# Handling Skewed Data: A Comparison of Two Popular Methods
## 1 Introduction  
In the biosciences, with the escalating numbers of studies involving many variables and subjects, there is a belief between non-biostatistician scientists that the amount of data will simply reveal all there is to understand from it. Unfortunately, this is not always true. Data analysis can be significantly simplified when the variable of interest has a symmetric distribution (preferably normal distribution) across subjects, but usually, this is not the case. The need for this desirable property can be avoided by using very complex modeling that might give results that are harder to interpret and inconvenient for generalizing--so the need for a high level of expertise in data analysis is a necessity. As biostatisticians with the main responsibility for collaborative research in many biosciences' fields, we are commonly asked the question of whether skewed data should be dealt with using transformation and parametric tests or using nonparametric tests. In this paper, the Monte Carlo simulation is used to investigate this matter in the case of comparing means from two groups. Monte Carlo simulation is a systematic method of doing what-if analysis that is used to measure the reliability of different analyses' results to draw perceptive inferences regarding the relationship between the variation in conclusion criteria values and the conclusion results [1]. Monte Carlo simulation, which is a handy statistical tool for analyzing uncertain scenarios by providing evaluations of multiple different scenarios in-depth, was first used by [PERSON] and [PERSON] in the 1940s. Nowadays, Monte Carlo simulation describes any simulation that includes repeated random generation of samplesand studying the performance of statistical methods' overpopulation samples [2]. Information obtained from random samples is used to estimate the distributions and obtain statistical properties for different situations. Moreover, simulation studies, in general, are computer experiments that are associated with creating data by pseudo-random sampling. An essential asset of simulation studies is the capability to understand and study the performance of statistical methods because parameters of distributions are known in advance from the process of generating the data [3]. In this paper, the Monte Carlo simulation approach is applied to find the Type I error and power for both statistical methods that we are comparing. Now, it is necessary to explain the aspects of the problem we are investigating. First, the normal distribution holds a central place in statistics, with many classical statistical tests and methods requiring normally or approximately normally distributed measurements, such as t-test, ANOVA, and linear regression. As such, before applying these methods or tests, the measurement normality should be assessed using visual tools like the Q-Q plot, P-P plot, histogram, boxplot, or statistical tests like the Shapiro-Wilk, Kolmogorov-Smirnov, or Anderson-Darling tests. Some work has been done to compare between formal statistical tests and a Q-Q plot for visualization using simulations [4; 5]. When testing the difference between two population means with a two-sample \(t\)-test, normality of the data is assumed. Therefore, actions improve the normality of such data that must occur before utilizing the \(t\)-test. One suggested method for right-skewed measurements is the logarithmic transformation [6]. For example, measurements in biomedical and psychosocial research can often be modelled with log-normal distributions, meaning the values are normally distributed after log transformation. Such log transformations can help to meet the normality assumptions of parametric statistical tests, which can also improve graphical presentation and interpretability (Figure 1a,b). The log transformation is simple to implement, requires minimal expertise to perform, and is available in basic statistical software [6].