Dr. Reem M. Alghanmi

2017 1st term

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Statistics and Spreadsheets

in Analytical Chemistry

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Standard Deviation of a Finite Set of

Experimental Data

Estimated Standard Deviation, s (N < 30)

For finite sets the precision is represented by s.

Standard deviation of the mean smean : or standard error

Relative standard deviation (%RSD): or coefficient of variation

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)( 2

N

xxs

i

N

sSEsmean

100% x

sCVRSD

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Confidence Intervals. How sure are you?

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Tests of Significance. Is there a difference?

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Example :

Determination of Cu in biological materials using new method by AAS,

the SRM Certified value = 11.7 ppm

Experimental results: 10.8± 0.7 ppm (N= 5)

Compare to ttable; df = 5- 1 = 4 at 95% CL

ttable(df=4,95% CL) = 2.776

If |tcalc| < ttable, results are not significantly different at the 95% CL.

If |tcalc| ttable, results are significantly different at the 95% CL.

For this example, tcalc t table, so experimental results are significantly different at the

95% CL, so there is a determined error in the new method.

875.27.0

5)7.118.10()(

s

Nxt

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Note that the F test can be used to simply

test whether or not two sets of data have

statistically similar precisions or not.

Can use to answer a question such as:

Do method one and method two provide

similar precisions for the analysis of the

same analyte?

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Example:

For a new colorimetric method for determining the glucose content of blood

serum. If N1 =7and N2 =6 , Let s1 = 2.88 and s2 = 2.19

Compare Fcalc to Ftable at df = (7-1, 6-1) = 6,5 and 95% CL.

If Fcalc Ftable, std. devs. are not significantly different at 95% CL.

If Fcalc Ftable, std. devs. are significantly different at 95% CL.

Ftable(df=6,5; 95% CL) = 4.95

Since Fcalc (1.73) < Ftable (4.95), std. devs. of the two sets of data are not

significantly different at the 95% CL (Precisions are similar.), the SD are from

the random error alone and don’t depend on the sample.

73.18.4

3.8

)19.2(

)88.2(2

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2

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1 s

sFcalc

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The Q Test for an Outlier

The Q test is used to determine if an “outlier” is due to a

determinate error. If it is not, then it falls within the expected

random error and should be retained.

Requires 4 or more data points to apply.

Calculate Qcalc and compare to Qtable

a = difference between “outlier” and nearest sorted result

w = range of results.

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w

aQcalc

QCalc = outlier difference/range.

If QCalc > QTable, then reject the outlier as due to a systematic error.

©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley)

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Consider set of data; Cl- values in pooled serum sample:

103, 106, 107, and 114 meq/L, one value appears suspect (outlier).

Determine if it can be ascribed to accidental error, at 95% CL.

The questionable data point (outlier) is 114

Compare Qcalc to Qtable for n observations and desired CL.

Qtable (n=4,95% CL) = 0.829

64.0)103114(

)107114(

w

aQcalc

Example 3.20:

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If Qcalc < Qtable, do not reject suspect data point at stated CL.

If Qcalc Qtable, reject suspect data point at stated CL.

From previous example,

Qcalc (0.64) Qtable (0.829), so the data point should not be rejected

at 95% CL.

Grubbs Test for an Outlier

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