BACKGROUND: Mainstream psychology is experiencing a crisis of confidence. Many of the methodological solutions offered in response have focused largely on statistical alternatives to null hypothesis statistical testing, ignoring nonstatistical remedies that are readily available within psychology; namely, use of small-N designs. In fact, many classic memory studies that have passed the test of replicability used them. That methodological legacy warranted a retrospective look at nonexperimental data to explore the generality of the reported effects.
METHODS: Various classroom demonstrations were conducted over multiple semesters in introductory psychology courses with typical, mostly freshman students from a predominantly white private Catholic university in the US Midwest based on classic memory experiments on immediate memory span, chunking, and depth of processing.
RESULTS: Students tended to remember 7 ± 2 digits, remembered more digits of π following an attached meaningful story, and remembered more words after elaborative rehearsal than after maintenance rehearsal. These results amount to replications under uncontrolled classroom environments of the classic experiments originally conducted largely outside of null hypothesis statistical testing frameworks.
CONCLUSIONS: In light of the ongoing replication crisis in psychology, the results are remarkable and noteworthy, validating these historically important psychological findings. They are testament to the reliability of reproducible effects as the hallmark of empirical findings in science and suggest an alternative approach to commonly proffered solutions to the replication crisis.

Psychology is undergoing major cultural changes methodologically, with efforts to redefine how psychologists analyze and report their data. Davidson (2018) argued that psychology\'s methodological crises stem from mechanical objectivity involving the adoption of an analytic tool as source of dependable knowledge. This has led to institutionalization, and eventually uncritical ritualistic use, such as happened with null hypothesis statistical testing. Davidson invoked the mythological symbol of the Ouroboros to represent the endless churning of statistical fads. Sidman (1960), in his Tactics of Scientific Research provided a shield from these problems in terms of the premium he placed on the experience, expertise, judgement, and decision-making of the scientist, that appear to be absent in psychology\'s ritualized processes.

UNASSIGNED: Advances in statistical methods and computing power have led to a renewed interest in addressing the statistical analysis challenges posed by Small-N Designs (SND). Linear mixed-effects modeling (LMEM) is a multiple regression technique that is flexible and suitable for SND and can provide standardized effect sizes and measures of statistical significance.
UNASSIGNED: Our primary goals are to: 1) explain LMEM at the conceptual level, situating it in the context of treatment studies, and 2) provide practical guidance for implementing LMEM in repeated measures SND.
UNASSIGNED: We illustrate an LMEM analysis, presenting data from a longitudinal training study of five individuals with acquired dysgraphia, analyzing both binomial (accuracy) and continuous (reaction time) repeated measurements.
UNASSIGNED: The LMEM analysis reveals that both spelling accuracy and reaction time improved and, for accuracy, improved significantly more quickly under a training schedule with distributed, compared to clustered, practice. We present guidance on obtaining and interpreting various effect sizes and measures of statistical significance from LMEM, and include a simulation study comparing two p-value methods for generalized LMEM.
UNASSIGNED: We provide a strong case for the application of LMEM to the analysis of training studies as a preferable alternative to visual analysis or other statistical techniques. When applied to a treatment dataset, the evidence supports that the approach holds up under the extreme conditions of small numbers of individuals, with repeated measures training data for both continuous (reaction time) and binomially distributed (accuracy) dependent measures. The approach provides standardized measures of effect sizes that are obtained through readily available and well-supported statistical packages, and provides statistically rigorous estimates of the expected average effect size of training effects, taking into account variability across both items and individuals.