True Population Values Research Articles

Leadership style and group decision effectiveness: Correlational and behavioral tests of Fiedler's contingency model

Experimental tests of Fiedler's “contingency model” of leadership effectiveness generally leave unanswered questions of precise criterion validity, due to limits on statistical significance of correlations based on small Ns. Seventy-five role-play groups were used in tests of one of the nine possible situations to which the model predicts. In this case, leaders with low LPC (Least-Preferred Co-Worker) scores (“task-oriented”) should be superior to high LPC (“relationship-oriented”) leaders. Two experiments ( N = 53 N = 22) yielded r = −.29 and −.19, respectively, between leaders' LPC and a group decision effectiveness score. Overall, r ave = −.26 ( P < .05). The obtained confidence level closely approximates that which could be reasonably expected for the N used if the predicted correlation (−.33) were, in fact, the true population value. This, and the consistency of results between the two independent experiments, justifies the conclusion that a small but significant relationship exists between leadership style and group effectiveness for the situation investigated. The practical utility of this relationship was discussed. Some behavioral differences between high and low LPC leaders were also examined and discussed.

A Note on Student's t Test in Multiple Regression

Recently, Cohen and Gujarati [2] have suggested that when multicollinearity is present there is “ …danger involved in mechanically dropping variables from multiple regression equations by t tests because t values of the regression coefficients may not be significantly different from zero when the true (population) values of these coefficients are in fact not zero…†The problem they discuss is not a new one and has been extensively treated in the existing literature. However, their approach is straightforward and will certainly aid the practitioner in his understanding of the problems associated with multicollinearity.

The Student's t Test in Multiple Regression Under Simple Collinearity

This paper is concerned with the validity of the conventional t tests on regression coefficients when there is serious multicollinearity between the explanatory variables. It is well known that increasing multicollinearity causes the true standard errors of regression coefficients to rise. The crucial question, however, is whether the conventional formulas will in practice reflect this rise. The purpose of this note is to show that the conventional t tests will in practice reflect this rise. But this note also points out the danger involved in mechanically dropping variables from multiple regression equations by t tests because t values of the regression coefficients may not be significantly different from zero when the true (population) values of these coefficients are in fact not zero, if the explanatory variables are highly intercorrelated.

An Analogue of Tchebycheff's Inequality in Terms of Range

Tchebycheff's inequality tells us that if the standard deviation of a distribution is a, and the mean is , then the proportion of the distribution which falls outside the limits ,+ ri is not greater than 1/r2. This inequality is remarkable because it holds good for any distribution, irrespective of whether it is normal, binomial, skew, or whatever. Thus, for example, we know that whatever the form of the distribution, the proportion falling outside the ? 3a limits is not greater than 1/9, or about 11%. Of course, if we know the distribution to be normal, or nearly so, we can put much smaller bounds on the amount falling outside the 3a limits. But in some cases the assumption that the distribution we are dealing with is normal is far from the truth. In such cases we can fall back on the Tchebycheff inequality. A discussion of practical applications of the Tchebycheff inequality is contained in Simon (1). It is essential to the correct use of Tchebycheff's inequality that the standard deviation a and the mean , should be the true population values. In practice, a large sample, or a large number of small samples, is necessary. Such data can sometimes be had from control chart records.