Help! Is my sample big enough?

© 2017 The Royal Statistical Society Anne Beeston writes: I am planning a study to evaluate the efficacy of a treatment to reduce the microbial load in dried flowers, and need some advice on sample size to allow the determination of statistically significant differences in two groups

Mathematics, statistics and operational research project B: Book of Abstracts 2014-2016

This collection of abstracts represents student work over the course of two academic years. It highlights the wide variety of project topics that are run under the banner of MSOR (b) projects.The motivation behind the research topics chosen by students doing this project module is varied. It can arise from personal interests, from placement experience, or research topics can be driven by collaborations with partners both inside and outside of UWE.Some projects presented here using real data collaborating with partners have associated reporting restrictions. The others, either based on using simulations or publically available data, or based on theoretical work, have no such restrictions.Each year has a separate table of contents. The advisors names have been included beside each project title to help inform potential students about the type of topics that staff members have previously advised upon.We want to congratulate those graduates whose research is included in this collection and thank them for the time and effort they have given in undertaking their projects. I am honoured to share in our graduates’ success and delighted to have this opportunity to open up their work to a wider audience. We wish all our graduates every success in their future

Scrambled statistics: What are the chances of finding multi-yolk eggs?

© 2016 The Royal Statistical Society Journalists ask a lot of questions of statisticians, but some are more bizarre than others. Statistical ambassador Deirdre Toher recounts one such experience

Why Welch’s test is Type I error robust

The comparison of two means is one of the most commonly applied statistical procedures in psychology. The independent samples t-test corrected for unequal variances is commonly known as Welch’s test, and is widely considered to be a robust alternative to the independent samples t-test. The properties of Welch’s test that make it Type I error robust are examined. The degrees of freedom used in Welch’s test are a random variable, the distributions of which are examined using simulation. It is shown how the distribution for the degrees of freedom is dependent on the sample sizes and the variances of the samples. The impact of sample variances on the degrees of freedom, the resultant critical value and the test statistic is considered, and hence gives an insight into why Welch’s test is Type I error robust under normality

How to compare the means of two samples that include paired observations and independent observations: A companion to Derrick, Russ, Toher and White (2017)

Standard approaches for comparing the means of two samples, comprising both paired observations and independent observations, involve the discarding of valuable information. An alternative test which uses all of the available data, is the partially overlapping samples t-test. Two variations of the test are available, one assuming equal variances, and one assuming separate variances. Issues with standard procedures, and considerations for choosing appropriate tests in the partially overlapping scenario are discussed. An example with details of how to apply the partially overlapping samples t-test is given along with an R package that implement these new tests

Challenge and change: Police identity, morale and goodwill in an age of austerity

One of the largest pieces of independent research on police attitudes in England and Wales. The research, led by Dr James Hoggett from UWE Bristol (the University of the West of England, Bristol), looked at police attitudes to current reform proposals that may impact on the profession. 13,591 police officers across 43 forces in England and Wales responded to a questionnaire into attitudes and morale amongst officers. The response rate reflects the views of about 10% of all serving police officers in England and Wales. The attitude and morale data provided consistent messages across the sample with only minor variations between ranks of officer or between police forces

An inverse normal transformation solution for the comparison of two samples that contain both paired observations and independent observations

Inverse normal transformations applied to the partially overlapping samples t-tests by Derrick et.al. (2017) are considered for their Type I error robustness and power. The inverse normal transformation solutions proposed in this paper are shown to maintain Type I error robustness. For increasing degrees of skewness they also offer improved power relative to the parametric partially overlapping samples t-tests. The power when using inverse normal transformation solutions are comparable to rank based non-parametric solutions

Test statistics for the comparison of means for two samples that include both paired and independent observations

©2017 JMASM, Inc. Standard approaches for analyzing the difference in two means, where partially overlapping samples are present, are less than desirable. Here are introduced two test statistics, making reference to the t-distribution. It is shown that these test statistics are Type I error robust, and more powerful than standard tests