In a murder trial in the 1990s, the defendant\'s blood was found at the crime sc

Question

In a murder trial in the 1990s, the defendant's blood was found at the crime scene. The prosecutor argued that blood was left by the defendant during the crime. The defense argued that police "planted" the defendant's blood from a sample collected later. Blood is normally collected in a vial containing the metal-binding compound EDTA as an anticoagulant with a concentration of ~4.5 mM after the vial has been filled with blood. At the time of the trial, procedures to measure EDTA in blood were not well established. Even though the amount of EDTA found in the crime-scene blood was orders of magnitude below 4.5 mM, the jury acquitted the defendant. This trial motivated the development of a new method to measure EDTA in blood.(a) To measure accuracy and precision of the method, blood was fortified with EDTA to known levels.

For each of the three spike levels in the table below, find the precision and accuracy of the quality control samples.

A)

Explanation / Answer

Solution:

Part (a)

The solutions are calculated using the given precision and accuracy formulae,

for 22.2 ng/ML { mean value = (33.3+19.5+23.9+20.8+20.8)/5 = 23.66 }

Accuracy = 100*(23.66 - 22.2) / 22.2 = 6.57 %

To calculate the Variance, take each difference, square it, and then average the result:

Variance = {(33.3-23.66)2+(19.5-23.66)2+(23.4-23.66)2+(20.8-23.66)2+(20.8-23.66)2} / 5

              = 25.227

Sts.Deviation = (Variance)0.5

                    = (25.227)0.5

                           =5.0226

Precision = 100* (5.0226 / 23.66)

               = 21.228 %

for 88.2 ng/ML { mean value = (83.6+69.0+83.4+100+76.4)/5 = 82.48 }

Accuracy = 100*(82.48 - 88.2) / 88.2 = - 6.48 % {negative sign means error in accuracy}

To calculate the Variance, take each difference, square it, and then average the result:

Variance = {(83.6-82.48)2+(69.0-82.48)2+(83.4-82.48)2+(100-82.48)2+(76.4-82.48)2} / 5

              = 105.545

Sts.Deviation = (Variance)0.5

                    = (105.545)0.5

                           = 10.273

Precision = 100* (10.273 / 82.48)

               = 12.455 %

for 314 ng/ML { mean value = (322+305+282+329+276)/5 = 302.8 }

Accuracy = 100*(302.8 - 314) / 314 = - 3.567 % {negative sign indicates error in accuracy}

To calculate the Variance, take each difference, square it, and then average the result:

Variance = {(322-302.8)2+(305-302.8)2+(282-302.8)2+(329-302.8)2+(276-302.8)2} / 5

              = 442.16

Sts.Deviation = (Variance)0.5

                    = (442.16)0.5

                           = 21.027

Precision = 100* (21.027 / 302.8)

               = 6.944%

Part (b)

Mean = 52.0

for 31.28 ng/ML { calculated from the given concentratino}

Accuracy = 100*(52 - 31.28) / 31.28 = 66.24 %

To calculate the Variance, take each difference, square it, and then average the result:

Variance = {(175-52)2+(104-52)2+(164-52)2+(193-52)2+(131-52)2+(189-52)2+(155-52)2+(133-52)2+(151-52)2+(176-52)2 / 10

              = 10223.9

Sts.Deviation = (Variance)0.5

                    = (10223.9)0.5

                           = 101.11

Precision = 100* (101.11 / 41.22)

               = more than 100% mot possible for the given dimensionless reading

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