Abstract
The human mind shows extraordinary capability at recognizing patterns, while at the same time tending to underestimate the natural scope of random processes. Taken together, this easily misleads researchers in judging whether the observed characteristics of their data are of significance or just the outcome of random effects. One of the best tools to assess whether observed features fall into the scope of pure randomness is statistical significance testing, which quantifies the probability to falsely reject a chosen null hypothesis. The central parameter in this context is the p-value, which can be calculated from the recorded data sets. In case of p-values smaller than the level of significance, the null hypothesis is rejected, otherwise not. While significance testing has found widespread application in many sciences including the life sciences, it is hardly used in (bio-)physics. We propose here that significance testing provides an important and valid addendum to the toolbox of quantitative (single molecule) biology. It allows to support a quantitative judgement (the hypothesis) about the data set with a probabilistic assessment. In this manuscript we describe ways for obtaining valid p-values in two selected applications of single molecule microscopy: (i) Nanoclustering in single molecule localization microscopy. Previously, we developed a method termed 2-CLASTA, which allows to calculate a valid p-value for the null hypothesis of an underlying random distribution of molecules of interest while circumventing overcounting issues. Here, we present an extension to this approach, yielding a single overall p-value for data pooled from multiple cells or experiments. (ii) Single molecule trajectories. Data from a single molecule trajectory are inherently correlated, thus prohibiting a direct analysis via conventional statistical tools. Here, we introduce a block permutation test, which yields a valid p-value for the analysis and comparison of single molecule trajectory data. We exemplify the approach based on FRET trajectories.
Highlights
One fundamental problem behind the interpretation of biological data relates to the question whether a specific data set agrees with a certain hypothesis or not
The lower the p-value, the likelier it is that the data set disagrees with the null hypothesis
The researcher defines a significance level α before performing the experiment, which is taken as threshold criterion for the decision: any p-value below α is considered as a rejection of the null hypothesis, whereas any p-value greater than α would count as agreement
Summary
One fundamental problem behind the interpretation of biological data relates to the question whether a specific data set agrees with a certain hypothesis or not. Significance testing can be considered as a powerful tool for a quantitative assessment of a particular experimental outcome In this context, quantification does not relate to a determination of the magnitude of certain biological parameters, but to a probabilistic assessment of the likelihood of the chosen null hypothesis or the deviation of it. We consider it important to first globally assess a data set via significance testing before using more detailed analysis tools for a quantification of the biological parameters of interest. In this manuscript, we provide a guideline how to use p-values for the analysis of single molecule microscopy data. We show how this problem can be solved via a block permutation testing approach
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