STATISTICAL PARAMETERS

CADD

1. STATISTICAL PARAMETERS BY HASIFUL ARABI J DEPT.OF PHARMACEUTICS

2. STATISTICAL PARAMETERS INVOLVED IN PHRMACEUTICAL RESEARCH &DEVELOPMENT Statistics: Statistics is an important tool in pharmacological research that is used to summarize (descriptive statistics) experimental data in terms of central tendency (mean or median) and variance (standard deviation, standard error of the mean, confidence interval or range) but more importantly it enables us to conduct hypothesis testing

3. CONTD…. Parameters: A parameter is something in an equation that is passed on in an equation. It means something different in statistics. It’s a value that tells you something about a  population  and is the opposite from a  statistic , which tells you something about a  small part  of the population.

4. STATISTICAL PARAMETERS The various statistical parameters are, Measures of central tendency Dispersion (also called Variability, Scatter, Spread ) Coefficient of Dispersion (COD)  Variance Standard Deviation (SD) σ Residuals  Factor Analysis Absolute Error (AE) Mean Absolute Error (MAE) Percentage Error of Estimate (PE)

5. 1. MEASURES OF CENTRAL TENDENCY: Measures of central tendency are also usually called as the averages . They give us an idea about the concentration of the values in the central part of the distribution. The following are the five measures of central tendency that are in common use: ( i ) Arithmetic mean , (ii) Median , (iii) Mode

6. CONTD…. MEAN: The average of the data  MEDIAN: The middle value of the data  MODE:   Most commonly occurring value

7. Mean (Average)  Mean locate the centre of distribution. Also known as arithmetic mean Most Common Measure The mean is simply the sum of the values divided by the total number of items in the set. Affected by Extreme Values.

8. Median: The median is determined by sorting the data set from lowest to highest values and taking the data point in the middle of the sequence. Middle Value In Ordered Sequence If Odd n, Middle Value of Sequence If Even n, Average of 2 Middle Value Not Affected by Extreme Values

9. Mode Measure of Central Tendency The mode is the most frequently occurring value in the data set. May Be No Mode or Several Modes Mode is readily comprehensible and easy to calculate. Mode is not at all affected by extreme values. Mode can be conveniently located even if the frequency distribution has class intervals of unequal magnitude

10. 2. Dispersion (also called Variability, Scatter, Spread) It is the extent to which a distribution is stretched or squeezed . Common examples of Statistical Dispersion are the variance, standard deviation and interquartile range . 3. Coefficient of Dispersion (COD ) It is a measure of spread that describes the amount of variability relative to the mean and it is unit less. 𝑪𝑶𝑫 = 𝝈/ 𝝁 ∗ 𝟏𝟎𝟎

11. 4. Variance  It is the expectation of the squared deviation of a random variable from its mean and it informally measures how far a set of random numbers are spread out from the mean. It is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and diving the sum of the squares by the number of values in the set.

12. The variance provides the user with a numerical measure of the scatter of the data.

13. 5. Standard Deviation (SD) σ It is a measure used to quantify the amount of variation or dispersion of a set of data values. It is a number that tells how measurement for a group are spread out from the average (mean) or expected value. A low standard deviation means most of the numbers are very close to the average while a high value indicates the data to be spread out. The SD provides the user with a numerical measure of the scatter of the data.

14. 6. Residuals It is the difference between the observed value of the dependent variable (y) and the predicted value (y ’). Each data point has one residual. Both the sum and the mean of the residuals are equal to zero. 𝑹 = 𝑶𝒃𝒔𝒆𝒓𝒗𝒆𝒅 𝒀 𝒗𝒂𝒍𝒖𝒆 − 𝑷𝒓𝒆𝒅𝒊𝒄𝒕𝒆𝒅 𝒀 𝒗𝒂𝒍𝒖𝒆

15. 7. Factor Analysis It  is a useful tool for investigating variable relationships for complex concepts allowing researchers to investigate concepts that are not easily measured directly by collapsing a large number of variables into a few interpretable underlying factors. 

16. 8. Absolute Error (AE)   It is the magnitude of the difference between the exact value and the approximation. The relative error is the absolute error divided by the magnitude of the exact value . 𝑨𝑬 = 𝑿 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 − 𝑿 𝒂𝒄𝒕𝒖𝒂𝒍 

17. 9.Mean Absolute Error (MAE) It is a quantity to measure how close forecasts or predictions are to the eventual outcomes . It is an average of the absolute errors . The simplest measure of forecast accuracy is MAE. The relative size of error is not always obvious.

18. 10. Percentage Error of Estimate (PE) It is the difference between the approximate and the exact values as a percentage of the exact value . %𝑬𝒓𝒓𝒐𝒓 = 𝑬𝒙𝒂𝒄𝒕 𝑽𝒂𝒍𝒖𝒆 − 𝑨𝒑𝒑𝒓𝒐𝒙𝒊𝒎𝒂𝒕𝒆 𝑽𝒂𝒍𝒖𝒆 𝑬𝒙𝒂𝒄𝒕 𝑽𝒂𝒍𝒖𝒆 ∗ 𝟏𝟎𝟎