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Most studies in the life sciences and other disciplines involve generating and analyzing numerical data of some type as the foundation for scientific findings. Working with numerical data involves multiple challenges. These include reproducible data acquisition, appropriate data storage, computationally correct data analysis, appropriate reporting and presentation of the results, and suitable data interpretation.
Finding and correcting mistakes when analyzing and interpreting data can be frustrating and time-consuming. Presenting or publishing incorrect results is embarrassing but not uncommon. Particular sources of errors are inappropriate use of statistical methods and incorrect interpretation of data by software. To detect mistakes as early as possible, one should frequently check intermediate and final results for plausibility. Clearly documenting how quantities and results were obtained facilitates correcting mistakes. Properly understanding data is indispensable for reaching well-founded conclusions from experimental results. Units are needed to make sense of numbers, and uncertainty should be estimated to know how meaningful results are. Descriptive statistics and significance testing are useful tools for interpreting numerical results if applied correctly. However, blindly trusting in computed numbers can also be misleading, so it is worth thinking about how data should be summarized quantitatively to properly answer the question at hand. Finally, a suitable form of presentation is needed so that the data can properly support the interpretation and findings. By additionally sharing the relevant data, others can access, understand, and ultimately make use of the results.
These quick tips are intended to provide guidelines for correctly interpreting, efficiently analyzing, and presenting numerical data in a useful way.
Motivation: Calculating the magnitude of treatment effects or of differences between two groups is a common task in quantitative science. Standard effect size measures based on differences, such as the commonly used Cohen's, fail to capture the treatment-related effects on the data if the effects were not reflected by the central tendency. The present work aims at (i) developing a non-parametric alternative to Cohen’s d, which (ii) circumvents some of its numerical limitations and (iii) involves obvious changes in the data that do not affect the group means and are therefore not captured by Cohen’s d.
Results: We propose "Impact” as a novel non-parametric measure of effect size obtained as the sum of two separate components and includes (i) a difference-based effect size measure implemented as the change in the central tendency of the group-specific data normalized to pooled variability and (ii) a data distribution shape-based effect size measure implemented as the difference in probability density of the group-specific data. Results obtained on artificial and empirical data showed that “Impact”is superior to Cohen's d by its additional second component in detecting clearly visible effects not reflected in central tendencies. The proposed effect size measure is invariant to the scaling of the data, reflects changes in the central tendency in cases where differences in the shape of probability distributions between subgroups are negligible, but captures changes in probability distributions as effects and is numerically stable even if the variances of the data set or its subgroups disappear.
Conclusions: The proposed effect size measure shares the ability to observe such an effect with machine learning algorithms. Therefore, the proposed effect size measure is particularly well suited for data science and artificial intelligence-based knowledge discovery from big and heterogeneous data.
Objectives: This study identified potential general influencing factors for a mathematical prediction of implant stability quotient (ISQ) values in clinical practice.
Methods: We collected the ISQ values of 557 implants from 2 different brands (SICace and Osstem) placed by 2 surgeons in 336 patients. Surgeon 1 placed 329 SICace implants, and surgeon 2 placed 113 SICace implants and 115 Osstem implants. ISQ measurements were taken at T1 (immediately after implant placement) and T2 (before dental restoration). A multivariate linear regression model was used to analyze the influence of the following 11 candidate factors for stability prediction: sex, age, maxillary/mandibular location, bone type, immediate/delayed implantation, bone grafting, insertion torque, I-stage or II-stage healing pattern, implant diameter, implant length and T1-T2 time interval.
Results: The need for bone grafting as a predictor significantly influenced ISQ values in all three groups at T1 (weight coefficients ranging from -4 to -5). In contrast, implant diameter consistently influenced the ISQ values in all three groups at T2 (weight coefficients ranging from 3.4 to 4.2). Other factors, such as sex, age, I/II-stage implantation and bone type, did not significantly influence ISQ values at T2, and implant length did not significantly influence ISQ values at T1 or T2.
Conclusions: These findings provide a rational basis for mathematical models to quantitatively predict the ISQ values of implants in clinical practice.