Using the Analytical Balance and Piso1 Statistics

Using the Analytical Balance and Piso1 Statistics

Chem 28.1-1Quantitative Inorganic Analysis LaboratoryDepartment of ChemistryUniversity of the Philippines-Visayas

Experiment 116 February 2015

Matinong, Kathleen Erica 2013-66202Naciongayo, Danielle2010-38490Sampani, Gian Justin2013-75094

I. AbstractThe laboratory report is mainly focused on the proper usage of the analytical balance and on the concept of precision using statistical methods. The mass of the Piso coins were determined in two ways namely weighing individually and weighing by difference. Ten coins (five coins minted 2004 and five coins minted 2004) were used in the experiment. In the method of weighing individually, each coin was weighed and its mass was recorded accordingly. In weighing by difference, five coins of the same group were piled up and each coin was removed and the mass was recorded deductively. The data collected were tabulated and analyzed using statistical parameters, specifically the mean, standard deviation, standard error of the mean (SEM), range, relative range, relative standard deviation (RSD) and pooled standard deviation. At 95% confidence level, it was determined that there is a significant difference between the masses of coins minted in two different years. However, there is no significant difference between the means and variances of the masses of coins using two weighing methods. As a final point, Piso coins from two different years have different masses; the two weighing methods produce the same results. Thus, the two weighing methods have the same precision.

II. IntroductionAnalytical chemistry is a measurement science. Quantitative analysis determines the relative amounts of these species, or analytes, in numerical terms.1 Measurements have errors associated with them. Two complementary terms are often used to describe measurements: accuracy and precision. The former refers to how close the measurement is to the true value, while the latter refers to the closeness of the measurements that have been obtained in the exact same way. Quantitative measurements of various samples are employed to assess the efficiency of a certain method or technique. In this experiment, statistical methods and concepts are applied in determining the weight variation of 1-piso coins through the use of the analytical balance. Specifically, it determines to know if Piso coins from two different year groups have the same mass; if the two weighing methods yield the same results; as well as if the two weighing methods have the same precision.In 1995, the New BSP series was introduced, including the 1-peso coin, which is made up of cupronickel. By 2004, BSP changed the composition of the coin to nickel-plated steel, which is lighter than the former (BSP, 2010). With that information, there is an expected significance in the difference of the results between the two-year groups that will be obtained using two methods (i.e. weighing individually and weighing by difference). This experiment is only limited to the Piso in the 1995 BSP series of coins. Only ten coins will be used, that is, five coins minted before 2004, and five coins minted after 2004. This experiment will be conducted at the Chemistry Laboratory, Department of Chemistry, University of the Philippines-Visayas, Miag-ao Campus, Miag-ao, Iloilo.

III. Materials and MethodsFor this experiment, we collected 10 1-piso coins wherein 5 of these were minted before or during () 2004 and the other five were minted during or after () 2004. Our collection was composed of coins from 2000, 2001, 2002, 2003 and 2004 for the 2004 group, and 2004, 2010, 2011, 2012 and 2013 for the 2004 group.Inside the laboratory, we used the analytical balance to weigh the coins we gathered, individually and by difference. For the first method of weighing, which was weighing individually, we first placed each coin in a labeled piece of paper to keep track of their identities. Then we randomized the order of weighing using a scientific calculator in order to avoid bias. Once the order of the coins was established, we moved on to the next step which was the weighing. Prior to placing the coin inside the analytical balance, we zeroed the analytical balance by pressing the zero or tare button. Then we placed an empty watch glass on the balance pan and zeroed the balance again. Finally, with the use of the tweezers, we placed each coin according to the order that weve established earlier on the receiving watch glass and recorded their individual masses on our notebooks.For the second method of weighing, which was weighing by difference, we first zeroed the balance before placing all five coins from the same group or year category on the watch glass. Once the total mass was determined and recorded, we removed each coin one by one, taking note of the year that the coin was minted and the mass of the remaining coins. This procedure was repeated until there was only one coin left on the watch glass. After all the masses were recorded, we solved for the individual masses using subtraction. After weighing all the coins using both methods, we proceeded in washing the coins with acetone. We first placed the coins in a 250-ml beaker and soaked them in acetone for 5 minutes. Next, we decanted the acetone, transferred the coins to a clean dry beaker and left them to dry totally. Finally, we weighed the masses of the coins using the same methods we used earlier. After all the data was collected, we were performed a statistical data analysis on the masses of the coins obtained by weighing by difference in both year categories. The statistical data analysis included computing for the mean, standard deviation, standard error of the mean (SEM), range, relative range, relative standard deviation (RSD) and the 95% confidence interval. Then we combined the data of the entire class to compute for the pooled standard deviation. Later we executed Grubbs test for the highest and lowest values on our groups data and also on the pooled data. After rejecting the discrepant data, we recalculated the statistical parameters required such as the mean, standard deviation, standard error of the mean (SEM), range, relative range, relative standard deviation (RSD) and the 95% confidence interval. We also checked if the rejected values lie outside of 3s and recomputed the pooled standard deviation.Following the execution of the Grubbs test was the usage of the t-test (at 95% confidence level) in comparing the mean masses of coins from two different year categories from both weighing methods. This was also followed by the paired t-test in order to determine whether there was a difference between the results obtained by the two methods. Afterwards, we performed the F test on the data from the group 2004 to compare the precision of the two weighing methods. The statistical test that should be used to confirm whether there is a difference of results before and after washing of acetone is the F-test.

