Comparing groups of time dependent data using locally weighted scatterplot smoothing alpha-adjusted serial T-tests

Abstract

BackgroundIn statistical analysis of time series researchers often pick key points from curves and run the venerable analysis of variance (ANOVA) to determine if a difference exists between groups. However, this approach fails to compare most of the data across time and thereby may throw out potentially valuable inferences. Research questionThis study illustrates a novel method termed LOESS alpha-adjusted serial t-testing (LAAST). LAAST employs locally weighted scatterplot smoothing (LOESS) on the data, serial correlation to make alpha adjustments, and point-wise Welch's t-tests to determine regional significance when comparing groups of time dependent data. It was expected that LAAST gives similar results to random field theory (RFT) based inferences while overcoming its shortcomings with respect to longitudinal data analysis. MethodsTwo data sets were analyzed with LAAST and RFT. The first contained two groups of five simulated random sinusoidal waveforms such that both inline time-series and equivalent time-offset longitudinal conditions were represented. The second data set was comprised of publicly available medial gastrocnemius forces from individuals with (N = 27) and without (N = 16) pain. ResultsResults for both data sets indicated similar corrected alpha levels regardless of analysis type, but the applied alpha level corrections were less conservative for LAAST than RFT or Holm-Bonferroni corrections, but often more conservative than Hochberg corrections. SignificanceAnalysis methods employing functional ANOVA and RFT have enabled researchers to effectively run comparisons between groups at all points within the time series and are gaining popularity. However, in some correction methods for multiple comparisons the alpha level correction can in turn lead to inflation of type II error. These results suggest that LAAST is comparable to RFT while also being appropriate for longitudinal type time series data analysis. Additionally, its use of Welch’s t-tests improves its validity on non-normally distributed data.