statistical analysis

1. STATISTICAL ANALYSIS
R.kaviyarsan

7. FUNCTIONS OF STATISTICS
 Expression of Facts in Numbers
 Simple Presentation
 Enlarges Individual Knowledge and Experience
 It Compares Facts
 It Facilitates Policy Formulation
 It Helps Other Sciences in Testing their Laws
 It Establishes Relationship between Facts- Statistics also
establishes relationship between two or more than two
facts.
 Enlarges individual Knowledge & Experience.

8. IMPORTANCE OF STATISTICS
 Administrators
 Economist
 Industry &Agriculture
 Politicians
 Social Reformer
 Science & Research
 Insurance Companies
 Education

9. LIMITATIONS OF STATISTICS
 Study of Numerical facts only.
 Study of Aggregates only.
 Homogeneity of Data.
 Results are true only on an Average.
 Without reference result may prove wrong.
 Can be Used only by Experts.
 Misuse of Statistics is possible.

10. MEASURES OF CENTRAL TENDENCY
 The single estimate of a series of data that
summarizes the data is known as parameter.
 Objective : Condense the entire mass of data
Facilitate comparison
 3 types:
 Mean
 Median
 Mode

11. Mean
• Simplest
• Sum of all
observations/nu
mber of
observations
Median
• Middle value in
a distribution
Mode
• Value of
greatest
frequency
Number of f surgeries done by five doctors in a week are
7,5,4,9,5
Calculation of Mode – 4,5,5,7,9
Mode = 5

14. PROBABILITY
 When we speak of the probability of something
happening, we are referring to the likelihood—or
chances—of it happening. Do we have a better chance
of it occurring or do we have a better chance of it not
occurring?
 Theoretical Probability
Other probabilities are determined using
mathematical computations based on possible results,
or outcomes. This kind of probability is referred to as
theoretical probability.

15. example.
If we flip a coin 5 times and it lands on
heads 2 times, then the empirical probability is
given by:
P(HEADS) = 2/5 or 0.4

17. CORRELATION ANALYSIS
 It is a statistical measure which shows
relationship between two or more variable
moving in the same or in opposite direction

18. TYPES OF CORRELATION
correlation
positive
& negative
Simple ,
multiple
& partial
Linear
& non-linear

19. METHODS OF CORRELATION
 Scatter diagram
 Product moment or covariance
 Rank correlation
 Concurrent deviation

20. VARIANCE
it is the square of the standard deviation.
In short, having obtained the value of the standard
deviation, you can already determine the value of
the variance.
It follows then that similar process will be
observed in calculating both standard deviation and
variance. It is only the square root symbol that
makes standard deviation different from variance.

21. VARIANCE FOR UNGROUPED DATA

22. VARIANCE FOR GROUPED DATA

23. ACCURACY
 It is the measure of how close the experimental
value is to the value is to the true value . Accuracy
studies, for drug substance and drug product are
recommended to be performed at 80%,100%and
120% levels of label claim . Three replicates of
each concentration should be there and the mean
is an estimate of accuracy.

24. PRECISION
it is a measure of repeatability of an analytical
method under normal operation and it is expressed
as % relative standard deviation(%RSD)
%RSD=100 S/X
where,
S=standard deviation
X=mean

25. DETERMINATION OF PRECISION
 Repeatability
it is obtained when analysis is carried out in one
laboratory by one operator using one piece of
equipment over relatively short time span at least 5 or 6
determinations of three different matrices at 2 or 3
different concentrations . The acceptance criteria for
compound analysis are 1% RSD
 Intermediate precision
it is determined by comparing the results of a method
run with in a single laboratory over a number of weeks .
A method intermediate precision may reflect
discrepancies in results obtained by different operators ,
from different instruments ,with standards and reagents
from different suppliers with column of different batches.

26.  Reproducibility:
it represents the precision obtained between
laboratories . The objective is to verify that the
method will provide the same results in different
laboratories . it is determined by analyzing aliquots
from homogenous lots in different laboratories with
different analysts with the specified parameters of
method.

27. CONFIDENCE INTERVALS
 Using Statistics
 Confidence Interval for the Population Mean When
the Population Standard Deviation is Known
 Confidence Intervals for  When  is Unknown -
The t Distribution
 Large-Sample Confidence Intervals for the
Population Proportion p
 Confidence Intervals for the Population Variance
 Sample Size Determination
 Summary and Review of Terms

28. STATISTICAL SIGNIFICANCE
 Statistical significance is calculated as a p-value
that ranges between 0-1
 .05 is the conventional cut-off point for significance
(p>.05 = significance; p<.05 = not significant)

29. TESTS FOR STATISTICAL
SIGNIFICANCE

32. CHI SQUARE
 Looks at each cell in a cross tabulation and measures the
difference between what was observed and what would be
expected in the general population.
 Chi-square is one of the most important statistics when you
are assessing the relationship between ordinal and/or
nominal measures.
 Chi-square cannot be used if any cell has an expected
frequency of zero, or a negative integer. It can be affected
by low frequencies in cells; if cells have a frequency of less
than 5, the test might be compromised.

33. EXAMPLE
 A chi-square is the statistic being used here because the relationship
between two ordinal variables (type of library worked at and awareness
of the term EBP) is being explored.
 It is simply the mathematical calculation of the chi-square. It is used to
then derive the p-value, or significance.

34.  Df =degrees of freedom.
 Df is the number of independent pieces of data being
used to make a calculation.
 Calculated by looking at the cross tabulation and
multiplying the number of rows minus one by the
number of columns minus one (r-1) x (c-1).
 (2-1) x (5-1) = 4

35. T-TESTS
 Compares the means between two values. It tests if any
differences in the means are statistically significant or can
be explained by chance.
 T-tests are normally used when comparing two groups or
in a before and after situation .
 A t-test involves means, therefore the variable you are
attempting to measure must be a ratio variable. The other
variable is nominal or ordinal.
 Limitations
 A t-test can only be used to analyze the means of two
groups. For more than two groups, use ANOVA.

36. EXAMPLE
 use a t-test?
• A t-test is used for these variables because we are comparing the
mean of one variable between 2 groups .
• An independent samples t-test is used here because the groups being
compared are mutually exclusive - male and female.

37. F-TEST
An F-test compares the spread of results in two
data sets to determine if they could reasonably be
considered to come from the same parent
distribution . the measure of spread used in F-test
is variance which is simply the square of the
standard deviation . The variances are ratioed to
get the test value.
F=S1²/S2²

38. CORRELATION AND REGRESSION
 Correlation
 The relationship between two quantitatively
measured variables
 Change in the value of one variable, results in a
change in the other
 Magnitude or degree of relationship between two
variables is called correlation coefficient (r)

39. CORRELATION AND REGRESSION
 Types of correlation
1. r = +1
2. r = - 1
3. 0 < r < 1
4. -1 < r < 0
5. r = 0
1
65
43
2

40. CORRELATION AND REGRESSION
 Regression
 Regression coefficient – measure of change in one
character (dependent variable - Y) , with one unit
change in the independent character (X)
 Denoted by “b”
 Regression line

41. Change of dependent variable in linear way
Y = a+bX
Y = dependent variable
a = Y value
b = regression coefficient
X = independent variable