In psychology, attempts to replicate published findings are less successful than expected. For properly powered studies replication rate should be around 80%, whereas in practice less than 40% of the studies selected from different areas of psychology can be replicated. Researchers in cognitive psychology are hindered in estimating the power of their studies, because the designs they use present a sample of stimulus materials to a sample of participants, a situation not covered by most power formulas. To remedy the situation, we review the literature related to the topic and introduce recent software packages, which we apply to the data of two masked priming studies with high power. We checked how we could estimate the power of each study and how much they could be reduced to remain powerful enough. On the basis of this analysis, we recommend that a properly powered reaction time experiment with repeated measures has at least 1,600 word observations per condition (e.g., 40 participants, 40 stimuli). This is considerably more than current practice. We also show that researchers must include the number of observations in meta-analyses because the effect sizes currently reported depend on the number of stimuli presented to the participants. Our analyses can easily be applied to new datasets gathered.

We present word frequencies based on subtitles of British television programmes. We show that the SUBTLEX-UK word frequencies explain more of the variance in the lexical decision times of the British Lexicon Project than the word frequencies based on the British National Corpus and the SUBTLEX-US frequencies. In addition to the word form frequencies, we also present measures of contextual diversity part-of-speech specific word frequencies, word frequencies in children programmes, and word bigram frequencies, giving researchers of British English access to the full range of norms recently made available for other languages. Finally, we introduce a new measure of word frequency, the Zipf scale, which we hope will stop the current misunderstandings of the word frequency effect.

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 < .05 and Bayesian analysis with BF > 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.