Heimann (1993) shows, however that, in a three-state world in which one is concerned about committing either a Type I or Type II error
(and where the third state is the correct decision), serial systems are superior because they reduce the likelihood of Type I errors--at is, rejecting the null hypothesis when it is actually correct (acting when no action is necessary or desirable).
The probability of committing a Type II error
, which we are willing to accept is called beta ([beta]).
Attempting to follow guidelines for best practice, the school counselor rejects a potential peer program because the researchers underestimated the magnitude of their results and failed to report power in their article, analogous to a Type II error
. Because the researchers misrepresented the data, the school counselor misses the opportunity to take advantage of a potential resource that could make a difference in the lives of the children in the district, and the students are denied an opportunity to receive an effective program.
The probability of type II error
([beta]) is not usually controllable (Keough and Mapstone, 1997) and to some extent, high and is not reported in studies with several methodology (psychology: Sedlmeier and Gigrenzer 1989; Cohen 1962; fishery and hydrology: Peterman 1990a; Studies of Environmental Effects: Fairweather 1991; Mapstone 1995).
More conservative criteria imply a very high probability of type II errors
, i.e., that clinically significant brain activations would remain undetected.
Conversely, a Type II error
arises when an anticompetitive merger is approved.
The aforementioned conservativeness of TA was reflected in extremely high Type II error
Moreover, there is evidence for the deficient performance, in terms of Type I and/or Type II errors
, of statistical techniques as diverse as ANOVA (Toothaker, Banz, Noble, Camp, & Davis, 1983), time-series analysis (Greenwood & Matyas, 1990), the split-middle method (Crosbie, 1987), and randomization tests (Ferron & Ware, 1995; Sierra, Solanas, & Quera, 2005).
As the results revealed in Table 6, the neural networks model has the lowest Type II error
in comparison with the other three approaches.
However, we have always to remember about the possibility to commit a Type I or Type II error
It is possible that a Type II error
may have occurred in the six follow-up analyses because the validity of the Smith's has not been determined, the educational program did not have a strong enough effect, an optical evaluation was not performed on participants, or due to study limitations and weaknesses, which are discussed in the next section.
This study then becomes an example of a type II error
where finding that there is no difference between the two groups is primarily a factor of the small sample size rather than a reflection of an actual lack of difference.