Results

Means, standard deviations and correlations are given in Table .

 

Table: Means, standard deviations and correlations of the observed variables (N=185)

			correlations
variable	mean	std dev	$\ln A$	$\ln(m_1-A)$	$\ln(m_2-A)$	$\ln Var_1$	$\ln Var_2$	age
lnmin	2.31	0.26	1.00	0.31	0.29	0.47	0.46	-0.69
$\ln m-A1$	1.26	0.54	0.31	1.00	0.89	0.46	0.51	-0.65
$\ln m-A2$	1.22	0.50	0.29	0.89	1.00	0.46	0.52	-0.62
lnvar1	0.71	1.00	0.47	0.46	0.46	1.00	0.41	-0.56
lnvar2	0.66	1.02	0.46	0.51	0.52	0.41	1.00	-0.53
age	11.08	3.13	-0.69	-0.65	-0.62	-0.56	-0.53	1.00

Note, that the means were not used in the EQS-analysis. The statistical test was not significant ( $\chi^2 = 10.747, df = 9, p = 0.294$), which implies that the model holds. The variance-covariance matrix of the observed variables can be described in terms of the parameters of the Poisson-Erlang model. The program produces also maximum likelihood estimates of the correlations between the theoretical variables; that is between $\ln A$, $\ln \lambda$, $\ln \delta$ and age (see Table ).

 

Table: Standard deviations and correlations of the theoretical variables (N=185)

	$\ln A$	$\ln \lambda$	$\ln \delta$	age
$\ln A$	1.00
$\ln \lambda$	-0.59	1.00
$\ln \delta$	-0.81	0.78	1.00
age	-0.69	0.10	0.57	1.00

Generally, one might expect a negative correlation between the real working time needed ($\ln A$) for the task and age, and a negative correlation between distraction time (inverse of $\ln \delta$) and age, that is a positive correlation between $\ln \delta$ and age. The results (r = -0.69 and r = +0.57) show corroborating evidence. Consequently, the task, as a psychological test, should be standardized to permit age allowances. This means in effect that separate norms are to be prepared for each age group. No correlations whatsoever is to be expected between the duration of the individual working times and age. This is exactly what has been found (r = 0.10). Moreover, an additional test was done, in which, in addition to the constraints given above, the correlation between age and $\ln \lambda$ (F₁) was fixed at zero. The statistical test of the model was again not significant ( $\chi^2 = 11.872, df = 10, p = 0.294$), which is in favor of the hypothesis that no correlation exists between the duration of the individual working times and age. The maximum likelihood estimates of the correlations between the theoretical variables are given in Table .

 

Table: Standard deviations and correlations of the theoretical variables (N=185).
The zero correlation was fixed.

	$\ln A$	$\ln \lambda$	$\ln \delta$	age
$\ln A$	1.00
$\ln \lambda$	-0.53	1.00
$\ln \delta$	-0.77	0.78	1.00
age	-0.67	0.00	0.48	1.00

A test, in which the correlation between age and $\ln \delta$(F₂) was fixed on zero, instead of the correlation between age and $\ln \lambda$ (F₁), was highly significant ( $\chi^2 = 31.180, df = 10, p = 0.001$). These results fit nicely with Spearman: "After intelligence, the most widely supported interpretation of g [the general factor] seems to be the power of attention" (Spearman, 1927, p.88). However, not only one has a theoretical confirmation here, but also a theoretical based measure, a measure of concentration: $\ln \delta$. "Intelligence" actually corresponds to the parameter A, which is inversely related to the speed of work. So, instead of the vague concept of intelligence, one should better use the concept of mental speed.