IV. ResultsThe following are the tabulated results of the data obtained after weighing the coins using two different weighing methods, after performing statistical data analysis, and after performing different tests on the data. The tests performed include Grubbs test for outliers, t test, paired t test, and F test. Table 1. Masses of coins obtained by the two weighing methods (before washing)Sample No.Weighing individually, gWeighing by difference, g

20006.068523.3987 17.3306 = 6.0681

20016.058129.4564 23.3987 = 6.0577

20025.995017.3306 11.3360 = 5.9946

20036.018211.3360 5.3180 = 6.0180

20045.31735.3180 0 = 5.3180

20045.333010.6749 5.3428 = 5.3321

20105.313026.7532 21.4415 = 5.3117

20115.359621.4415 16.0821 = 5.3594

20125.407616.0821 10.6749 = 5.4072

20135.34325.3428 0 = 5.3428

Table 2. Masses of coins obtained by the two weighing methods (after washing)Sample No.Weighing individually, gWeighing by difference, g

20006.067723.3987 17.3306 = 6.0681

20016.057729.4564 23.3987 = 6.0577

20025.994317.3306 11.3360 = 5.9946

20036.017411.3360 5.3180 = 6.0180

20045.31695.3180 0 = 5.3180

20045.332010.6749 5.3428 = 5.3321

20105.311326.7532 21.4415 = 5.3117

20115.358421.4415 16.0821 = 5.3594

20125.407116.0821 10.6749 = 5.4072

20135.34265.3428 0 = 5.3428

Table 3. Statistical parameters for masses of coins in each year category obtained by weighing by differences Year Category

MeanStd. Dev.RSD (in ppt)S.E.MRangeRelative Range95% C.ISp

20045.98130.3218554.6310.143940.750112.732%5.89130.310.30379

20045.35060.0360466.73680.016120.09551.7848%5.35060.030.052152

Table 4. Grubbs Test for OutliersDataYear CategorySuspect ValuesGcalcGcritConclusion

Group 2004H: 6.06810.549321.715Outlier, remove

L: 5.31801.7813Not an outlier, retain

2004H: 5.40721.57021.715Not an outlier, retain

L: 5.31171.0792Not an outlier, retain

Pooled 2004H: 6.08242.65402.87Not an outlier, retain

L: 5.3106.8233Outlier, remove

2004H: 5.47664.81872.87Outlier, remove

L: 5.006910.6104Outlier, remove

Table 5. Recalculated statistical parameters for masses of coins in each year category obtained by weighing by differences Year Category

MeanStd. Dev.RSD (in ppt)S.E.MRangeRelative Range95% C.ISpooled

20046.03460.034315.64910.017050.07351.2180%6.03460.040.013445

20045.35060.036056.73680.016120.09551.7848%5.35060.030.052152

Table 6. Comparison of masses of coins from two different year categories (t-test)MethodtcalctcritConclusion

Weighing individually28.8302.365We reject the null hypothesis and accept the alternative hypothesis

Weighing by difference28.8232.365We reject the null hypothesis and accept the alternative hypothesis

Table 7. Comparison of two weighing methodsTestCalculatedCriticalConclusion

Paired t-test 2004 20042.2362.647

2.572.57Accept the null hypothesisWe failed to reject the null hypothesis and cannot accept the alternative hypothesis.

