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Back Calculation of True Values for Solid Unknowns Laboratory classes in quantitative analysis use unknown solid samples purchased from a limited number of commercial suppliers. Since the actual number of unknowns is finite, much care is taken to protect the integrity of these unknown sample values. Threats to this intecrity are now being created by the presence of "computer hackers" in classes and by the manner in which grades are report& It is neither pas~ihle nor desirahie to reduce the fkst threat, but attention to grading practices can greatly reduce the second danger to sample integrity. Grades for determining unknowns are usually calculated by allowing a small reasonable error, perhaps 0.5% relative error, before penalizing the student at some preselected rate of points per percent error. Good educational practice didates that students know the grading scheme. On an individual basis this knowledge does not pose a threat to sample integrity, hut if the student knows the grading mechanism, the actual numerical grade, and the reported value, the student can calculate backwards and solve for the deviation of the correct value from its reported value. These calculations provide two values, one higher and one lower than his reported value. One of these is the true value and the other erroneous. A computer program to calculate and select true values and discard erroneous values was written and tested. Data from a class of about 60 students was employed. Utilizing students' reported values, actual numerical grades, and the mechanism of eomoutine the mades. true values for 13 unknown samdes of ootassium acid nhthalate analvzed in the class were selected. ,~ .. ~n~ . Thrse werr correct wirhin O.Imr relative error glf the true v.~lue reported hy thr supplier. Whm exact ur numher grndei arc reported to the studrnr.. fvur samples uf any partirulnr unknown arc ndequore t,, p,o\.ide a goon estimation of the true value. It is the reported usage of the sample that is significant and not the time interval over which the data is collected. Ten-gram student samples would provide 11 usages from a '14-lb sample. I t does not matter if these usages all occur in a single year or the data is collected and saved by student organizations from previoue years. It matters only that within a reasonable time span the students acquire data from four reported usages. With large classes this data can he obtained within asingle vear. Smaller classes will take a loneer oeriod of time. , ,. . The author uouhl likr 10 make three rrcommrndat:ons to protrrt the valuer of cohd unknuwnr. First, rvnluation of student analyses should he given onlv a,a letrtr prnde not as anexnet numrrl8nlgradp. If the wadeson the individual (In- knownr arc repurted onlv 2% s letter grade wrh a 16-point spread, th? difficulty in the hnok ralrulation is increased tonsid. erahly and the numher of usages of a particular sample required for an appropriate selection of the true value is greatly iu- creased. Second, chemistry departments should purchase unknown samples in small sizes, such as %-lh amounts, thus providing for more frequent refreshing of the pool. Third, manufacturing companies should offer samples in smaller-sized lots. There is no way to insure absolutesecurity for thevaluesof unknowns, but an awarenessof the potential problemand adoption of correct grading practices could provides measure of protection. The program is written in Microsoft BASIC for a system controlled by CPIM. With printout routines and sorting routines it comprises 89 lines. The program generates two tables. The first table is a listing of student numerical grades, reported values, two possible true values, and thenumber of matches that each ofthe truevalues has with the other true values. The second table is a sorted listing of the selected true values, arranged in order of decreasing magnitude. This program may be obtained by writing to the author on your academic letterhead and enclosing a stamped, self-addressed envelope. E. B. Buchanan, Jr. UniverSity 01 bwa Iowa City. IA 52240 120 Journal of Chemical Education

Back calculation of true values for solid unknowns

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Page 1: Back calculation of true values for solid unknowns

Back Calculation of True Values for Solid Unknowns Laboratory classes in quantitative analysis use unknown solid samples purchased from a limited number of commercial

suppliers. Since the actual number of unknowns is finite, much care is taken to protect the integrity of these unknown sample values. Threats to this intecrity are now being created by the presence of "computer hackers" in classes and by the manner in which grades are report& I t is neither pas~ihle nor desirahie to reduce the fkst threat, but attention to grading practices can greatly reduce the second danger to sample integrity.

Grades for determining unknowns are usually calculated by allowing a small reasonable error, perhaps 0.5% relative error, before penalizing the student at some preselected rate of points per percent error. Good educational practice didates that students know the grading scheme. On an individual basis this knowledge does not pose a threat to sample integrity, hut if the student knows the grading mechanism, the actual numerical grade, and the reported value, the student can calculate backwards and solve for the deviation of the correct value from its reported value. These calculations provide two values, one higher and one lower than his reported value. One of these is the true value and the other erroneous.

A computer program to calculate and select true values and discard erroneous values was written and tested. Data from a class of about 60 students was employed. Utilizing students' reported values, actual numerical grades, and the mechanism of eomoutine the mades. true values for 13 unknown samdes of ootassium acid nhthalate analvzed in the class were selected. ,~ .. ~n~ ~ . Thrse werr correct wirhin O.Imr relative error g l f the true v.~lue reported hy thr supplier. Whm exact ur numher grndei arc reported to the studrnr.. fvur samples uf any partirulnr unknown arc ndequore t,, p,o\.ide a goon estimation of the true value.

I t is the reported usage of the sample that is significant and not the time interval over which the data is collected. Ten-gram student samples would provide 11 usages from a '14-lb sample. I t does not matter if these usages all occur in a single year or the data is collected and saved by student organizations from previoue years. It matters only that within a reasonable time span the students acquire data from four reported usages. With large classes this data can he obtained within asingle vear. Smaller classes will take a loneer oeriod of time. , ~~ ~~ ,. .

The author uouhl likr 10 make three rrcommrndat:ons to protrrt the valuer of cohd unknuwnr. First, rvnluation of student analyses should he given onlv a,a letrtr prnde not as anexnet numrrl8nlgradp. If the wadeson the individual (In- knownr arc repurted onlv 2% s letter grade wrh a 16-point spread, th? difficulty in the hnok ralrulation is increased tonsid. erahly and the numher of usages of a particular sample required for an appropriate selection of the true value is greatly iu- creased. Second, chemistry departments should purchase unknown samples in small sizes, such as %-lh amounts, thus providing for more frequent refreshing of the pool. Third, manufacturing companies should offer samples in smaller-sized lots. There is no way to insure absolutesecurity for thevaluesof unknowns, but an awarenessof the potential problemand adoption of correct grading practices could provides measure of protection.

The program is written in Microsoft BASIC for a system controlled by CPIM. With printout routines and sorting routines it comprises 89 lines. The program generates two tables. The first table is a listing of student numerical grades, reported values, two possible true values, and thenumber of matches that each ofthe truevalues has with the other true values. The second table is a sorted listing of the selected true values, arranged in order of decreasing magnitude. This program may be obtained by writing to the author on your academic letterhead and enclosing a stamped, self-addressed envelope.

E. B. Buchanan, Jr. UniverSity 01 bwa

Iowa City. IA 52240

120 Journal of Chemical Education