Understanding statistical power in the context of applied research

Estimates of statistical power are widely used in applied research for purposes such as sample size calculations. This paper reviews the benefits of power and sample size estimation and considers several problems with the use of power calculations in applied research that result from misunderstandings or misapplications of statistical power. These problems include the use of retrospective power calculations and standardized measures of effect size. Methods of increasing the power of proposed research that do not involve merely increasing sample size (such as reduction in measurement error, increasing ‘dose’ of the independent variable and optimizing the design) are noted. It is concluded that applied researchers should consider a broader range of factors (other than sample size) that influence statistical power, and that the use of standardized measures of effect size should be avoided (except as intermediate stages in prospective power or sample size calculations)

How many participants do we have to include in properly powered experiments? A tutorial of power analysis with reference tables

Given that an effect size of d = .4 is a good first estimate of the smallest effect size of interest in psychological research, we already need over 50 participants for a simple comparison of two within-participants conditions if we want to run a study with 80% power. This is more than current practice. In addition, as soon as a between-groups variable or an interaction is involved, numbers of 100, 200, and even more participants are needed. As long as we do not accept these facts, we will keep on running underpowered studies with unclear results. Addressing the issue requires a change in the way research is evaluated by supervisors, examiners, reviewers, and editors. The present paper describes reference numbers needed for the designs most often used by psychologists, including single-variable between-groups and repeated-measures designs with two and three levels, two-factor designs involving two repeated-measures variables or one between-groups variable and one repeated-measures variable (split-plot design). The numbers are given for the traditional, frequentist analysis with p 10. These numbers provide researchers with a standard to determine (and justify) the sample size of an upcoming study. The article also describes how researchers can improve the power of their study by including multiple observations per condition per participant

Rapid mapping of digital integrated circuit logic gates via multi-spectral backside imaging

Modern semiconductor integrated circuits are increasingly fabricated at untrusted third party foundries. There now exist myriad security threats of malicious tampering at the hardware level and hence a clear and pressing need for new tools that enable rapid, robust and low-cost validation of circuit layouts. Optical backside imaging offers an attractive platform, but its limited resolution and throughput cannot cope with the nanoscale sizes of modern circuitry and the need to image over a large area. We propose and demonstrate a multi-spectral imaging approach to overcome these obstacles by identifying key circuit elements on the basis of their spectral response. This obviates the need to directly image the nanoscale components that define them, thereby relaxing resolution and spatial sampling requirements by 1 and 2 - 4 orders of magnitude respectively. Our results directly address critical security needs in the integrated circuit supply chain and highlight the potential of spectroscopic techniques to address fundamental resolution obstacles caused by the need to image ever shrinking feature sizes in semiconductor integrated circuits

Standardized or simple effect size: what should be reported?

It is regarded as best practice for psychologists to report effect size when disseminating quantitative research findings. Reporting of effect size in the psychological literature is patchy – though this may be changing – and when reported it is far from clear that appropriate effect size statistics are employed. This paper considers the practice of reporting point estimates of standardized effect size and explores factors such as reliability, range restriction and differences in design that distort standardized effect size unless suitable corrections are employed. For most purposes simple (unstandardized) effect size is more robust and versatile than standardized effect size. Guidelines for deciding what effect size metric to use and how to report it are outlined. Foremost among these are: i) a preference for simple effect size over standardized effect size, and ii) the use of confidence intervals to indicate a plausible range of values the effect might take. Deciding on the appropriate effect size statistic to report always requires careful thought and should be influenced by the goals of the researcher, the context of the research and the potential needs of readers

An investigation of the grindability of two torrefied energy crops

The process of torrefaction alters the physical properties of biomass, reducing its fibrous tenacious nature. This could allow increased rates of co-milling and therefore co-firing in coal fired power stations, which in turn would enable a reduction in the amount of coal used and an increase in the use of sustainable fuels, without the need for additional plant. This paper presents an experimental investigation of the pulverisation behaviour of two torrefied energy crops, namely: willow and Miscanthus. A multifactorial method approach was adopted to investigate the three process parameters of temperature, residence time and particle size, producing fuels treated using four different torrefaction conditions. The untreated and torrefied fuels were subjected to standard fuel analysis techniques including ultimate analysis, proximate analysis and calorific value determination. The grindability of these fuels was then determined using a laboratory ball mill and by adapting the Hardgrove Grindability Index (HGI) test for hard coals. After grinding, two sets of results were obtained. Firstly a determination similar to the HGI test was made, measuring the proportion of sample passing through a 75 mu m sieve and plotting this on a calibrated HGI chart determined using four standard reference coals of known HGI values. Secondly the particle size distributions of the entire ground sample were measured and compared with the four standard reference coals. The standard fuel tests revealed that temperature was the most significant parameter in terms of mass loss, changes in elemental composition and energy content increase. The first grindability test results found that the untreated fuels and fuels treated at low temperatures showed very poor grindability behaviour. However, more severe torrefaction conditions caused the fuels to exhibit similar pulverisation properties as coals with low HGI values. Miscanthus was found to have a higher HGI value than willow. On examining the particle size distributions it was found that the particle size distributions of torrefied Miscanthus differed significantly from the untreated biomass and had comparable profiles to those of the standard reference coals with which they had similar HGI values. However, only the torrefied willow produced at the most severe conditions investigated exhibited this behaviour, and the HGI of torrefied willow was not generally a reliable indicator of grindability performance for this energy crop. Overall it was concluded that torrefied biomass can be successfully pulverised and that torrefied Miscanthus was easier to grind than torrefied willow

Beyond baseline and follow-up : the case for more t in experiments

The vast majority of randomized experiments in economics rely on a single baseline and single follow-up survey. If multiple follow-ups are conducted, the reason is typically to examine the trajectory of impact effects, so that in effect only one follow-up round is being used to estimate each treatment effect of interest. While such a design is suitable for study of highly autocorrelated and relatively precisely measured outcomes in the health and education domains, this paper makes the case that it is unlikely to be optimal for measuring noisy and relatively less autocorrelated outcomes such as business profits, household incomes and expenditures, and episodic health outcomes. Taking multiple measurements of such outcomes at relatively short intervals allows the researcher to average out noise, increasing power. When the outcomes have low autocorrelation, it can make sense to do no baseline at all. Moreover, the author shows how for such outcomes, more power can be achieved with multiple follow-ups than allocating the same total sample size over a single follow-up and baseline. The analysis highlights the large gains in power from ANCOVA rather than difference-in-differences when autocorrelations are low and a baseline is taken. The paper discusses the issues involved in multiple measurements, and makes recommendations for the design of experiments and related non-experimental impact evaluations.Scientific Research&Science Parks,Science Education,Statistical&Mathematical Sciences,Disease Control&Prevention,Economic Theory&Research