Analysis" in "Handbook of Social Psychology" (Editors: LINDZEY AND ARONSON), Addison Wesley, 1968, pp. 80200), it is pointed out that the assumption of a normal population distribution is often unwarranted. They suggest, therefore, that variability should be directly assessed wherever possible. Using the computer, I calculated the 95% confidence limits around the mean of the reported copper sulfide analysis by the direct assessment method. The 266 values were randomly divided (by shuffling) into 17 groups and the mean of each group g,, was calculated. The mean of these values is
5
estimates F , the population mean. The estimated is calculated by the formula variance of ?j sta = (g; - ))//17(17
- 1)
and the 950jo confidence limits around y are given by -
III It&..G
*
The result is 78.40 2.26 X 1.99, or (78.40 + 4.50)% copper. This result is quite surprising, considering the average value of 78.3 0.7 reported by Diugledy and Patrie. Repeating my calculation on 17 reshuffled 3.71. Using the jackknife groups yielded 78.40 method (see Mosteller and Tukey, above), confidence limits were placed around the standard deviation, of the 17 group means in the first calculation
*
8;
= 1.99
8;.
= 2.03 (jackknifed value
The standard deviation of s;:* =0.38. dence limits around si* are 2.03
of
* 2.12 X 0.38
2.03
+ 0.81
The 95% confi-
or the interval from 1.22 to 2.84. It is seen that the value of s; = 1.99, calculated by the "direct assessment" method is well within the 950j0 confidence range, while the reported standard error value of 0.34 is outside this range. These results would suggest that a much more liberal distribution of grades for student analyses is in keeping with the more realistic direct assessment of variability. I wish to thank Dr. Dingledy for supplying the raw data for this analysis.
786 / Journol o f Chemical Education
To the Editor: I t is commonplace to represent atomic and molecular orbitals by horizontal limes in a vertical scale of energies. (See, for example, in J. CHEM.EDUC., 46,679,747,806, 812 (1969)). It is also commonplace to represent the electrons filling these orbitals by arrows pointing up and down. What puzzles me is that it is not equally commonplace to show pairing energies of these electrons on the same vertical scale. This can be done easily by letting the point of the arrow indicate the energy of the electron. The first one in an orbital is drawn pointing down, the second one (of opposite spin) pointing up, and the length of the arrow then shows the extra energy needed to put the second electron in the same orbital. With this convention it becomes obvious how crystalor ligand-field splitting of the d orbitals influences the pairing of the electrons and hence the paramagnetism of the ion in the field. Take as an example a dj ion such as Mn2+ or Pea+ in an octahedral field. If the splitting A. between the e , and hr sets of d orbitals is less than the pairing energy, then to give the electrons the lowest energies they must all be pointing down; the ground state will have five unpaired electrons and "high spin"
8,)
* ltxsla.~X 0.38
2.03
Representing Pairing Energy of Electrons
If, on the other hand, the splitting is greater than the pairing energy, then to put the electrons in the lowest positions four of them must be paired off, giving a "low spin" ground state
If we draw all the arrows the same length we are dealing only with an average pairing energy, but this is sufficient to illustrate the principle.
