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Re-examination of Traditional Statistics
Published in Chong Ho Alex Yu, Data Mining and Exploration, 2022
Contrary to popular belief, hypothesis testing does not address the issue of treatment effectiveness or efficacy (Wasserstein and Lazar 2016). It is common for researchers to declare a finding as “significant” when p < .05. Unfortunately, this terminology is so misleading that most people equate “significance” with “importance”, even though a p-value has nothing to do with importance. Rather, a p-value is just an indicator of rareness or extremity Thus, a large or so-called insignificant p value indicates that the data are not unusual or extreme given the model, but it cannot ascertain that the theory is incorrect. Specifically, it is the chance of observing the test statistics derived from the data given the chance (null) hypothesis is true. It is hypothesized that the same study is repeated in the long run, as expressed by the infinite sampling distribution. Needless to say, this is just theoretical because no one would repeat the same study ten thousand times. Very often researchers interpret a “significant” p-value as evidence of treatment effectiveness or efficacy, or how “right” an alternate hypothesis is. For example, if a p-value is 0.01, many researchers misinterprets that the probability of correctly detecting the effect is 99% (Colling and Szucs 2018). In this case these researchers confuse p-values with alpha levels.
Similarity Principle—The Fundamental Principle of All Sciences
Published in Mark Chang, Artificial Intelligence for Drug Development, Precision Medicine, and Healthcare, 2020
The p-value is the probability of finding the test statistic equal to or more extreme than the observed value when the null hypothesis is true. However, a p-value does not directly answer the underlying scientific question. We ask: what is the probability the drug is effective and how effective? The p-value, p, says: “If the drug is ineffective, you will have probability p of observing data equal to or more extreme than what you have observed.” In hypothesis testing, we use a predetermined significance level α and p ≤ α to control the type-I error rate, but knowing that type-I errors (e.g., errors on different endpoints) have different impacts, some being more severe than others, why don’t we control the loss due to error rather than the error rate?
Statistical Inference II
Published in Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos, Statistical and Econometric Methods for Transportation Data Analysis, 2020
Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos
The purpose of a hypothesis test is to determine whether it is appropriate to reject or not to reject the null hypothesis. The test statistic is the sample statistic upon which the decision to reject, or fail to reject, the null hypothesis is based. The nature of the hypothesis test is determined by the question being asked. For example, if an engineering intervention is expected to change the mean of a sample (the mean of vehicle speeds), then a null hypothesis of no difference in means is appropriate. If an intervention is expected to change the spread or variability of data, then a null hypothesis of no difference in variances should be used. Many different types of hypothesis tests can be conducted. Regardless of the type of hypothesis test, the process is the same: the empirical evidence is assessed and will either refute or fail to refute the null hypothesis based on a prespecified level of confidence. Test statistics used in many parametric hypothesis testing applications rely upon the Z, t, F, and χ2 distributions.
Emended Harris Hawk Optimizer for Mixed Energy Generation Scheduling Problem
Published in Electric Power Components and Systems, 2023
The WSRT is a non-parametric statistical test that compares two related or paired samples. It is used when the data does not meet the assumptions of normality required for parametric tests like the t-test. This test is designed to determine if there is a significant difference between the medians of the paired observations. WSRT assigns positive ranks to the positive differences (indicating an increase from the first to the second measurement) and negative ranks to the negative differences (showing a decrease). Disregard the zero differences. WSRT compares the obtained test statistic to the null distribution to calculate the p-value. The p-value represents the probability of observing a test statistic as extreme as, or more potent than, the one obtained if the null hypothesis is true. The null hypothesis is rejected if the p-value is less than a predetermined significance level (e.g., 0.05), indicating a significant difference between the paired samples.
Hierarchical RNN-based framework for throughput prediction in automotive production systems
Published in International Journal of Production Research, 2023
Mengfei Chen, Richard Furness, Rajesh Gupta, Saumuy Puchala, Weihong (Grace) Guo
The test statistic is used to test the null hypothesis . When the -value is smaller, it is more likely that is rejected. Therefore, instead of directly comparing , we compare -values among assets and identify assets with significantly small -values as most associated with the undesired throughput. The -value associated with is calculated by Equation (15): where is the probability density function of the distribution with degree of freedom and .
Examining two-wheelers' overtaking behavior and lateral distance choices at a shared roadway facility
Published in Journal of Transportation Safety & Security, 2020
Yanyong Guo, Tarek Sayed, Mohamed H. Zaki
To identify the theoretical distribution of the lateral distance, four commonly used distributions were examined in this study: Normal distribution, Lognormal distribution, Gamma distribution, and Weibull distribution. The maximum likelihood estimation (MLE) technique was utilized to estimate the parameters of the distributions. The goodness-of-fit test was conducted to select the best-fitted distribution among the given candidate distributions. The Kolmogorov–Smirnov (K–S) test has been widely used to compare a sample with a particular probability distribution in transportation research (Ibeas, Cordera, dell'Olio, & Moura, 2011; Páez, Trépanier, & Morency, 2011). With the null hypothesis that the data follows a specified distribution, the K–S statistic estimates the largest vertical difference between the theoretical and the empirical cumulative distribution function (Washington et al., 2003). The null hypothesis is rejected at the chosen significance level if the test statistic is greater than the certain critical value. In this study, the K– test was conducted to test the hypothesis whether the lateral distance followed a particular probability distribution. The null hypothesis is accepted at a (1 − α)% level of confidence if Where, n is the samples size; Dn is the K–S statistic; Kα is the critical value (CV); α = .05 in this study.