Q & a – Accuracy and Precision

Food Analysis – FScN 4312W Laboratory: Assessment of Accuracy and Precision Key to Questions 1. Theoretically, how are standard deviation, coefficient of variation, mean, percent relative error, and 95% confidence interval affected by: (1) more replicates, and (2) a larger size of measurement? Was this evident in looking at the actual results obtained using the volumetric pipettes and the buret, with n = 3 vs n = 6, and with 1mL vs 10mL? Ans: (1) As the sample size increases (more replicates) - Calculated mean approaches the true mean - Standard deviation is inversely proportional to the square root of sample size, hence it decreases - CV decreases, as standard deviation approaches 0 for larger sample size - % Relative error decreases as calculated mean approaches true mean - 95% confidence interval narrows down (2) Larger size of measurement - Mean is close to true mean - Standard deviation might be larger due to larger size - CV decreases - % Relative error decreases, as calculated mean is close to true mean - 95% confidence interval narrows down Not all of the above assumptions were confirmed in this experiment according to the data observed. One reason could be that the sample size was very small (n = 3 and n = 6), to notice significant differences, another reason could be human error and variation from one person’s measuring technique to another. 2. Why are percent relative error and coefficient of variation used to compare the accuracy and precision, respectively, of the volumes from pipetting/dispensing 1 and 10mL with the volumetric pipettes and buret in parts 2 and 3, rather than simply the mean and standard deviation, respectively? Ans: Mean calculated from the readings gives the calculated mean, which may differ from the true mean. Although good precision is obtained, accuracy is not guaranteed. On the other hand, percent relative error calculates the error in the calculated mean with respect to the true mean. Hence, percent relative error gives more information about how close the calculated mean is to the true mean. Co-efficient of variation (C.V) provides information about how much the standard deviation is different form the calculated mean in terms of percentages. For example, if mean = 2 and standard deviation = 0.1, then C.V = 0.05*100 = 5%. Therefore, we can infer that standard deviation is 5% off from the calculate mean. Depending on the coefficient of variation we can reject the data. Usually, 5% is the cutoff for accepting the data. But, we cannot vaguely reject the data based on standard deviation. Standard deviation can be large for large measurements and relatively small for small measurements. We cannot reject the data on the fact that standard deviation is large for large measurements as compared to small measurements, unless C.V is calculated. Hence, C.V is more useful parameter in data analysis as compared to standard deviation. 3. Compare and discuss the accuracy and the precision of the volumes for the 1mL pipetted/dispensed using a volume pipette, buret, and mechanical pipettor (parts 2, 3, and 4). Are these results consistent with that what would be expected? Volumetric pipette had more accuracy as compared to buret and mechanical pipette. Also, as the sample size increased accuracy also increased for volumetric pipette and buret, but there was no large change in the accuracy of mechanical pipette. This does not comply with what is expected as mechanical pipette is supposed to be more accurate than volumetric pipette and buret. Perhaps the mechanical pipette needed calibration. On the other hand, the precision of mechanical pipette is better than buret and volumetric pipette which is expected. This can be attributed to the fact that, human error in mechanical pipette is much less. Generally, precision increases as sample size increases. 4. If accuracy and / or precision using the mechanical pipettor are less than should be expected, what would you do to improve its accuracy and precision? Ans: - Follow the instructions of how to use a mechanical pipettor closely - Calibrate 5. In a titration experiment using a buret, would you expect to use much less than a 10mL volume in each titration? Would you expect your accuracy and precision to be better using a 10mL buret or a 50mL buret? Why? Ans: Large volumes are associated with small errors, i.e. the error due to 1mL in 10mL titration is 10%, whereas the error due to the same 1mL in 100mL titration is 1%. Thus, we can reduce the magnitude of error by increasing the measuring capacity. Thus, it is best to use diluted reagents and therefore need a larger volume of the titrant to reach the end point. However, when less than 10 mL is needed to reach the end point it is recommended to use 10mL buret as it is more graduated than a 50mL buret. Thus, small amounts can be dispensed more accurately from a 10mL buret as compared to a 50mL buret. 6. How do your results from part #5 of this lab differentiate “to contain” and “to deliver”? Is a volumetric flask “to content” or “to deliver”? Which is a volumetric pipette? Ans: Glassware is termed “to deliver” if it can dispense the entire amount of solvent it contains, ex: buret. Whereas, some glassware can only store solvents, upon transfer of the solvent from this glassware to another, the entire amount is not transferred. Volumetric flask is “to contain” and volumetric pipette is “to deliver”. 7. From your results from part #6 of this lab, would you now assume that since a balance reads a 0.01 g that it is accurate to 0.01 g? Ans: Not really. One balance can read 50 g standard weight as 50.02 g and another read 49.93 g. The error may be due to instrument and hence cannot be avoided. Not to forget also that the last figure might have been rounded up. Also, the balances have to be regularly calibrated. 8. What sources of error (human and instrumental) were evident or possible in parts #2-4, and how could these be eliminated or reduced? Explain? Ans: Systematic errors: This error explains the difference between precision and accuracy. The results will be consistent but away from the true value. In other words, the results would be precise but won’t be accurate. Identifying this type of error is very difficult as they are related to faulty instruments, or non-calibrated equipment. Sometimes, human error can also lead to systematic error; one example is that of buret. The proper way of taking readings from a buret is to make sure that the bottom of the meniscus of the liquid is touching the top of the line you wish to measure. If this rule is not followed every titration will be associated with an error of 0.2mL, although consistent results are obtained. Other example is parallax error, which can be avoided by ensuring that viewer's eyes are at the level of the graduation. These types of errors can also be reduced by proper calibration of the instruments. Random errors: Natural errors associated with instrument type or model, and all with each experimenter’s techniques. These are impossible to avoid, but usually they are very small. Blunders: Can be easily identified, as they are very obvious. These types of errors include using a wrong reagent or instrument. This type of error is mainly caused by human negligence, therefore proper practice and being careful will eliminate these kinds of errors. 9. You are considering adopting a new analytical method on your lab to measure the moisture content of cereal products. How would you determine the precision of the new method and compare it to the old method? How would you determine (or estimate) the accuracy of the new method? Ans: - Have multiple replications and then calculate and compare the standard deviation/coefficient of variation and % relative error of the data produced by the old and new method. - Compare the data obtained from the new method with that of the data present in literature (or) from data obtained by employing standard or official methods. - Run a standard reference analysis using the new method and compare the result to that of the previous method. .

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