The concepts of hypothesis testing, trade-offs between Type I and Type II error, and the use of power in choosing an appropriate sample size based on power when designing an experiment are routinely included in many introductory statistics courses. However, many students do not fully grasp the importance of these ideas and are unable to implement them in any meaningful way at the conclusion of the course. This paper presents a number of applets intended to help students understand the role of power in hypothesis testing and which allow them to obtain numerical values without having to perform any calculations for a variety of scenarios, complementing some of the applets presented in
Aberson, Berger, Healy, and Romero (2002). Ideas are given about how to incorporate the materials into an introductory course.
Key Words: Internet; Java applet; One-sample hypothesis test; Two-sample hypothesis test.
Advances in technology coupled with increasing student enrollment numbers have led some universities to begin offering on-line classes. This paper discusses a study comparing a traditional offering of elementary statistics with a "hybrid" offering. In the hybrid offering the class met once a week, but students were required to learn the material on their own using web-based materials and a textbook. We examined differences in student performance, student satisfaction and investment of both student and instructor time. Performance of students in the hybrid offering equaled that of the traditional students, but students in the hybrid were slightly less positive in their subjective evaluation of the course.
Key Words: Distance learning; Teaching elementary statistics; Web-based instruction
Many elementary statistics textbooks recommend the sign test as an
alternative to the t-test when the normality assumption is violated.
This recommendation is not always warranted, as we demonstrate by
extending previous studies of the effects of skewness, kurtosis, and
shifting of the location parameter on the size and power of the t-
and sign tests for the one-sample case. For skewed populations our
simulations reveal that the power of the t-test can actually be
higher than that of the t-test for a normal parent population when
the location parameter is shifted in the opposite direction of the
skewness of population. In that same instance, the power of the t-test
is also significantly greater than that of the sign test.
Furthermore, our simulations reveal that for low-kurtosis populations
the power of the t-test is again greater than that of the sign test.
Key Words: Level of significance; Power; Robustness.
In this article, a very simple and yet useful feature of Excel called the SPIN BUTTON is used to illustrate two concepts associated with attribute acceptance sampling plans.
The first concept is calculating the probability of lot acceptance based on which the operating characteristic (OC) curve of an attribute sampling plan is drawn. The SPIN BUTTON can show, visually, that the exact probability of lot acceptance calculated using the Hypergeometric distribution can be approximated by the Binomial distribution. The second concept is how the probability of lot acceptance changes when either one of the three parameters
N, n, c of a sampling plan changes. The SPIN BUTTON can also visually show us how the shape of the OC curve of a sampling plan changes when the parameters vary.
Key Words: Attribute sampling; Binomial distribution; Excel; Hypergeometric distribution.
The estimation of proportions is a subject which cannot be circumvented in a first survey sampling course. Estimating the proportion of voters in favour of a political party, based on a political opinion survey, is just one concrete example of this procedure. However, another important issue in survey sampling concerns the proper use of auxiliary information, which typically comes from external sources, such as administrative records or past surveys. Very often, an efficient insertion of the auxiliary information available will improve the precision of the estimations of the mean or the total when a regression estimator is used. Conceptually, it is difficult to justify using a regression estimator for estimating proportions. A student might want to know how the estimation of proportions can be improved when auxiliary information is available. In this article, I present estimators for a proportion which use the logistic regression estimator. Based on logistic models, this estimator efficiently facilitates a good modelling of survey data. The paperís second objective is to estimate a proportion using various sampling plans (such as a Bernoulli sampling and stratified designs). In survey sampling, each sample possesses its own probability and for a given unit, the inclusion probability denotes the probability that the sample will contain that particular unit. Bernoulli sampling may have an important pedagogical value, because students often have trouble with the concept of the inclusion probability. Stratified sampling plans may provide more insight and more precision. Some empirical results derived from applying four sampling plans to a real data base show that estimators of proportions may be made more efficient by the proper use of auxiliary information and that choosing a more satisfactory model may give additional precision. The paper also contains computer code written in S-Plus and a number of exercises.
Key Words: Auxiliary information; Bernoulli sampling; Confidence interval; Logistic regression estimator; Sampling plan; Survey sampling.
This study investigated the relationship between a constructivist learning environment and students' attitudes
toward statistics. The
Constructivist Learning Environment Survey (CLES) and the
Attitude Toward Statistics scale (ATS) were used to measure the environment and attitudes respectively. Participants were undergraduate students of an introductory college statistics course. They were drawn from Seattle Pacific University in the US and the University of Zimbabwe.
The study had two components. One component addressed hypotheses examining potential differences between groups and the other explored relationships between variables. The environment was not manipulated and the data was collected from courses that already existed in the form studied. For this reason, the overall design of the study had causal comparative and correlational elements. A constructivist learning environment was found to be significantly related to students' attitude toward statistics. Furthermore, there were significant differences between the groups based on location.
The study examined the similarities and differences in perceptions and attitudes of students from two very different learning milieus. Cross-cultural comparisons have the potential to generate new insights into statistical pedagogy and the role noncognitive socio cultural variables play in teaching statistics to college-age students.
Key Words: Anxiety; Attitude Toward Statistics scale; Constructivist Learning Environment Survey; Non-cognitive factors.
Teaching Bits: A Resource for Teachers of Statistics
This department features information sampled from a variety of sources that may be of
interest to teachers of statistics. Deb Rumsey abstracts information from the literature on
teaching and learning statistics, while Bill Peterson summarizes articles from the news and
other media that may be used with students to provoke discussions or serve as a basis for
classroom activities or student projects.