Literature Index

Displaying 3051 - 3060 of 3326

  • Understanding repeated simple choices

    Author(s):
    Gal, I., & Baron, J.
    Year:
    1996
    Abstract:
    This study examined students' reasoning about simple repeated choices. Each choice involved "betting" on two events, differing in probability. We asked subjects to generate or evaluate alternative strategies such as betting on the most likely event on every trial, betting on it on almost every trial, or employing a "probability matching" strategy. Almost half of the college students did not generate or rank strategies according to their expected value, but few subjects preferred a strategy of strict probability matching. High-school students showed greater deviations from expected value than college students. Similar misunderstandings were observed in a choice task involving real (not hypothetical) repeated trials. Large gender differences in prediction strategies and in related computational skills were observed. Subjects who understand the optimal strategy usually do so in terms of independence of successive trials rather than calculation. Some subjects understand the concept of independence but fail to bring it to bear, thinking it can be overridden by intuition or local balancing (representativeness).

  • Understanding replication: Confidence intervals, p values, and what's likely to happen next time.

    Author(s):
    Cumming, G.
    Editors:
    Rossman, A., & Chance, B.
    Year:
    2006
    Abstract:
    Science loves replication: We conclude an effect is real if we believe replications would also show the effect. It is therefore crucial to understand replication. However, there is strong evidence of severe, widespread misconception about p values and confidence intervals, two of the main statistical tools that guide us in deciding whether an observed effect is real. I propose we teach about replication directly. I describe three approaches: Via confidence intervals (What is the chance the original confidence interval will capture the mean of a repeat of the experiment?); Via p values (Given an initial p value, what is the distribution of p values for replications of the experiment?): and via Peter Killeen's 'prep', which is the average probability that a replication will give a result in the same direction. In each case I will demonstrate an interactive graphical simulation designed to make the tricky ideas of replication vividly accessible.
    Location:
    http://www.stat.auckland.ac.nz/~iase/publications/17/7D3_CUMM.pdf

  • Understanding Statistical Misconceptions

    Author(s):
    Callaert, H.
    Editors:
    Phillips, B.
    Year:
    2002
    Abstract:
    This paper reports on a preliminary study conducted for gaining better insight in the complexity of students' misconceptions of representativeness. Data from 156 students (112 high school graduates and 44 students with a university degree) are presented. The overall outcome indicates a lack of ability to refer problems about specific experiments to their correct context. Some results seem to contradict part of the representativeness heuristic described by Kahneman and Tversky (1972). They might also indicate that multiple-choice tests, even with two-part questions, are not able to fully capture the deep complexity of students' misunderstandings.
    Location:
    http://www.stat.auckland.ac.nz/~iase/publications/1/10_07_ca.pdf

  • Understanding statistics

    Author(s):
    Bodmer, W. F.
    Year:
    1985
    Abstract:
    Some understanding of statistics is needed at all levels in society from the individual in his or her personal life to the professional statistician in the university or research institute, in Government or in business. Simple statistical and experimental principles underlie the understanding and interpretation of many everyday phenomena. There is a very strong case for improving the level of numeracy and statistical understanding at all levels in our society.

  • Understanding Statistics and Statistics Education: A Chinese Perspective

    Author(s):
    Ning-Zhong Shi, Xuming He, and Jian Tao
    Year:
    2009
    Abstract:
    In recent years, statistics education in China has made great strides. However, there still exists a fairly large gap with the advanced levels of statistics education in more developed countries. In this paper, we identify some existing problems in statistics education in Chinese schools and make some proposals as to how they may be overcome. We hope that our study can benefit the development of statistics education in China, and encourage statistics educators and researchers in other countries to help address these important issues in China and possibly in other developing countries.
    Location:
    http://www.amstat.org/publications/jse/v17n3/shi.html

