STATISTICAL TOOLS USED IN ANALYTICAL CHEMISTRY

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

References1. www.fao.org/docrep/w7295E/w 7295e08.htm

2. www.inorganicventures.com

3. Statistical process control charts by Dr.Scott Sampson @2012

4. Quantitative Toch for service operations management by Dr.Scott Sampson@2012

5. Skoog/west Fundamentals of analytical chemistry by F.James holler and Stanley

R.Crouch

6. Applied statistics in chemistry.doc by Roy Jensen 2002

7. Abraham, B., & Ledolter, J. (1983). Statistical methods for forecasting. New York:

Wiley.

8. Adorno, T. W., Frenkel-Brunswik, E., Levinson, D. J., & Sanford, R. N. (1950). The

authoritarian personality.New York: Harper.

9. Agrawal, R., Imielinski, T., & Swami, A. (1993). Mining association rules between sets

of items in large databases. Proceedings of the 1993 ACM SIGMOD Conference,

Washington, DC.

10. Agrawal, R. & Srikant, R. (1994). Fast algorithms for mining association

rules. Proceedings of the 20th VLDB Conference. Santiago, Chile.

11. Agresti, Alan (1996). An Introduction to Categorical Data Analysis. New York: Wiley.

12. Akaike, H. (1973). Information theory and an extension of the maximum likelihood

principle. In B. N. Petrov and F. Csaki (Eds.), Second International Symposium on

Information Theory. Budapest: Akademiai Kiado.

13. Akaike, H. (1983). Information measures and model selection. Bulletin of the

International Statistical Institute: Proceedings of the 44th Session, Volume 1. Pages 277-290.

14. Aldrich, J. H., & Nelson, F. D. (1984). Linear probability, logit, and probit models. Beverly

Hills, CA: Sage Publications.

15. Almon, S. (1965). The distributed lag between capital appropriations and

expenditures. Econometrica, 33, 178-196.

16. American Supplier Institute (1984-1988). Proceedings of Supplier Symposia on Taguchi

Methods. (April, 1984; November, 1984; October, 1985; October, 1986; October, 1987; October,

1988), Dearborn, MI: American Supplier Institute.

17. Anderson, O. D. (1976). Time series analysis and forecasting. London: Butterworths.

18. Anderson, S. B., & Maier, M. H. (1963). 34,000 pupils and how they grew. Journal of

Teacher Education, 14, 212-216.

19. Anderson, T. W. (1958). An introduction to multivariate statistical analysis. New York: Wiley.

20. Anderson, T. W. (1984). An introduction to multivariate statistical analysis (2nd ed.).

21. Anderson, T. W., & Rubin, H. (1956). Statistical inference in factor

analysis. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and

Probability. Berkeley: The University of California Press.

22. Andrews, D. F. (1972). Plots of high-dimensional data. Biometrics, 28, 125-136.

23. ASQC/AIAG (1990). Measurement systems analysis reference manual. Troy, MI: AIAG.

24. ASQC/AIAG (1991). Fundamental statistical process control reference manual. Troy,

MI: AIAG.

25. AT&T (1956). Statistical quality control handbook, Select code 700-444. Indianapolis,

AT&T Technologies.

THANK YOU