Comparability- how to Q&C skills Workshop 1 2 Some examples of - PowerPoint PPT Presentation

1 Comparability- how to Q&C skills Workshop 1

2 Some examples of ‘normalisation’ ● Proportions ○ comparing relative content or rescaling between a minimum and maximum (unity-based) ● Standardisation (z scores) ○ to compare values from different normal distributions ● Coefficient of variation ○ a standardised measure of variance to compare repeatability ● Log to base 2 ○ for ratio data to be comparable for increases and decreases ● Subtraction of noise/background ● Scaling ○ Accounting for dilution or ‘half-measures’; reversing experimental steps ● Specific normalisation methods ○ particular functions or combination or above

3 Proportions Of a total: > relativebonemass <- bonemass / totalmass

4 Proportions scaled: unity-based normalisation Original Mark : 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 63 65 values Frequency: 1 3 3 3 8 3 8 13 11 24 19 17 24 25 20 17 25 13 14 18 12 5 5 4 3 1 1 To get proportion > newmark <- round((x1 - min(x1))/ (max(x1)-min(x1)),digits = 2) (unrounded) use Mark : 0 0.04 0.07 0.11 0.14 0.18 0.21 0.25 0.29 0.32 0.36 0.39 0.43 0.46 0.5 0.54 0.57 0.61 0.64 0.68 0.71 0.75 0.79 0.82 0.86 0.89 0.93 0.96 1 Frequency: 1 1 2 1 5 2 7 7 5 11 12 10 17 22 25 25 19 29 19 14 21 16 12 6 4 4 1 1 1 To get rounded > newmark <- round(100*(x1 - min(x1))/ (max(x1)-min(x1)),digits = 0) % Mark : 0 4 7 11 14 18 21 25 29 32 36 39 43 46 50 54 57 61 64 68 71 75 79 82 86 89 93 96 100 Frequency: 1 1 2 1 5 2 7 7 5 11 12 10 17 22 25 25 19 29 19 14 21 16 12 6 4 4 1 1 1

5 Standardisation: z scores > summary(x1) Min. 1st Qu. Median Mean 3rd Qu. Max. 4.510 8.500 9.820 9.727 11.180 13.490 Difficult to compare > summary(x2) Min. 1st Qu. Median Mean 3rd Qu. Max. 25.10 61.99 70.50 70.32 81.59 98.48 > newx1 <- (x1 - mean(x1))/sd(x1) > newx2 <- (x2 - mean(x2))/sd(x2) > summary(newx1) Min. 1st Qu. Median Mean 3rd Qu. Max. -2.49600 -0.58710 0.04429 0.00000 0.69480 1.80000 > summary(newx2) Min. 1st Qu. Median Mean 3rd Qu. Max. -3.12700 -0.57590 0.01275 0.00000 0.77930 1.94700 Can compare

6 Coefficient of variation Are measurements of concentration repeatable? > concA [1] 0.0394 0.0396 0.0335 0.0370 0.0387 0.0343 0.0443 0.0397 0.0335 0.0378 0.0405 0.0325 0.0356 0.0379 0.0306 > concB [1] 19.65 20.66 22.43 20.88 24.98 17.67 22.11 19.49 19.34 16.10 19.30 21.87 19.53 19.96 20.34 > var(concA) Variance is on same scale as the measure thus hard to [1] 1.318924e-05 > var(concB) compare [1] 4.350792 Coefficient of variation: CV is approximately equal ~10% > sd(concA) / mean(concA) [1] 0.09817172 Measurements are equally repeatable > sd(concB) / mean(concB) [1] 0.1028156

7 Log 2 > value [1] 0.015625 0.031250 0.062500 0.125000 0.250000 0.500000 1.000000 [8] 2.000000 4.000000 8.000000 16.000000 32.000000 64.000000 > logvalue <- log2(value) > logvalue [1] -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6