Explorations in statistics: correlation

Quantitative study of lecture attendance and the association between this attendance and academic outcomes for nursing and nonnursing students in an introductory pathophysiology course

Since the availability of lecture recordings, there have been limited studies of any associations between face-to-face lecture attendance and academic outcomes. The aims of the study, in an introductory pathophysiology course, where lecture recordings were available, were 1) to quantify lecture attendance and any associations between academic outcomes and lecture attendance, and 2) to determine why students do or do not attend lectures. Data were analyzed for the whole cohort before separating the nursing (∼60%) and nonnursing students. Of 288 enrolled students, 205 consented to sign the attendance register, and 139 to undertake the online survey. Lecture attendance was higher (41%) before the midsemester exam than afterwards (24%), P < 0.001, due to higher attendance by the nursing than nonnursing students. Students who attended ≥50% of lectures consistently got higher academic outcomes than those that attended <50%, e.g., examinations, 11 percent points higher. Pearson's or Spearman's correlation coefficients for students from both the sign-in and survey showed that there were positive associations between lecture attendance and academic outcomes, which were mainly weak for nursing students (P ≤ 0.05), with no association for nonnursing students. From the survey, most students who attended lectures did so because they considered they learned more by attending lectures, whereas not liking the lecture time was the most common reason for not attending lectures. In conclusion, even though students have access to lecture recordings, lecture attendance is still a determinant of academic outcomes for some students of pathophysiology.

Statistical considerations in reporting cardiovascular research

The problem of inadequate statistical reporting is long standing and widespread in the biomedical literature, including in cardiovascular physiology. Although guidelines for reporting statistics have been available in clinical medicine for some time, there are currently no guidelines specific to cardiovascular physiology. To assess the need for guidelines, we determined the type and frequency of statistical tests and procedures currently used in the American Journal of Physiology-Heart and Circulatory Physiology. A PubMed search for articles published in the American Journal of Physiology-Heart and Circulatory Physiology between January 1, 2017, and October 6, 2017, provided a final sample of 146 articles evaluated for methods used and 38 articles for indepth analysis. The t-test and ANOVA accounted for 71% (212 of 300 articles) of the statistical tests performed. Of six categories of post hoc tests, Bonferroni and Tukey tests were used in 63% (62 of 98 articles). There was an overall lack in details provided by authors publishing in the American Journal of Physiology-Heart and Circulatory Physiology, and we compiled a list of recommended minimum reporting guidelines to aid authors in preparing manuscripts. Following these guidelines could substantially improve the quality of statistical reports and enhance data rigor and reproducibility.

Explorations in statistics: the log transformation

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This thirteenth installment of Explorations in Statistics explores the log transformation, an established technique that rescales the actual observations from an experiment so that the assumptions of some statistical analysis are better met. A general assumption in statistics is that the variability of some response Y is homogeneous across groups or across some predictor variable X. If the variability-the standard deviation-varies in rough proportion to the mean value of Y, a log transformation can equalize the standard deviations. Moreover, if the actual observations from an experiment conform to a skewed distribution, then a log transformation can make the theoretical distribution of the sample mean more consistent with a normal distribution. This is important: the results of a one-sample t test are meaningful only if the theoretical distribution of the sample mean is roughly normal. If we log-transform our observations, then we want to confirm the transformation was useful. We can do this if we use the Box-Cox method, if we bootstrap the sample mean and the statistic t itself, and if we assess the residual plots from the statistical model of the actual and transformed sample observations.

Explorations in statistics: the assumption of normality

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This twelfth installment of Explorations in Statistics explores the assumption of normality, an assumption essential to the meaningful interpretation of a t test. Although the data themselves can be consistent with a normal distribution, they need not be. Instead, it is the theoretical distribution of the sample mean or the theoretical distribution of the difference between sample means that must be roughly normal. The most versatile approach to assess normality is to bootstrap the sample mean, the difference between sample means, or t itself. We can then assess whether the distributions of these bootstrap statistics are consistent with a normal distribution by studying their normal quantile plots. If we suspect that an inference we make from a t test may not be justified-if we suspect that the theoretical distribution of the sample mean or the theoretical distribution of the difference between sample means is not normal-then we can use a permutation method to analyze our data.

Explorations in statistics: statistical facets of reproducibility

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This eleventh installment of Explorations in Statistics explores statistical facets of reproducibility. If we obtain an experimental result that is scientifically meaningful and statistically unusual, we would like to know that our result reflects a general biological phenomenon that another researcher could reproduce if (s)he repeated our experiment. But more often than not, we may learn this researcher cannot replicate our result. The National Institutes of Health and the Federation of American Societies for Experimental Biology have created training modules and outlined strategies to help improve the reproducibility of research. These particular approaches are necessary, but they are not sufficient. The principles of hypothesis testing and estimation are inherent to the notion of reproducibility in science. If we want to improve the reproducibility of our research, then we need to rethink how we apply fundamental concepts of statistics to our science.

Explorations in statistics: the analysis of change

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This tenth installment of Explorations in Statistics explores the analysis of a potential change in some physiological response. As researchers, we often express absolute change as percent change so we can account for different initial values of the response. But this creates a problem: percent change is really just a ratio, and a ratio is infamous for its ability to mislead. This means we may fail to find a group difference that does exist, or we may find a group difference that does not exist. What kind of an approach to science is that? In contrast, analysis of covariance is versatile: it can accommodate an analysis of the relationship between absolute change and initial value when percent change is useless.

Explorations in statistics: the analysis of ratios and normalized data

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This ninth installment of Explorations in Statistics explores the analysis of ratios and normalized-or standardized-data. As researchers, we compute a ratio-a numerator divided by a denominator-to compute a proportion for some biological response or to derive some standardized variable. In each situation, we want to control for differences in the denominator when the thing we really care about is the numerator. But there is peril lurking in a ratio: only if the relationship between numerator and denominator is a straight line through the origin will the ratio be meaningful. If not, the ratio will misrepresent the true relationship between numerator and denominator. In contrast, regression techniques-these include analysis of covariance-are versatile: they can accommodate an analysis of the relationship between numerator and denominator when a ratio is useless.

Explorations in statistics: permutation methods

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This eighth installment of Explorations in Statistics explores permutation methods, empiric procedures we can use to assess an experimental result-to test a null hypothesis-when we are reluctant to trust statistical theory alone. Permutation methods operate on the observations-the data-we get from an experiment. A permutation procedure answers this question: out of all the possible ways we can rearrange the observations we got, in what proportion of those arrangements is the sample statistic we care about at least as extreme as the one we got? The answer to that question is the P value.

Explorations in statistics: regression

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of Explorations in Statistics explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive connection. Regression helps us answer three questions: does some variable Y depend on another variable X; if so, what is the nature of the relationship between Y and X; and for some value of X, what value of Y do we predict? Residual plots are an essential component of a thorough regression analysis: they help us decide if our statistical regression model of the relationship between Y and X is appropriate.