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

Comparability- how to

Q&C skills Workshop 1

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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

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Proportions

> relativebonemass <- bonemass / totalmass

Of a total:

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Proportions scaled: unity-based normalisation

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 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

> newmark <- round((x1 - min(x1))/ (max(x1)-min(x1)),digits = 2) > newmark <- round(100*(x1 - min(x1))/ (max(x1)-min(x1)),digits = 0)

To get proportion (unrounded) use To get rounded %

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Original values

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 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

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 > summary(x2)

• Min. 1st Qu. Median Mean 3rd Qu. Max.

25.10 61.99 70.50 70.32 81.59 98.48

Difficult to compare

> 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

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Coefficient of variation

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> 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) [1] 1.318924e-05 > var(concB) [1] 4.350792

Variance is on same scale as the measure thus hard to compare Are measurements of concentration repeatable? Coefficient of variation:

> sd(concA) / mean(concA) [1] 0.09817172 > sd(concB) / mean(concB) [1] 0.1028156

CV is approximately equal ~10% Measurements are equally repeatable

Log2

> 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

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