0.30 0.25 0.20 0.15 0.10 0.05 0.00 Y = 0.0469X + 0.0282 R 2 = 0.92 0 2 4 6 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 Y = 0.0097X + 0.0211 R 2 = 0.9726 0 10 20 30 40 A Figure A3-2 Suspend solids (m g /l) by Standard M ethod B Suspend Solid (m g /l) by Standard M ethod Standard curve for suspended solids (mgl -1 ) versus absorbance at 810 nm in samples taken from effluents of CGF pilot units (A) and Full scale plants (B). Samples were taking again from CGF effluents and were analysed for SS with both Gooch and spectrophometric methods. The obtained results were used to validate spectrophometric method. Descriptive statistics of data originated from pilot plant samples are presented in table A3-1. These data have a lineal regression given by the equation Y = 0.047X + 0.028 (r 2 = 0.92), in which Y and X are suspended solid values obtained by the spectrophometric and Gooch methods respectively. The data originated from full-scale plants have a lineal regression given by the equation Y = 0.0097X + 0.0211 (r 2 = 0.97). Table A3-1 Descriptive statistics of SS measurements (mgl -1 ) with samples taken from effluents of CGF pilot units using both Gooch and spectrophometric methods. Descriptive Statistic Method Gooch Spectrophometric Mean 2.82 2.75 Standard Deviation 2.46 2.50 Minimum 0.40 0.10 Maximum 12 11 Data (number) 58 58 Based on the results obtained with samples from both pilot and full-scale plants the spectrophometric method was used for SS measurements with samples having low turbidity values, below 20 NTU. Comparison between the statistical evaluation for gravimetric and spectrophometric methods was made with t-student test verifying that the slope of these line will be 1. The result with 5% of statistical significance level indicate that does not exist statistic evidence for disprove the hypothesis. Applying the same test and statistical significance level, the result indicated that does not exist statistical evidence for deny that the Y intercepted was 0. In others words, with 5% of statistical significance level, both procedures can be used to estimate SS concentrations. Furthermore, the adopted spectrophometric method can be used for the determination of suspended solids when great amount of analyses are required because is faster than the volumetric procedure described and recommended in the Standard Methods. References APHA, AWWA and WPCF, (1989). Satandard Methods for the Examination of Water and Wastewater. Joint Editorial Board. Washington, DC 20005. USA. Sawyer, C.; McCarty, P., and Parkin, G, (1994). Chemistry for Environmental Engineering, McGraw Hill International Editions, Fourth edition. USA. Krawzyk, D. and Gonglewski, N, (1959). Sewage and industrial wastewater, Vol. 31, Pp 1159-1164. A3-2
Annex 4: Example of F-Test (Analysis of Variance) application This example presents an application of F-Test (Analysis of Variance) to mean suspended solids (SS) removal efficiencies in DyGF units during Phase I, Period I, of this research work. The statistical model used is the randomised block design as represented by equation A4-1.(Vargas, 1991) Yij = µ + τi + βj + εij (A4-1) Y ij: SS removal efficiencies in i-treatment levels (i = 1,2,3, because three DyGF filtration rates were tested during Period I) with j-blocks (j = 1,2,3,4,.......,33, because there were b = 33 blocks, sampling sessions or repetitions per each filtration rate during Period I). µ: Mean SS removal efficiency of all Y ij values, without distinguishing between treatment levels. τ i : Effect due to i-treatment level. In this case i takes values between 1 and 3. τ i represents D y GF filtration rate i tested during Period I: τ 1 . = 0.9mh -1 , τ 2 = 1.3 mh -1 , and τ 3 = 1.4 mh -1 , (t = 3). β j : Effect due to block j of observed values in each sampling session, with j changing from 1 to b, b = 33 SS-sampling sessions during Period I. ε ij : Random variation associated with the i-treatment level in the j-block of observed values (the experimental error) The basic assumption (null hypothesis) used to apply the model described in the equation A4-1 is that all observed values during test runs, divided among several groups according to treatment levels and sampling sessions, are all from the same population. This means that there are not statistically significant differences between the group means. In this case the null (H o ) and the alternate (H a ) hypotheses are as follows. H 0 : τ 1 = τ 2 = τ 3, Ha: τ i ≠ τ k (i≠k), filtration Rate differences in DyGF units do not imply statistically significant differences in the mean SS-removal efficiencies of all DyGF units, Vs, filtration Rate differences in DyGF units does imply statistically significant differences in at least a pair of DyGF mean SS-removal efficiencies. The process to accept or reject the null hypothesis (H o ), with an established level of significance (α), involves the F-Test, after the British statistician, Sir Ronald A. Fisher, who developed the method called analysis of variance (ANOVA) on which the F-test rests (Fisher, 1947, quoted by Mesa, 1999; Rowntree, 1981). The calculations required by the ANOVA technique to decide about Ho are summarised in the table A.4-1 Table A4-1 Summary of Analysis of Variance (ANOVA) with the randomised blocks design. Source of Variation Degrees of Freedom Sum of squares (SS) Mean square (MS) F c Treatment (between) t –1 SSTreat SSTreat/(t –1) = MSTreat MSTreat / MSE Blocks (between) b – 1 SSBlocks SSBlocks/(b – 1) = MSBlocks MSBlocks / MSE Error (within) (t –1)(b –1) SSE SSE/((t –1)(b –1)) = MSE Total tb - 1 SST H 0 is rejected when F c > F (α, t-1, (t-1)(b-1)), where F (α, t-1, (t-1)(b-1)) is the F-distribution with t-1 and (t-1)(b-1) degrees of freedom for the numerator and denominator respectively. α is the significance level of the test. A general notation for the observed data used in this example is shown in the table A.4-2. A4-1
We are a wholesale supplier of products, solutions and services in water treatment.
We provide only businesses companies such as distributors, retailers, manufacturers and assemblers.
A catalog that includes products carefully selected from the most prestigious brands in the Water Treatment market, operative site, personalized services, logistics precise and efficient, flexible organization, but also the basic importance that is attributed to human factors and relationships with partners, are of Sinergroup Srl a reference for many companies of the sector.