1. Field Methods of Monitoring Aquatic Systems Unit 2 – Statistics Copyright © 2008 by DBS

2. Quote All measurements have some degree of uncertainty

3. Types of Errors Systematic – values that are all higher/lower than actual value –Analyst errors –Instrument errors e.g. weighing a sample and forgetting to zero Random errors – some values that are higher, some lower –Statistical –Minimized via repitiion

4. Precision and Accuracy Accuracy Refers to how close a measurement is to the real value - has low errors Precision Measurements in close agreement i.e. reproducible - measurements have more “significant figures” - the sloppiness of measurement is the degree of precision - low RE, but may have SE

5. Standards Instruments must be calibrated against known standards to insure accuracy A very precise measurement is not necessarily accurate e.g. pH meter reading of 6.06 is more precise than pH paper but may not be as accurate

6. Question What possible sources of error are there for recording an accurate pH measurement? - meter may not have been recently calibrated - temperature of sample different to temperature of calibration solutions - meter may not have been allowed to warm up

7. Significant Figures All digits reported are expected to be known definitely except the last More precise results have more S.F.s Scientific notation is not usually used (e.g.1150 mg L -1 is preferred and not 1.15 x 10 3 mg L -1 ) See p132-133 For pH retain in the mantissa (the number to the right of the decimal point in the logarithm) the same number of SF as there are in the number whose logarithm is being found e.g. [H + ] = 1 x 10 -7, pH = -log 10 [1 x 10 -7 ] = 7.0 1 S.F.1 D.P.

8. Question Complete the following table of pH values [H + ]pHSignificant Figures 1 x 10 -7 7.01 1.0 x 10 -7 6.80 4.39 1.78 x 10 -11 1.6 x 10 -7 2 3 2 4.1 x 10 -5 2 7.00 10.750

9. Statistics Average (mean): calculated by adding all data values and dividing by the no. of measurements (N) x Median: the middle result when arranged by increasing or decreasing value X is not representative if a few values are extremely different e.g. 19 paupers and billionaire

10. Standard Deviation Standard Deviation: the spread of data around an average value

11. Relative Standard Deviation SD may be reported as a %-age of the average value RSD = s x

12. Question Given the following set of data calculate the average, standard deviation, and relative standard deviation for the data Sample No.Lead Concentration (ppm) 15.138 25.109 35.098 45.117 55.022 65.021 N = 6 x = 5.084 s = 0.050, RSD = 1 % Data is uncertain in 1/100 place and should be reported as ± 0.05 e.g. Sample 1: 5.14 ± 0.05

13. Throwing Out Data 1. Calculate x including the questionable data point 2. Calculate s 3. Assess whether the questionable data point is within 2s (2σ) of the mean 4. If it is keep the data, if not, throw it out

14. Exercise 1 1.Calculate x 2.Calculate s 3.Calculate uncertainty (2s) 4.Calculate RSD (precision) A.How should 4.325 ppm PO 4 3- be reported? B.What type of errors are present? C.Which ion concentrations are more precise? N.B. this is easily accomplished in MS Excel if you have installed the data analysis pack

15. Plotting Data Should be old hat by now

16. Plotting Data Site no.vs. conc.Correlation plots R 2 > 0.60 is meaningful Source may be gypsum

17. Exercise 2 1. Plot the data in the Anza-practice file (available from: http://academics.rmu.edu/faculty/short/envs4010/excel/Anza- practice.xls by location (4) http://academics.rmu.edu/faculty/short/envs4010/excel/Anza- practice.xls 2. Examine (via correlation plots) the connections between: (i) fecal coliform (x-axis) and the various ions (y-axis) (ii) conductivity (x-axis) and the various ions (y-axis) (iii) fecal coliform (x-axis) and conductivity (y-axis) 3. Discuss your graphs

18. Text Books Rump, H.H. (2000) Laboratory Manual for the Examination of Water, Waste Water and Soil. Wiley-VCH. Nollet, L.M. and Nollet, M.L. (2000) Handbook of Water Analysis. Marcel Dekker. Keith, L.H. and Keith, K.H. (1996) Compilation of Epa's Sampling and Analysis Methods. CRC Press. Van der Leeden, F., Troise, F.L., and Todd, D.K. (1991) The Water Encyclopedia. Lewis Publishers. Kegley, S.E. and Andrews, J. (1998) The Chemistry of Water. University Science Books. Narayanan, P. (2003) Analysis of environmental pollutants : principles and quantitative methods. Taylor & Francis. Reeve, R.N. (2002) Introduction to environmental analysis. Wiley. Clesceri, L.S., Greenberg, A.E., and Eaton, A.D., eds. (1998) Standard Methods for the Examination of Water and Wastewater, 20th Edition. Published by American Public Health Association, American Water Works Association and Water Environment Federation.