Because rmcorr takes into account non-independence, it tends to yield much greater power than data that are averaged in order to meet the IID assumption for simple regression/correlation. Unlike the Pearson correlation, which assesses the inter-individual association because it assumes each paired data point is Independent and Identically Distributed (IID), rmcorr evaluates the overall or common intra-individual association between two measures. Also akin to the Pearson correlation, the null hypothesis for rmcorr is ρ rm = 0, and the research/alternative hypothesis is ρ rm ≠ 0. Like a Pearson correlation coefficient (r), the rmcorr coefficient ( r rm) is bounded by −1 to 1 and represents the strength of the linear association between two variables. By removing measured variance between-participants, rmcorr provides the best linear fit for each participant using parallel regression lines (the same slope) with varying intercepts. Rmcorr accounts for non-independence among observations using analysis of covariance (ANCOVA) to statistically adjust for inter-individual variability. Here, we refer to the technique as the repeated measures correlation (rmcorr). Furthermore, analysis of individual differences can be useful as a strong test for theory ( Underwood, 1975 Vogel and Awh, 2008).īland and Altman (1995a, b) introduced the within-participants correlation in biostatistics to analyze the common intra-individual association for paired repeated measures, which are two corresponding measures assessed for each participant/case/individual on two or more occasions. This aggregation may resolve the issue of non-independence but can produce misleading results if there are meaningful individual differences ( Estes, 1956 Myung et al., 2000). One common solution is to average the repeated measures data for each participant prior to performing the correlation. Analyzing non-independent data with techniques that assume independence is a widespread practice but one that often produces erroneous results ( Kenny and Judd, 1986 Molenaar, 2004 Aarts et al., 2014). For example, if a study collected height and weight for a sample of people at three time points, there would likely be non-independence in the errors of the three observations belonging to the same person. However, the assumption of independence is violated in repeated measures, in which each participant provides more than one data point. For example, when correlating the current height and weight of people drawn from a random sample, there is no reason to expect a violation of independence. This assumption does not pose a problem if each participant or independent observation is a single data point of paired measures (i.e., two data points corresponding to the same individual such as height and weight). However, widely used techniques for correlation, such as simple (ordinary least squares with a single independent variable) regression/Pearson correlation, assume independence of error between observations ( Howell, 1997 Johnston and DiNardo, 1997 Cohen et al., 2003). All results are fully reproducible.Ĭorrelation is a popular measure to quantify the association between two variables. Rmcorr is well-suited for research questions regarding the common linear association in paired repeated measures data. The examples are used to illustrate research questions at different levels of analysis, intra-individual, and inter-individual. We introduce the R package (rmcorr) and demonstrate its use for inferential statistics and visualization with two example datasets. To make rmcorr accessible, we provide background information for its assumptions and equations, visualization, power, and tradeoffs with rmcorr compared to multilevel modeling. Rmcorr estimates the common regression slope, the association shared among individuals. Also, rmcorr tends to have much greater statistical power because neither averaging nor aggregation is necessary for an intra-individual research question. Unlike simple regression/correlation, rmcorr does not violate the assumption of independence of observations. Simple regression/correlation is often applied to non-independent observations or aggregated data this may produce biased, specious results due to violation of independence and/or differing patterns between-participants versus within-participants. Repeated measures correlation (rmcorr) is a statistical technique for determining the common within-individual association for paired measures assessed on two or more occasions for multiple individuals. 2US Army Laboratory South Field Element, Human Research and Engineering Directorate, University of Texas Arlington, Arlington, TX, USA.1US Army Research Laboratory, Human Research and Engineering Directorate, Aberdeen Proving Ground, USA.
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