Importance, limitation and scope of statistical methods Statistical concepts Statistical terms (normal distribution, probability, degree of freedom) Types of biostatistics References 3/24/2013 2

INTRODUCTION:

INTRODUCTION Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. Statistics is the science of collecting, analyzing and drawing conclusions from data. Statistics is the study of variability and uncertainty. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities. 3/24/2013 3

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The main function of statistics are: To simplify data in an understandable way. To help in formulating prediction and testing hypothesis. To provide tools to measure the results and comparisons between different factors understudy. IMPORTANCE OF STATISTICAL METHODS

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LIMITATIONS OF STATISTICS The following are some limitations of statistics: Statistics is not useful in individual cases. Statistics results are not universally true. Statistics can be misused. SCOPE OF STATISTICS In Industries. Statistics in state. In Economics. In Social science. In agriculture, computer and natural sciences.

Statistical concepts:

Statistical concepts Data ‘Variable’ concept Population and sample Sampling Measurements scales and types of data Discrete variables Continuous variables Nominal scale Ordinal scale Interval scale Ratio measurement 3/24/2013 6 Data

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Discrete variables Characterized by gaps or interruptions in the values it assumes like number of death in a hospital. This can take only a whole number like 0, 1, 2, 3, . .etc. but it can’t be an integer like 0.1,1.2, . .etc. Continuous variables Unlike the discrete variable doesn’t possess the gaps or interruptions. Example-Height and weight of individuals . 3/24/2013 7

Levels of Measurement:

Levels of Measurement Nominal level of measurement: characterized by data that consist of names, labels, or categories only, and the data cannot be arranged in an ordering scheme (such as low to high) Ordinal level of measurement involves data that can be arranged in some order, but differences between data values either cannot be determined or are meaningless Interval level of measurement : like the ordinal level, with the additional property that the difference between any two data values is meaningful, however, there is no natural zero starting point (where none of the quantity is present) Ratio level of measurement : the interval level with the additional property that there is also a natural zero starting point (where zero indicates that none of the quantity is present); for values at this level, differences and ratios are meaningful. 3/24/2013 8

Sampling stages :

Sampling stages Stage 1- Defining the population under study. Stage 2- Specify a sampling frame, which are a set of items or events possible to measure. Stage 3- specify a sampling method for selecting events from the frame. simple random sampling systematic sampling cluster sampling matched random sampling etc. stage 4- sample size determination C:\Users\shiva shanker rai\Desktop\2013-03-15\samsizeTheory.pdf 3/24/2013 9

Sample size calculation:

Sample size calculation 3/24/2013 10 Assess the difference expected Find out the SD of variables Set the level of significance (alpha) Set the beta level Select the appropriate formula Calculate the sample size Give allowances for drop-outs and non-compliance

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The normal distribution / The normal probability distribution is the most useful continuous distribution and it plays a prominent role in probability theory. Normal distribution is an approximation to binomial distribution when ‘n’ becomes large. DEFINITION : A continuous random variable ‘x’ is said to have a normal distribution with parameters μ and σ 2 and it’s density function is given by: 1. NORMAL DISTRIBUTION SOME BASIC STATISTICAL TERMS AND CONCEPTS

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e and π are the two mathematical constants whose values are 2.7188 and 3.1416 respectively. μ and σ are two parameters denoting the mean and standard deviation respectively. X ̴ N( μ , σ 2 ) is used as a notation to denote that the random variable (x) follows a normal distribution with μ (mean) and σ 2 (variance). If μ = 0 and σ = 1 ; then the variate is called STANDARD NORMAL VARIATE.

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2.PROBABILITY If the results can be predicted with certainty it is known as deterministic phenomena. ex., if dilute acid is added to Zinc we get Hydrogen. Most of the physical & chemical sciences are deterministic in nature. When results cannot be predicted with certainty it is known as Probability phenomenon . ex., in toss of a coin we are not sure if we shall get head or tail. The probability of occurrence is expressed on a scale ranging from 0 (impossible) to 1 (certainty).

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3/24/2013 14 It denotes the number of samples that a researcher has the freedom to choose. It is based on a concept that one could not have exercised his/her freedom to select all the samples. The concept can be explained by an analogy : X + Y = 10 ……….(1) In the above equation you have freedom to choose a value for X or Y but not both because when you choose one, the other is fixed. If you choose 8 for X, then Y has to be 2. So the degree of freedom here is 1. X+ Y+Z = 15 ……..(2) 3. Degrees of Freedom ( df )

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3/24/2013 15 In the formula (2), one can choose values for two variables but not all. You have freedom to choose 8 for X and 2 for Y. If so, then Z is fixed. So the df is 2. df is calculated by subtracting 1 from the size of each group. For example df for Student’s t test is calculated by n -1 (paired design) and N1+N2 – 2 (for unpaired) [N1 – size of group 1, N2 – size of group 2]. The methods of df calculation may vary with the test used. 3. Degrees of Freedom ( df ) contd.

