In the Laboratory
A Didactic Experience of Statistical Analysis for the Determination of Glycine in a Nonaqueous Medium Using ANOVA and a Computer Program
W
M. J. Santos-Delgado* and L. Larrea-Tarruella Department of Analytical Chemistry, Complutense University, 28040 Madrid, Spain; *
[email protected] Equilibria in nonaqueous media are interesting because many relevant reactions are carried out in these media. It is important for chemistry students to know that substances that give poor endpoints in normal aqueous titrations and substances that are not soluble in water can be titrated satisfactorily in nonaqueous media. Amphiprotic solvents, such as acetic acid (HAc), are frequently used. Glycine titration is a typical application for studying equilibria in a nonaqueous media (1). Some knowledge of statistics is vital for chemistry undergraduate students. In particular, knowledge about comparisons between experimental data, which are increasingly used in analytical laboratories to find out whether there are significant differences between techniques, is useful. This Journal has published several articles dealing with general statistical experiments (2), statistical studies by computer simulation (3), direct comparison of experimental data (4, 5), comparison of relative standard deviation values (6), and statistical comparisons using different tests (confidence intervals, contrast of hypothesis, normal distribution, and t, Q, F, χ 2 tests; ref 7–14 ). In analytical chemistry research comparisons often involve more than two means. In this exercise the means of the analyte concentrations obtained in the titration by different analysts or by different methods are examined using ANOVA (analysis of variance). In both cases there are two causes of variation; the first, which is always present, is due to random error, and the second, known as the controlled factor, is represented by the analysts carrying out the titration, or by the methods, and is due to systematic errors. ANOVA is also used when there is more than one controlled factor simultaneously (analysts and methods). In this case ANOVA allows the separation of the three causes of variation: analysts, methods, and random error (15). This article describes the statistical comparison of two back-titration methods for the determination of glycine in a glacial HAc medium. The titration is carried out using perchloric acid. The glycine quantities obtained were determined by several groups of students on the same day (three groups a day, on average; a total of 32 groups during the academic year) and were compared by two-way ANOVA with the Statgraphics Plus 3.0 (16) computer program. The laboratory exercise discussed in this article is recommended for fourth-year undergraduates. Objectives •
Introduce the students to reactions (titrations) in nonaqueous media.
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Use ANOVA to compare two analytical techniques; semiautomatic titration with potentiometric determination of the endpoint and manual titration with colorimetric indication of the endpoint.
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Use ANOVA to compare the results of different groups of analysts who used the same technique.
Experimental
Apparatus and Material Metrohm 655D titrator Calomel–platinum combination electrode Metrohm E536 potentiometric register Mechanical stirrer 10-mL Microburet Statgraphics Plus 3.0 (for Windows 95)
Chemicals 0.1 N Perchloric acid in acetic anhydride, prepared fresh daily 0.01 N Potassium hydrogen phthalate (KHP) in glacial HAc 0.1 N Sodium acetate in glacial HAc 2% Methyl violet in chlorobenzene
Procedures Glycine was titrated manually with a HClO4 solution using a colorimetric indication of the endpoint (method 1). First the HClO4 solution was standardized by titration with a KHP solution containing methyl violet. The endpoint was determined when the violet color changed to pale yellow. Then 1.6–2 milliequivalents of glycine were dissolved in 25.0 ml of the HClO4 solution and two drops of methyl violet were added. The excess of HClO4 was back-titrated against a standard 0.1 N NaOOCCH3 solution. The endpoint was detected by the violet color formed. Glycine was then titrated semiautomatically with a HClO4 solution using a potentiometric detection of the endpoint (method 2). Glycine, 1.6–2 milliequivalents, was dissolved in 25.0 ml of the HClO4 solution. A Calomel– platinum combination electrode was dipped into this solution inside a titration cell, taking care to stir throughout. The excess of HClO4 was back-titrated against 0.1 N NaOOCCH3 solution. The endpoint was obtained potentiometrically. Using statistical analysis, students compared data derived from both one-way ANOVA of the HClO4 standardization and two-way ANOVA of the glycine titration. Hazards HClO4 is a strong acid and therefore is corrosive. It is also a strong oxidizing agent and when in contact with organic