  • Understanding Student Attempts to Find a Line of Fit

    Author(s):
    M. Alejandra Sorto, Alexander White and Lawrence M. Lesser
    Year:
    2011
    Abstract:
    The least squares method of fitting a line is not one that naturally occurs to students. We present three tasks to understand student views on how lines may be fit.
    Location:
    http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9639.2010.00458.x/abstract

  • Understanding Students' Beliefs About Probability

    Author(s):
    Konold, C.
    Editors:
    von Glasersfeld, E.
    Year:
    1991
    Abstract:
    Although I don't want here to defend my point of view, it will serve my purposes to exemplify what I regard as a contrary one. My assumption is that students have intuitions about probability and that they can't check these in at the classroom door. The success of the teacher depends on large part on how these notions are treated in relation of those the teacher would like the student to acquire. Additionally, I think it is a myth that mathematics, either as a discipline or in the mind of a mathematician, develops independently from concerns about objects and relations that are believed to have real-world referents. This was certainly not so in the case of the development of probability theory.

  • Understanding Students' Experiences of Statistics in a Service Course

    Author(s):
    Gordon, S.
    Editors:
    Joliffe, F., & Gal, I.
    Year:
    2004
    Abstract:
    In this paper we explore issues surrounding university students' experiences of statistics drawing on data related to learning statistics as a compulsory component of psychology. Over 250 students completed a written survey which included questions on their attitudes to learning statistics and their conceptions of statistics. Results indicated that most students were studying statistics unwillingly. A minority of students acknowledged that statistics was necessary for psychology, but statistics was seen by many as boring or difficult. Students' conceptions of statistics were analysed from a perspective developed from phenomenography (Marton & Booth, 1997). The aim of phenomenographic research is to describe the qualitative variation in the ways people experience or conceptualise a phenomenon - in this case students' interpretations of the topic statistics. The conceptions fell into five categories of description including: statistics as decontextualised processes and algorithms, statistics as a tool for professional life and statistics as a way to self-development and enhanced perspectives on our world. Excerpts from interviews with selected students indicate the diversity of experiences in learning statistics. The perceptions of two teachers flesh out the learning and teaching environment. The findings raise challenges for supporting the learning of "occasional users" (Nicholls, 2001) of statistics in higher education.
    Location:
    http://www.stat.auckland.ac.nz/~iase/serj/SERJ3(1)_gordon.pdf

  • Understanding students' statistical thinking: An error analysis approach

    Author(s):
    Nasser, F.
    Year:
    2000
    Abstract:
    This exploratory study examined errors that students commit solving multiple-choice questions about descriptive statistics and basic concepts in research methods. The sample consisted of 81 undergraduate students in an introductory statistics course. The results indicated that the most frequently detected errors were confusing concepts, misinterpreting descriptive information, applying inappropriate procedures and applying partial information. Analysis reveal potential sources of students' errors include assimilation of statistical concepts into inappropriate schemata, failure to use knowledge sources, and lack of ability to relate and combine knowledge from different sources.

  • Understanding the Effects of Sample Size on the Variability of the Mean

    Author(s):
    Well, A. D., Pollatsek, A., & Boyce, S. J.
    Year:
    1990
    Abstract:
    In the first three experiments, we attempted to learn more about subjects' understanding of the importance of sample size by systematically changing aspects of the problems we gave to subjects. In a fourth study, understanding of the effects of sample size was tested as subjects went through a computer-assisted training procedure that dealt with random sampling and the sampling distribution of the mean. Subjects used sample size information more appropriately for problems that were stated in terms of the accuracy of the sample average or the center of the sampling distribution than for problems stated in terms of the tails of the sampling distribution. Apparently, people understand that the means of larger samples are more likely to resemble the population mean but not the implications of this fact for the variability of the mean. The fourth experiment showed that although instruction about the sampling distribution of the mean led to better understanding of the effects of sample size, subjects were still unable to make correct inferences about the variability of the mean. The appreciation that people have for some aspects of the law of large numbers does not seem to result from an in-depth understanding of the relation between sample size and variability.

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The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education