# Handling Skewed Data: A Comparison of Two Popular Methods
## 4 Discussion  
In this work, we compared the use of a \(t\)-test on log-transformed data and the use of GLM on untransformed skewed data. The log transformation was studied because it is one of the most common transformations used in biosciences research. If such an approach is used, the scientist must be careful about its limitations; especially when interpreting the significance of the analysis of transformed data for the hypothesis of interest about the original data. Moreover, a researcher who uses log transformation should know how to facilitate log-transformed data to give inferences concerning the original data. Furthermore, log transformation does not always help make data less variable or more normal and may, in some situations, make data more variable and more skewed. For that, the variability and normality should always be examined after applying the log transformation. On the other hand, GLM was used because other nonparametric tests' inferences concern medians and not means. In addition, GLM models deal differently with response variables depending on their population distributions, which provides the scientist with flexibility in modeling; GLM allows for response variables to have different distributions, and each distribution has an appropriate link function to vary linearly with the predicted values. Each comparison was made for two simulated groups from several sampling distributions with varying sample sizes. The comparisons regarded Type I error rates, power rates and estimates of the means. Overall, the \(t\)-test method with transformed data produced smaller Type I error rates and closer estimations. The GLM method, however, produced a higher power rate compared to \(t\)-test methods, though both reported acceptable power rates. For gamma distribution, Type I error rates in the \(t\)-test case were very close to 0.05 (0.0497 to 0.0504), while the Type I error rates of the GLM method had a wider range (0.0490 to 0.0577). For most examples in the gamma-distributed data, the Type I error rates of the \(t\)-test method were smaller than the respective rates in the GLM method. Regarding power, the GLM rates were higher in about 85% of the settings than the ones using the \(t\)-test, with absolute values of differences, ranging from 0.000 to 0.363. Figure 7: The normal Q–Q plots (up) for the Assets variable before and after transformation and the frequency histogram of the Assets on the left (down) fitted to an exponential distribution (red). The back-transformed estimates of the mean differences in the \(t\)-test case were not significantly different from the estimates of the original data mean differences in the \(t\)-test method. The GLM estimates, in contrast, were significantly different from the estimates of the original data. So, if we are looking for lower Type I error and closer estimates, we can use the \(t\)-test method with transformed data. However, if we are looking for a method with higher power rates, we recommend choosing the GLM method. In the exponentially distributed data, the GLM method has achieved a noticeably lower Type I error rate and higher power in most of the settings than the \(t\)-test method. Regarding the estimates, the \(t\)-test method gave closer estimates. Despite the closer estimates for the \(t\)-test method, our advice is to use the GLM method. For beta distributed data, Type I error rates seem to favor the \(t\)-test method with transformed data. The power rates of the GLM method were higher than the power rates in the \(t\)-test method, with absolute values of differences ranging from 0 to 0.0884. Furthermore, by looking at Figure 4, we can see that the two methods have very close power rates. So, both methods seem to be good enough in this matter. Nevertheless, since the \(t\)-test method has lower Type I rates and closer estimates in the beta distributed data, we recommend it over GLM. The missing rates for some of the parameters' combinations, especially in calculating power rates, are due to two reasons.