Types of biostatistics:

Types of biostatistics Descriptive statistics Inferential statistics 3/24/2013 16

Descriptive statistics:

Descriptive statistics Grouped data the frequency distribution table Measures of central tendency Measures of variability Measures of shape of distribution: graphs, skewness , Inferential statistics (drawing of inferences) Estimation Hypothesis testing reaching a decision Parametric statistics Non-parametric statistics << Distribution-free statistics Modeling, Predicting 3/24/2013 17

Descriptive statistics:

Descriptive statistics Class Limit Frequency Relative frequency Cumulative Frequency Cumulative Relative Frequency ... ... A. Grouped data the frequency distribution tables B. Measures of central tendency The Mean (arithmetic mean) The Median The Midrange Mode 3/24/2013 18

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Mean A. Arithmetic mean: calculated by dividing the sum of data items with the number of data items . X = = 7.6 B. Geometric mean : the geometric mean of n number is obtained by multiplying them all together and then taking the nth root. 3/24/2013 19

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Median It is the central value of all observations arranged from the lowest to highest. Ex. 5, 5, 7, 9 , 11 , 12, 15, and 18 has median 11. Mode It is the most frequently occurring value in a series of observation. ex- 2,2,5,7,9,9,9,10,10,11,12, and 18 has mode 9 3/24/2013 20

Descriptive statistics :

Descriptive statistics Range Variance Standard Deviation Coefficient of Variance C. Measures of dispersion 1. Range: The difference between two extreme scores of the distribution is called the range. range = Highest score - lowest score 3/24/2013 21

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2. Standard deviation :- This is universally used to show the scatter of individual measurement around the mean in a given distribution. It is calculated in following way Find out mean µ of the observation(X) Then find out deviation of each value from mean(X- µ) Each deviation is squared and values are added ∑(X- µ) 2 Variance is calculated by dividing this sum by number of observations minus one. Variance = ∑(X- µ) 2 n-1 3/24/2013 22

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Coefficient of variation (CV): Useful measure of relative variation CV= standard deviation*100 Mean When square root of variance is taken out standard deviation is obtained. σ = 3/24/2013 23

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Ex. 5 rats with different diet show increase in body weight is 25, 40, 30,35 and 50 gm. X = = S 2 = SD= = = 9.61 Rats Increase in weight (gm) X-X (X-X) 2 1 2 3 4 5 25 40 30 35 50 25-36=-11 40-36=4 30-36=-6 35-36=-1 50-36=14 121 16 36 1 196 Total (n=5) ∑X= 180 0 ∑(X-X) 2 =370 3/24/2013 24

Descriptive statistics :

Descriptive statistics Frequency distribution Relative frequency of occurrence proportion of values Nominal, Ordinal level Bar chart Pie chart Interval, Ratio level Histogram : frequency histogram & relative frequency histogram Frequency polygon : midpoint of class interval Pareto chart : bar chart with descending sorted frequency Cumulative frequency Cumulative relative frequency D. Measures of shape of distribution graphs 3/24/2013 25

Descriptive statistics:

Descriptive statistics Skewness ( S k ), Pearsonian coefficient, is a measure of asymmetry of a distribution around its mean. Kurtosis characterizes the relative flatness of a distribution compared with the normal distribution. D. Measures of shape of distribution graphs contd. 3/24/2013 26

Standard error of the mean (SE) :

Standard error of the mean (SE) In a small sample size arithmetic mean would be approximation of “true mean” of whole population & therefore subjected to error. In such cases error of the observed mean is calculated. SE allows to find out the range in which true mean lie. SE = SD SAMPLE SIZE

Null hypothesis:

Null hypothesis It is hypothesis of number of difference between treated and control group. When it is accepted then the difference between two groups is not significant. If hypothesis is rejected then one can say that there is significant difference between treated and control groups. 3/24/2013 28

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Design Data summary Statistics & Tests 2 independent groups Proportions Rank Ordered Mean Survival Chi-square, Fisher-exact Mann-Whitney U Unpaired t-test Mantel-Haenzel, Log rank 2 related groups Proportions Rank Ordered Mean McNemar Chi-square Sign test Wilcoxon signed rank Paired t-test More than 2 independent groups Proportions Rank Ordered Mean Survival Chi-square Kruskal-Wallis ANOVA Log rank More than 2 related groups Proportions Rank Ordered Mean Cochran Q Friedman Repeated ANOVA Study of Causation; one independent variable (univariate) Proportion Mean Relative Risk Odd Ratios Correlation coefficient Study of Causation; more than one independent variable (Multivariate) Proportion Mean Discriminant Analysis Multiple Logistic Regression Log Linear Model Regression Analysis Multiple Classification Analysis 3/24/2013 29

References Biostatistics: A Foundation for Analysis in the Health Sciences. Wayne W. Daniel. Georgia State University, 1991. Introduction to Research Methodology by Kothari. Handbook of experimental Pharmacology by S K Kulkarni Fundamentals of experimental pharmacology , 3 rd Edition by M N Ghosh . Introduction to Bio statistics and research methods by S S Sundar Rao and J. Richard. 3/24/2013 31

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3/24/2013 32 Queries Queries?

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3/24/2013 33

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