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In the Laboratory
matter is heat-, shock-, friction-, and impact-sensitive. Acetic anhydride can react violently with water, alcohols, and oxidizing agents; such reactions are exacerbated in the presence of acid or higher temperatures. Glacial acetic acid reacts exothermically and sometimes violently with bases and with oxidizing agents. It reacts with many metals to produce hydrogen, a flammable and explosive gas. Sodium acetate reacts with strong acids to release fumes of acetic acid. Chloro-
Table 1. Data Matrix for One-Way ANOVA Group
[HClO4]/M
16
0.103
16
0.0998
17
0.103
17
0.101
18
0.0950
18
0.104
Table 2. Data Matrix for Two-Way ANOVA Group
Method
Glycine (%)
16
1
96.8
16
1
97.3
16
2
97.3
16
2
95.1
17
1
96.1
17
1
96.9
17
2
95.6
17
2
96.3
18
1
94.0
18
1
94.9
18
2
96.4
18
2
92.3
Table 3. Results for One-Way ANOVA Between groups
Within groups
Total (corrected)
6.81 × 10᎑6
4.76 × 10᎑5
5.44 × 10᎑5
2
3
5
3.41 × 10᎑6
1.59 × 10᎑5
Characteristic Sum of squares Df Mean square F Ratio
0.21
p Value
0.818
benzene irritates skin, eyes, and nose; it causes drowsiness, lack of coordination, and central-nervous-system depression. Methyl violet is irritating to eyes, respiratory system, and skin. To minimize the risks the KHP solution is prepared and titrations (with microburet) are undertaken in a fume hood. Results Every day three student groups carried out the experiment. Each student group made two titrations for the HClO4 solution standardization and two titrations for each method to determine the glycine concentration. One-way ANOVA was used to compare the mean values obtained by the different groups from the daily standardization of the HClO4 solution, while two-way ANOVA was used to compare the glycine results of the groups and of the two methods. The data from the experiments performed on the same day by groups 16, 17, and 18 were selected at random from a total of 32 groups. Tables 1 and 2 (for one-way ANOVA and twoway ANOVA with interaction) show data matrices that were inserted in the Statgraphics program. The dependent variable and the factor to be studied were specified to obtain the following results: the source of variation, s◊[ of squares, degrees of freedom (Df ), mean squares (variance), the F ratio, and the value of α (p value) (Tables 3 and 4). In to3 one-way ANOVA assessment, the p value of the F test is greater than 0.05, indicating that there was no significant statistical difference between the mean values of HClO4 concentration obtained by the different student groups at a 95% confidence level (Table 3). Similarly, in the two-way ANOVA assessment, the comparisons gave a p value greater than 0.05 (Table 4). Therefore, it can be assumed that none of the studied factors—method, group, or method– group interaction effect—had a significant statistical effect on the mean percentage of glycine at a 95% confidence level. In the graph of mean confidence intervals corresponding to the one-way ANOVA results (Figure 1), HClO4 concentration versus student group, the bars overlap each other, indicating that there were no significant statistical differences (as has already been seen in Table 3). In the two-way ANOVA graphs (Figure 2), it is apparent that there were no significant statistical differences between methods, nor between groups. If we compare the mean values of glycine obtained within each set of three groups on each day over the academic year (all 32 groups) there are no significant differences with respect to the method, except for groups 13, 14, and 15 (see the Supplemental MaterialW). With respect to the group factor only 12 groups out of 32 showed significant differences. Lastly, a comparison was made of glycine percentages obtained by the 32 student groups over the academic year.
Table 4. Results for Two-Way ANOVA Characteristics Sum of Squares Df Mean Square
a
98
Main Effects
Interactions
Residual
Total (corrected)
0.285
11.9
24.2
2
6
11
0.143
1.99
A: Method
B: Group
AB
0.750
11.3
1
2
0.750
5.63
F Ratioa
0.38
2.83
0.07
p Value
0.562
0.136
0.932
All F ratios are based on the residual mean square error.