F test 2004 20041.000.9969.6059.605Accept the null hypothesisAccept the null hypothesis

V. DiscussionThis section will provide scientific explanation and support with the claims mentioned in the Introduction. The statistical parameters of the masses of coins from two year categories presented in Table 3 are not close to one another, except for the value of the means. The obtained means for the Data set 1 (2004) and the Data set 2 (2004) were 5.8913 and 5.3506, respectively. A possible reason for the large difference between the parameters is the material of the coins. This is because the materials used in both groups of coins differ from one another. The coins made before 2004 were made up of Cupro-Nickel while the coins made after were made up of Nickel-Plated Steel. This is due to the shortage of one peso coins due to coin smuggling and negative seignorage.2In computing for the confidence interval, a 95% probability was used to determine if the sample means lie within the population means. The confidence interval for data set 1 was calculated to be 5.8913 0.31, at =0.05. This means that there is a 95% probability that the true mean for data set 1 is within the mentioned interval. Meanwhile, the confidence interval for the data set 2 was calculated to be 5.3506 0.03. This means that there is only a 5% probability that the expected mass of a coin falling in this data set is less than 5.3206 g or more than 5.3806 g.Grubbs test is performed to identify the extreme values, or outliers, in a given data set. Outliers are data that are not consistent with the remaining data. The observations are either rejected or accepted depending on the comparison of the calculated G value and critical value. It is accepted if the value of Gcalc is lower than Gcrit, otherwise, it is rejected. The use of this test is restricted; it should only be used on one value per data set. Grubbs test provides a means for researchers to eliminate outliers that may compromise any meaningful analysis of the data. The outlier, which lies outside the body of data, is examined only in extreme values.In comparing the values obtained for the Gcalc to the critical value G (Gcrit) in Table 4, four suspected values were discovered to be outliers and were removed from their respective data sets. The statistical parameters of the data sets were therefore recomputed without the irregular rejected value.After the computation of the statistical parameters without the presence of the outliers, the values recorded in Data set 1 reduced. This is because omitting an outlier leads to a decrease of the variance of the estimator and therefore an increase of the absolute accuracy of prediction.3 The values in Table 5 were again recomputed to test if there are still any existing outliers between the data. The test showed no signs of outliers. The coins in data set 1 weighed 5.3173-6.0581 g while coins after 2004 weighs 5.3117-5.4072 g. According to BSP (2010), coins minted before 2004 were composed of cupronickel and weigh about 6.1 g, while coins after 2004, they were composed of nickel-plated steel, weigh 5.35 g. In terms of accuracy, the results of this experiment are close to the true value of the masses of the coins in the information provided by The Mint and Refinery Operation Department of BSP.For the comparison of masses of coins, the t-test is used because it can determine if the difference between two means is significant. Using , the , and the critical values on both tails are 2.365. The tcalc value for both weighing individually and by difference are 28.830 and 28.823, respectively. The null hypothesis for both methods used in weighing is rejected because both values are greater than the tcrit value. This shows that the means of the two data sets are significantly different. Which also means that the masses of the coins minted in two different years are different.A paired t-test is used to test the significance since two methods of weighing were applied to the same set of materials. Given the and using , the critical values on both tails are 2.57. The null hypothesis is rejected if the tcalc values are greater than the tcrit values. The tcalc value for data set 1, which is 2.236, is lower than tcrit value and this means the null hypothesis is accepted. But since the tcalc value for data set 2, which is 2.647, is higher than the tcrit value, the null hypothesis is rejected and we accept the alternative hypothesis. This implies that the means are significantly different, and this also entails that the masses of the coins using the two weighing methods are not the same.The F-Test was also used to determine differences between the variances of the two methods. Table 7 shows the comparison of the two weighing methods using F-test. Given the and using , the critical values on both tails are 9.605. The null hypothesis will be rejected if the calculated value is greater than the critical value. Since the calculated F values are 1.00 which is lesser than its critical value the null hypotheses are accepted, which means, the variances are equal and are not significantly different. It suggests that, the precision of the two weighing methods are the same.

