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STATISTICAL TOOLS USED IN ANALYTICAL CHEMISTRY
G.S.Nithej,b.pharm,s.p.s.p
STATISTICS
Definition
Introduction
Statistics Importance
Analytical Chemistry
Need Of Statistics
Error is the collective noun for any departure of the result from the true value.
Error
Bias
Accuracy
Precision
The “Trueness” or the ‘’closeness’’ of the analytical result to the true value.
The consistent deviation of analytical results from the true value caused by systemic errors in a procedure
The closeness with which results of replicate analysis of a sample agree.
Measures of central tendency and results
Mean
Standard deviation
Relative standard deviation
Confidence limits
Propagation of errors
I. Propagation of Random errors
II. Propagation of Systematic errors
1.Summation calculations2.Multiplication calculations
• The calculation of Kjeldahl-Nitrogen may be as follows
Statistical Process Control Analysis: Control Charts
Types of Control charts
X-bar Charts
R- Charts
P-Charts
C-Charts
X-Charts
R-Charts
P-Charts and c-charts These are the control charts for attributes, which
are not continuous variables but are things that can be counted.
A p-chart and c-chart considers the portion of a sample that is defective, where each item in the sample is either defective or not.
Confidence levels If we want to reduce the risk of falsely categorizing
a good result as not being significant, we can use a higher confidence level.
To reduce the risk of falsely categorizing a non-significant result as significant, we can use a lower confidence level.
Statistical tests
Two-sided vs One-sided test
F-test for Precision
t-Test for bias
Linear correlation and regression
Analysis of variance (ANOVA)
Two-sided vs one sided test
These tests for comparison, for instance between methods A and B, are based on the assumption that there is no significant difference.
1. Are A and B different ? (Two-sided test)
2. Is A higher or lower than B ? (One-sided test).
t-Test1.Students t – test. Student's t-test for comparison of two independent sets of data with very similar standard deviations.
2.Paired t – test
The paired t-test for comparison of strongly dependent sets of data.
F-TestThe F-test (or Fisher's test) is a comparison of the spread
of two sets of data to test if the sets belong to the same
population, in other words if the precisions are similar or
dissimilar. These are calculated by:
df1 = n1-1
df2 = n2-1
Linear correlation and regression
1. When the concentration range is so wide that the
errors, both random and systematic, are not
independent which is the assumption for the t-tests.
2. When pairing is inappropriate for other reasons,
notably a long time span between the two analyses.
ANOVA
When results of laboratories or methods are
compared where more than one factor can be
of influence and must be distinguished from
random effects, then ANOVA is a powerful
statistical tool to be used.
Summary Statistics
Need of statistics
Measures of central tendancy and results
Statistical process control analysis : control charts
Statistical tests
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