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Figure 1. Results of one-way ANOVA for the HClO4 standardization. A 97
96
95
94 1
B
Supplemental Material Instructions for the students, notes for the instructor, theoretical background material, and glycine results obtained for all 32 groups are available in this issue of JCE Online. Literature Cited
98
96
94
16
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2
Method
W
17
18
Group Figure 2. Results of two-way ANOVA for determination of glycine, Gly (groups 16, 17, and 18): (A) Gly vs Method; (B) Gly vs Group.
A
Fraction Gly (%)
92
91
90 1
2
Method B
Fraction Gly (%)
1. Skoog, D. A.; West, D. M.; Holler, F. J. Fundamentos de Química Analítica; Editorial Reverté S.A.: Barcelona, Spain, 1997. 2. Stone, C. A.; Numaw, L. D. J. Chem. Educ. 1995, 72, 518– 524. 3. Lötz, A. J. Chem. Educ. 1995, 72, 128–129. 4. Sparks, L.; Bleasdell, B. D. J. Chem. Educ. 1986, 63, 638– 639. 5. Harrison, A. M.; Peterman, K. E. J. Chem. Educ. 1989, 66, 772–773. 6. Kovács-Hadady, K.; Fábián, I. J. Chem. Educ. 1996, 73, 461– 462. 7. Harvey, D. T. J. Chem. Educ. 1991, 68, 329–331. 8. Labandera-Gaggero, F. V.; Luaces, V. M. J. Chem. Educ. 1992, 69, 934–935. 9. Paselk, R. A. J. Chem. Educ. 1985, 62, 536. 10. Vitha, M. F.; Carr, P. W. J. Chem. Educ. 1997, 74, 998–1000. 11. Sheeran, D. J. Chem. Educ. 1998, 75, 453–456. 12. Pandey, S.; Borders, T. L.; Hernández, C. E.; Roy, L. E.; Reddy, G. D.; Martinez, G. L.; Jackson, A.; Brown, G.; Acree, W. E., Jr. J. Chem. Educ. 1999, 76, 85–87. 13. Thomasson, K.; Lofthus-Merschman, S.; Humbert, M.; Kulevsky, N. J. Chem. Educ. 1998, 75, 231–233. 14. Salzsieder, J. C. J. Chem. Educ. 1995, 72, 623. 15. Miller, J. N.; Miller, J. C. Estadística y Quimiometría para Química Analítica, 4th ed.; Prentice Hall: Madrid, Spain, 2002. 16. Statgraphics Plus for Windows, 3.0: Statistical Graphics Corp., 1997.
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Group
Fraction Gly (%)
Conclusions The results obtained for the determination of glycine over the academic year imply that at a confidence level of 95% there were no significant differences between the methods used for the experiment. However, there were significant differences in the mean values of glycine owing to the group factor and the method–group interaction effect because of systematic errors. Nevertheless, the glycine results obtained by the students throughout the academic year were all over 80%.
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Fraction Gly (%)
Figure 3A shows no significant statistical differences between methods for the determination of glycine at a 95% confidence level. However, it can be observed that there were important differences in the mean values between one group and another at a 95% confidence level (Figure 3B), even though the glycine results obtained were all over 80%. Furthermore, the glycine percentage results tend to fall either in the 80–85% range or in the 95–100% range. These deviations could only be explained by systematic errors. The most likely errors are inaccurate volume and weight measurements and incomplete drying of laboratory material. In addition, it was observed that the interaction effects influenced the mean values of glycine, αmethod–group< 0.05. The ANOVA results can also be obtained using other packages, such as Microsoft Excel.
[HClO4] / (mol/L)
In the Laboratory
100
90
80 3
6
9 12 15 18 21 24 27 30
Group Figure 3. Results of two-way ANOVA for determination of glycine, Gly (all groups):(A) Gly vs Method; (B) Gly vs Group.
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