VI. ConclusionProper handling and using of the analytical balance was studied prior to the experiment in order to maximize the quality of its utilization. Application of correct calibration techniques, taring and zeroing of the balance was present in the experiment.For the experiment proper, ten 1-piso coins wherein 5 of these were minted before or during () 2004 and the other five were minted during or after () 2004 were used. The coins were weighed using the two different weighing methods, i.e. weighing individually and weighing by difference. The analytical balance was used to measure the weight of the coins. The obtained data were used to determine their statistical parameters and which were used for the succeeding statistical tests (t-Test, paired t-Test, Grubbs Test, and F-test). Using 95% confidence level, it has been found out that there is a significant difference between the masses of coins minted in two different years. Nonetheless, there is no significant difference between the variances of the masses of coins using two weighing methods. However there is a difference in the means of the masses of coins using two weighing methods. Possible sources of errors that caused the detection of outliers were noted and will be avoided and the skills will be improved for the next experiments.

VII. Contribution of AuthorsAll members contributed equally during the execution of the experiment inside the laboratory. During the writing of the actual lab report, the tasks were distributed to each member.

Kathleen Erica MatinongContributed in the writing of the lab report particularly in the introduction, as well as in the materials and methods. Danielle NaciongayoContributed in the writing of the lab report by organizing the results of the experiment in tabulated form and presenting them in the Section IV (Results). Also discussed the obtained results from the experiment in Section V (Discussion).Gian Justin SampaniContributed in writing of the lab report but creating the Section I (Abstract).

VIII. Literature Cited

(1) Skoog, DA, West DM, Holler FJ, SR crouch, 2010, Fundamentals of Analytical Chemistry 8th edition. CENGAGE Learning Asia, Pte. Ltd.(2) Palanca, T. (2013, July 7). On Melting Coins and Negative Seignorage. Retrieved February 15, 2015. From http://www.jumbodumbothoughts.com/2013/07/on-melting-coins-and-negative-seignorage.html(3) Ziller, M. (2003). Quantifying the relative accuracy of data based prediction. Proc. ASIM 2003, 9. 12. June, Almaty, Kasachstan, 486 489.

IX. AppendixAppendix A Statistical Formulas

Experiment 1: Using the Analytical Balance and Piso Statistics KE Matinong, D Naciongayo, GJ Sampani

x= sum of all datan=number of samplesMean

This is used to find the most probable value of the weight of the coin.

n-1=degrees of freedomStandard Deviation

This is used to measure the precision and the spread of the weights of the coin.

Standard Deviation of the Mean

This is used to measure the variation of the distribution of the most probable value of the weight of the coin.

Range

This is used to determine the measure of precision and the difference between the highest and the lowest weight of the coin.Relative Standard Deviation (in ppt)

This is used to depict the size of the s relative to its mean.

Relative Range (in ppt)

This is the ratio of the range to the absolute value of the mean expressed in parts per thousand.95% Confidence Interval

t= Students tThis is to determine if the sample mean lies within the population mean with a 95% probability.

k= number of groupsPooled Standard Deviation

This is used to get a better estimate of the population standard deviation given the several sets of data.

Grubbs test for outliers

This is used to determine if the farthest weight from the mean is anomalous and should be removed or retained.

sp= pooled stTest

This is used to test if there is a significant difference between the means of the weights of coins from the two different year groups.

= mean deviationsd= s of the mean deviationsPaired t-Test

This is used to determine if there is a significant difference between the means of weights of coins using two different methods.

F-Test

This is used to determine if there is a significant difference between the variances of the methods.

Appendix B Calculations

95% Confidence Interval

2004CI = 5.8913 = 5.8913 0.30687 = 5.8913 0.31

2004CI = 5.3506 = 5.3506 0.034368 = 5.3506 0.03

Grubbs test for outliers

H0 : suspect value = Ha : suspect value = 0.05 (95% Confidence Interval) 2004Suspect value = 5.3180Mean (= 5.8913Standard deviation (s) = 0.32185

G = 1.7813

2004Suspect value = 5.4072Mean (= 5.3506Standard deviation (s) = 0.036046

G = 1.5702