Practicing Quality Control in a Bioanalytical Experiment Juliana Marcos, Angel Nos, and Miguel Valcarcel Department of Analytical Chemistry, University of Cordoba, E-14004 Cordoba, Spain The quality of analytical results frequently requires assessment, which has fostered treatment of this subject in a host of chemical books for students. Accordingly, new experiments need he devised in order to help students to adapt to it. This paper presents a straightforward exercise to demonstrate how quality control and the analysis of variance technique are implemented in practice. The exercise also is attractive because the analyte (chlorophyll)is determined in real samples (plants) that students can collect by themselves. In this way, they can realize the significance of sampling and learn how to do it properly Statistical Methods Quality control programs rely on various statistical procedures and principles. Calibration with standard solutions is a basic step of the analytical process in which regression analysis is customarily used (1).At a later stage, sample analysis can be monitored continuously in order to ensure that it is performed under statistical control (i.e., measurements can be subject to random errors but not systematic errors). For this purpose, a control sample (a standard with a time-stable concentration) is used to monitor the measurement process. At the beginning, the signal produced by the control sample is measured a significant number of times (from 10 to 15). The collected data are used to calculate concentrations from calibration equations, and the mean (Z) and standard deviation (s) for the control sample are obtained. Control Charts The statistical values obtained for the control sample are used to construct control charts [Shewhart and Cusum graph (2, 311. The Shewhart chart (4) is used more frequently than the Cusum chart. In a Shewhart chart, the concentration of the control sample is plotted against the
a1
number of sample (the control sample is analyzed a t regular intervals between samples). The mean value (G) is marked on the graph, in addition to four horizontal lines at Z f 2s and Z f 3s called "warning lines" (upper and lower) and "action lines" (upper and lower), respectively If the analytical process is under statistical control, all the values obtained will he within the Z i 3s range. However, if two consecutive values are outside the Z k 2s interval, the results are subject to a significant systematic error (when both points lie on the same side) or a major random error (when they lie above and below the Z value, respectively). If only a single point lies outside the Z f 3s range, then the measuring system is out of control and must be corrected before any new results are delivered. Analysis of Variance (ANOVA) The analysis of variance (ANOVA) is a statistical test used to compare the mean results obtained for the influence of several possible effects operating simultaneously (2, 5).ANOVA is used to identify and estimate the different random sources of variation that occur in both sampling C%etween-samples")and analysis ("within-samples"). The general procedure is well described in monographs as references 2 and 3 (moreover, adapted to computer programs, such as STATGRAPHICS).The variances obtained betweensamples and within-samples finally are compared through the F-test (6).The experimental value thus obtained is evaluated by comparison with the critical Fvalue (7).If the calculated F values are greater than the critical F value (tabulated) there is a significant difference between the means for the samples, and at least one sample would give a result different from the rest. This may reflect nonhomogeneity in the analyte content in the samples or some error in the sampling scheme used.
R,:- C H 3 (Chlorophyll a ) - c ~ o(Chlorophyll b )
Figure 1. Formula (a)and spectra (b) of chrorophyll a and b Volume 72 Number 10 October 1995
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Table 1. Results Obtained for the Control Sample of Chlorophyll a and b while the Samples Were Being Analyzed
Four-Step Experimental Procedure 1. Sampling, 2. Sample treatment, 3. Calibration and analysis, and 4. Data processing and evaluation (quality control and analysis of variance). Solutions and Instruments
An acetone solution (80% vlv in water) and standard solutions of chlorophyll a and b were used. A Hewlett-Packard 8452A diode array spectrophotometer was used for absorbance measurements.
Chlorophyll a Control sample number
target value=3.13gl-';
Cb
0.00
1.oo 0.97 0.99 0.98 0.97 0.98 0.97
- 0.06 +0.02
- 0.01 +0.01 +0.03 +0.02
Sample Treatments
A,, A,,,
+ 17.11C, + 45.60Cb = 0.0014 + 81.91C, + 10.33Cb
= 4.0143
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Set
Chlorophyll a
Chlorophyll b
#I #2 #3
3.265 77.443 3.045
1.157 34.916 0.973
Journal of Chemical Education
Cb-target value +0.02
- 0.01 +0.01 0.00 - 0.01 0.00 - 0.01
Table 2. Concentrations of Chlorophyll a and b Found in the Blade Samples (Results in mg Chlorophyll per gram of Blade) Sample
Chlorophyll a
I
Chlorophyll b
Set #I
Set 82 1 2 3 4 5
Set #3
where C, and Cbdenote the concentration of chlorophyll a and b , respectively, in g I-'. These equations were applied to the sample solutions (the exercise used three different sets of samples, being integrated each set by five plant samples, four aliquots of each are analyzed). A new measurement of the control sample was performed after each three samples in order to construct the control chart and check whether the measurement process was under statistical control. The concentrations obtained are shown in Table 1:those of chloro~hvll . . a and b in the s a m ~ l e s plmt blades, are gwen in r n ~ l h ~ a m schlomphyll ol prr&nm of blade in Table 2 F I L ~2 ~shows C the corns~ondmacontrol charts for both types $chlorophyll, as can be Been, tge measurement Drocess was affected bv no systematic error. The A~Jo\'Avalues obtained fbr ~hlorophylla and b are shown in Table 3. The cnlculated F'values were
Sb=O.OI 26
%target value
Three different sets of samples integrated by five collectine mots each were selected in a countrvside area of -1 Ha t h i t t'waas cultured with ordinary gramiheals. At each spot (five altogether in every set), blades were collected from the same type of plant and stored in plastic bottles.
