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Statistical analysis & errors (lecture 3)
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- 2. What is statisticalanalysis ? The science that deals with the collection, analysis, and interpret ation of numerical data, often using probability theory. The data themselves In data there is always errors due to human and instrumental errors some can be corrected and avoided but some can not because they are inderminate
- 3. Determinate Errors—They Are Systematic Determinateor systematic errors are nonrandom and occur when something is intrinsically wrong in the measurement. They can be avoided or corrected
- 4. Measurements errorscan be divided into two components Non random errors Systematic errors
- 5. Non Randomerror They have slight order. Systematic error repeatable error associated with faulty equipment or a flawed experiment design. These errors are usually caused by measuring instruments that are incorrectly calibrated or are used incorrectly.
- 6. Determinate errors(systematic errors) are those that, as the name implies, are determinable means they can be corrected or avoided. 1) Mis-calibration of apparatus. This can be removed by checking the apparatus against a standard. (2) Faulty observation. This is avoidable, and therefore should not be cited as a source of error in any well-performed experiment.
- 7. The errorcan be proportional to sample size or may change in a more complex manner Variation are usually unidirectional As in the case of solubility loss of precipitate due to its solubility . Such an example is the change in solution volume and concentration occurring with changes in temperature. This can be corrected for by measuring the solution temperature. Such measurable determinate errors are classed as systematic errors.
- 8. Inderminate errors orrandom errors Inderminate errors are always random errors and can not be avoided Random errors ( inderminate) It is caused by inherently unpredictable fluctuations in the readings of a measurement apparatus or in the experimenter's interpretation of the instrumental reading.
- 9. Random errorsare often called as accidental error. Random errors are indeterminate which means they can not be determined/ calculated. But, we can make a certain conclusion about these random errors by applying mathematical more precisely statistical rules.
- 10. Gaussian curve Statistical rulewhich is applied to make a conclusion about random errors is normal distribution curve often called as Gaussian distribution curve. Y axis (pdf) Probabality Denstiy Function x –axis (variables) standard deviation from the mean
- 11. Significant figures Definition the number of digits necessary to express the results of a measurement consistent with the measured precision. Since there is uncertainty in any measurement of atleast +_ 1 in the last significant figures. Rules Non-zero digits are always significant. Any zeros between two significant digits are significant. Zeros on the left side are always non-significant while zeros on right side always significant.
- 12. For example 0.216Three significant figures 90.7 Three significant figures 800.0 Four significant figures 0.0670 Three significant figures
- 13. Rounding off data Definition. Rounding off is a kind of estimating. To round off decimals: Find the place value you want (the "rounding digit") and look at the digit just to the right of it. If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it. For example 4.7892 rounding of data into two decimal = 4.8
- 14. Mean, Median, Mode Mean. Thesum of a group of measurements divided by the number of measurements; the average. Mode. The most frequently occurring value in the group of measurement. 2, 3, 4, 2, 5, 2, 7, 5, 2 so 2 is mode in it Median. In a even data set, the median is the average of two middle numbers. 2, 4, 6,8,10 then 6 is median here
- 15. What is standarddeviation For a series of ‘n’ measurement of the same measurand, the quantity S characterizing dispersion of results X= measutrements X = mean N= numbers
- 16. Tests F-test: isused to determinate when two variances are satisfactorily different from each other . F= S / S2 T-test Is used to determinate when two sets are satisfactorily different. Q-test Is used to determine when outlier is due to determinate error. If it is not , then falls within expected random error and should be retained.
- 17. QC/QA A goodlaboratory practice (GLP) means who is defining for and what purpose. A good laboratory should have Management Personnel Facilities Equipment Operation Method validation Quality assurance
- 18. Good laboratorypractices have been established by worldwide bodies such as the Organization for Economic Cooperation and Development (OECD) and the International Organization for Standardization (ISO). Government agencies have adopted them for their purposes as rules that must be followed for laboratories involved in analyzing substances that require regulation. Examples are pharmaceutical formulations, foods, and environmentally important samples.
- 19. GLPs GLPs (good laboratory practice) a body of rules, operating procedures, and practices established by a given organization that are considered to be mandatory with a view to ensuring quality and correctness in the results produced by a laboratory. GLP ensures correct results are reported.
- 20. The laboratoryshould have two things 1. SOPs ( standard operating procedures) 2. QAU (quality assurance unit)
- 21. SOPs Standard operatingprocedures provide detailed descriptions of activities performed by the laboratory. 1) sample custody chain 2)sample handling and preparation 3) the analytical method 4) instrument maintenance 5) record keeping
- 22. QAU (quality assuranceunit) The QAU is responsible for assuring good laboratory practices are implemented. Everyone in the lab is responsible for following them.
- 23. Validation of analyticalmethods Validation process 1) selectivity 2) Linearity 3) accuracy 4) Precision 5) Sensitivity
- 24. 6) Range 7)Limit of detection (LOD) 8) Limit of quantitation 9) Ruggedness or robustness
- 25. Selectivity Selectivity isbasically the extent that the method can measure the analyte of interest in the matrices of sample being analyzed without interference from the matrix. Matrix effect may be either positive or negative Matrix Matrix is everything in a sample except the actual analyte
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- 29. The sensitivity isdetermined by slope of the calibration curve and generally reflects the ability to distinguish two different concentrations You can measure slope or measure sample of closely related conc. At high, intermediate, and low concentrations
- 31. Range Range isactually an interval between upper and lower concentrations of analyte in sample
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