Literature Index

This study provides an investigation of relationships among different types of errors occurring during probability problem-solving. Fifty non-mathematically sophisticated graduate student subjects enrolled in an introductory probability and statistics course were asked to solve a set of probability problems, and their attempts at solution were analyzed for presence and type of errors. The errors contained within these solutions were categorized according to a coding scheme which identifies 110 specific kinds of errors in four categories: text comprehension errors, conceptual errors, procedural errors, and arithmetic/computation errors. Relationships among types of errors included in each category were investigated using hierarchical clustering via additive trees. Implications of these relationships for the teaching and learning of probability problem-solving are discussed.

In many books on Statistics, it is often stated that correlation between two variables X and Y is positive if, as X increases Y also increase. Equivalently, correlation between X and Y is positive, if large values of X most often correspond to the large values of Y and small values X, most often correspond to small values of Y. The correlation is negative if large values of X most often correspond to small values of Y and visa versa. With an example we show that this statement in not always correct. We also give the correct interpretation for the sign of the correlation and its relation to the behavior of the two random variables.

We describe a web-based interactive graphic that can be used as a resource in introductory classes in mathematical statistics. This interactive graphic presents 76 common univariate distributions and gives details on (a) various features of the distribution such as the functional form of the probability density function and cumulative distribution function, graphs of the probability density function for various parameter settings, and values of population moments; (b) properties that the distribution possesses, for example, linear combinations of independent random variables from a particular distribution family also belong to the same distribution family; and (c) relationships between the various distributions, including special cases, transformations, limiting distributions, and Bayesian relationships. The interactive graphic went online on 11/30/12 at the URL www.math.wm.edu/ leemis/chart/UDR/ UDR.html.

The research question in this study was assessing possible relationships between formal<br>knowledge of conditional probability as well as biases related to conditional probability reasoning: fallacy of<br>the transposed conditional; fallacy of the time axis; base rate fallacy; synchronic and diachronic situations;<br>conjunction fallacy; and confusing independence and mutually exclusiveness. Two samples of university<br>students majoring in psychology and following the same introductory statistics course were given the CPR<br>test before (n = 177) and after (n = 206) formal teaching of conditional probability. Results indicate a<br>systematic improvement in formal understanding of conditional probability and in problem solving capacity<br>but little change in those items related to psychological biases