Literature Index

It is common to summarize statistical comparisons by declarations of statistical<br>significance or non-significance. Here we discuss one problem with such declarations,<br>namely that changes in statistical significance are often not themselves statistically<br>significant. By this, we are not merely making the commonplace observation that<br>any particular threshold is arbitrary - for example, only a small change is required to<br>move an estimate from a 5.1% significance level to 4.9%, thus moving it into statistical<br>significance. Rather, we are pointing out that even large changes in significance levels<br>can correspond to small, non-significant changes in the underlying variables.<br>The error we describe is conceptually different from other oft-cited problems - that<br>statistical significance is not the same as practical importance, that dichotomization into<br>significant and non-significant results encourages the dismissal of observed differences<br>in favor of the usually less interesting null hypothesis of no difference, and that any<br>particular threshold for declaring significance is arbitrary. We are troubled by all of<br>these concerns and do not intend to minimize their importance. Rather, our goal is to<br>bring attention to what we have found is an important but much less discussed point.<br>We illustrate with a theoretical example and two applied examples.

Different studies on how well people take sample size into account have found a wide range of solution rates. In a recent review Sedlmeier and Gigerenzer (1997) suggested that a substantial part of the variation in results can be explained by the fact that experimenters have used two different types of sample-size tasks, one involving frequency distributions and the other sampling distributions. This suggestion rested on an analysis of studies that , with one exception, did not systematically manipulate type of distribution versions. In Study 1, a substantial difference between solution rates for the two types of tasks was found. Study 2 replicated this finding and ruled out an alternative explanation for it, namely, that the solution rate for sampling distribution tasks was lower because the information they contained was harder to extract than that in frequency distribution tasks. Finally, in Study 3 an attempt was make to reduce the gap between the solution rates for the two types of tasks by giving participants as many hints, the gap in performance remained. A new computational model of statistical reasoning specifies cognitive processes that might explain why people are better at solving frequency than sampling distribution tasks.

After 4 decades of severe criticism, the ritual of null hypothesis significance testing - mechanical dichotomous decisions around a sacred .05 criterion - still persists. This article reviews the problems with this practice, including its near-universal misinterpretation of p as the probability that H 0 is false, the misinterpretation that its complement is the probability of successful replication, and the mistaken assumption that if one rejects H 0 one thereby affirms the theory that led to the test. Exploratory data analysis and the use of graphic methods, a steady improvement in and a movement toward standardization in measurement, an emphasis on estimating effect sizes using confidence intervals, and the informed use of available statistical methods is suggested. For generalization, psychologists must finally rely, as has been done in all the older sciences, on replication.

The present work aims to investigate the educational value of statistics as perceived by teachers involved in the teaching of this subject in schools of every type and level in the city of Palermo. To achieve this aim a preliminary fact-finding investigation was performed.