Results and Discussion Chlorophylls a and b a r e sparingly soluble in water, but highly soluble in organic solvents (acetone, ethanol). Thus, they can be extracted readily from green plants by using a n acetone-water solution (8).The spectra of chlorophyll a which allows their and b are quite different (see Fig. 1)(9), simultaneous determination in mixtures by using two different wavelengths (645 and 663 nm in this experiment). The calibration equations were obtained by using five standard mixtures of chlorophyll a and b:
target value=0.98gr';
Sa=0.0206
Sampling
Blades were cut into very small pieces by using a pair of scissors. Each sample was used to prepare four aliquots as follows: 1. An amount of -0.1 g of blades was weighed accurately in a balance. 2. Blade pieces were placed in a glass mortar and some acetone (80% vlv) was added. The blades were then ground in order to extract the chlorophylls. When the liquid turned green, it was filtered and collected in a beaker. These operations were remated three or four times until the blades lost their meen color. 3. The extracted liquid was transferred to a 25-mL flask, and 80% acetone was added to the mark.
Chlorophyll b
1.02 1.48 0.99 1.01 1.08
0.93 1.57 0.94 0.88 1.02
0.98 1.59 1.06 0.95 1.03
0.27 0.51 0.33 0.26 0.37
1.06 1.51 1.08 0.97 0.96,
0.31 0.55 0.30 0.33 0.34
0.30 0.48 0.26 0.31 0.28
0.25 0.56 0.28 0.25 0.30
I
There were four degrees of freedom between samples and 15 within samples. As can be seen, the F values obtained were smaller than the critical F4,15 value (3.804)for sets #1 and #3, but for the set #2 ANOVA detected a clear heterogeneity of samples ( F values higher than the critical value). Here heterogeneity means that variance between samples in set #2 is very different from the variance within-sample (samples contained different types of leaves). Sets #1 and #3 are constituted by homogeneous samples, indicating a correct sampling procedure and, hence. the re~resentativenessof the results obtained. Consequently, thkre was no significant difference between the sample means within each set (#1and #3). However, a
Chlorophyll a Variability
Sum of squares
d.f.
0.3189 0.6850 0.3662
4 19 15
0.9453 0.9911 0.0458
19 15
Chlorophyll b Mean square
Sum of squares
d.f.
Mean square
Set #I
Between-sample Total Within-sample Set #2
Between-sample Total Within-sample
4
Number of control sample Chlorophyll b
Set #3
Between-sample Total Within-sample
0.0201 0.0449 0.0248
4 19 15
d.f. = degrees of freedom.
comparision of the standard deviations (F-test) and the means (t-test) of sets #1 and #3 allowed to detect significant differences between them: Experimental values Chlorophyll a F
t
Number of control sample lure 2. Shewarichartsobtained by plotting the experiment2
Critical values
ta.
Chlorophyll b F
t
F
t
As F experimental values are higher than the critical values of F, the standard deviations of #1 and #3 are significantly different. Moreover, t h e m e a n s also differ significantly ( t experimental values critical value of t). Therefore, sets #1 and #3 are constituted by samples corresponding to different populations. As si < sl, the population defined by the set of samples #3 has a narrower distribution.
Conclusions Statistics is a useful tool for evaluating analytical chemical results. Students should acquire some statistical skill,
preferably through practical exercises. The straightforward proposed exercise can help students to understand the bases for statistical tests and how they are used. The experiment allowed two statistical problems to be solved: statistical control of chemical results (highly significant to quality of the results obtained in routine analyses) and statistical evaluation of a sampling procedure by using the ANOVA test, which provides a means for assessing representativeness. In this way, the overall quality of the analytical results (representativeness + accuracy) is assured.
Literature Cited 1. MeCormiek, D.: Roach A,; Mmsunmnl, Sfofiafiii and Computolion; ACOL Series; John Wiley & Sons: Nerv York, 1987, pp 330386. 2. Miller, J. C.; Miller. J. N. Sfofisficsforhlylicol Chemistry, 2nd ed.; Ellis Horwood Ltd.: Chichester, 1992. 3. Massart, D. L.; vsndegmste. B. G. M.; Deming, S. N.; Michdte, Y; Itadman, L. Chem0miries:A kerboo): E1esevier:Amsterdam. 1988. 4. Laquer. ?I C. J. Ckem. Educ. IsW). 67,SW. 5. O'Reillv, J. E. J. Chem. Educ. 1986.63.894. J Chem. Educ 1985.62.536.
6. Paselk,R.A.
7. Haswell. S. JProcticd Guideto Chemomlrics: Mareel Dekker. he.: NewYork, 1992. 8. Rabinowitch, E.; Go%ndjee,X PhofasynNI~sia;John Wiley & Sons: New York. 1969. 9. Stryer, L. Biochrmiafq, 3rd ed.;W. H. Freeman & Co.: New Ymk. 1988.
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