Paul A. Games

Power of the Analysis of Variance of Independent Groups on Non-Normal and Normally Transformed Data

THE science of data analysis, as described by Tukey (1962), (in contrast to statistics), has a goal closely tied to the real world: to derive certain conclusions about the &dquo;state of the world&dquo; from a sample of evidence. Statistics, on the other hand, is a mathematical discipline and can’t be evaluated by the same empirical considerations. Consequently, although data analysis finds statistics very useful, it is helpful to maintain a distinction when approaching the practical problems considered here. Two aspects of data analysis

COMPARISON OF TWO TESTS OF BRAIN DAMAGE.

The Bender-Gestalt (B-G) and the Memory-for-Designs (MFD) test by Graham & Kendall were administered to 60 “first admissions” to a state mental hospital and then scored by four raters for indications of brain damage. Results of the MFD and B-G ratings were compared with the brain-damage criterion, hospital staff diagnosis of either “organic” or “non-organic.” The validity coefficients of the B-G (.55) and the MFD (.67) were not significantly different, but scorer agreement on the MFD was significantly higher than on the B-G. The easier-to-score MFD thus may provide a more effective rough measure of brain damage than the B-G, especially when used by relatively inexperienced clinicians.

COMMENTS ON "A POWER COMPARISON OF THE F AND L TESTS—I"

Boersma, Dejonge, and Stellwagen (1964) fail to consider any sitution except that where the specific ordered alternative of the L test is true. They thus fail to consider the general statistical inference consequences of using ordered-hypothesis tests vs. omnibus tests. The power comparison provides little useful information on the parametric vs. nonparametric choice of tests in either the ordered-hypothesis or omnibus test situations. The conclusion of consistently superior power of the L test is somewhat dubious in that the authors failed to demonstrate equal risks of Type I error in the 2 tests and used computer simulation of data that was inappropriate for either the randomizedblocks analysis of variance or the L test.

A Missing Observations Correlation Program

IN many factor analysis or multiple regression studies it is necessary to administer a large test battery of m tests to a relatively small number of subjects in each administration. When many subjects are desired, this results in many administrations, and a substantial likelihood that occasionally one or more tests will be improperly administered for one group of subjects, resulting in &dquo;missing observations&dquo; in the matrix of scores. If the groups of subjects may be conceived of as random samples from the same population, the best way to provide the complete m by m matrix of correlations between all tests is to use a &dquo;missing observations&dquo; correlation computation procedure. Computer programs have been written that compute the correlation between test I and test J by using only the data of subjects who have scores for both tests (Dixon, 1964; Dick, 1964) and that apply the conventional correlation formula on these data. The. major problem with such programs is that they must keep separate records for each pair of tests on each of the following variables: 7~/ = the number of subjects for whom both observations simultaneously exist and the sums over these nij subjects for Xi, Xj, XJ[j, X~2 and X f2. Since there are m (m 1 ) /2 combinations of pairs of tests in a battery of m tests, nii and each of these five sums must be dimen-

Adaptation to Cyclic Food Deprivation in the Acquisition of an Instrumental Running Response

Groups of 16 rats were placed on a 23-hr. deprivation schedule either 2, 4, 8, or 20 days prior to 10 days of acquisition training in a straight alley. Analyses of daily median latencies and running times, or a log transformation of these, yielded only one significant difference between group means; the 8- and 20-day deprivation groups were faster than the 2- or 4-day groups on log running times over Days 6 to 10. The 8- and 20-day groups had consistently lower variances (within groups) than did the 2- and 4-day groups. A minimum of eight days deprivation is recommended.