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Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings. The statistical analysis gives meaning to the meaningless numbers, thereby breathing life into a lifeless data. The results and inferences are precise only if proper statistical tests are used. This article will try to acquaint the reader with the basic research tools that are utilised while conducting various studies. The article covers a brief outline of the variables, an understanding of quantitative and qualitative variables and the measures of central tendency. An idea of the sample size estimation, power analysis and the statistical errors is given. Finally, there is a summary of parametric and non-parametric tests used for data analysis.

Solar photovoltaic (PV) systems can be significantly enhanced through the use of accurate solar cell models. Unfortunately, the absence of precise parameters from manufacturers limits the accuracy of these models. Given the impossibility of reliable modeling without such parameters, this paper introduces a multi‐objective optimization algorithm to estimate the necessary parameters effectively. The problem of suboptimal optimization results often arises due to local minima and premature convergence of the optimization algorithm, even though there are a number of optimization algorithms that address this issue. This paper is intended to examine the reliability of the proposed algorithm to determine if it is reliable. For the purpose of showing the proficiency of the proposed optimization algorithms, their performance is compared with that of some other well‐known algorithms to show their superiority. The performance of the algorithm is validated by comparing experimental results, including analyses based on statistical data, with estimated parameters based on statistical analysis. Furthermore, the results obtained with the proposed algorithms indicate that they are better suited for estimating solar PV models than the other algorithms i.e., rmse of the proposed algorithm for three diode model is 4.21E−13 as well as 3.20E−13 for four diode model. A simple structure and high accuracy are the main characteristics of the proposed algorithm, which indicates its potential for a variety of applications in the solar energy field in the future. Moreover, the proposed algorithm is computationally efficient as well as easy to use and can be applied to a number of applications.

Understanding the spatiotemporal distribution of tornado events is increasingly imperative, not only because of the natural phenomenon itself and its tremendous complexity but also because we can potentially reduce the risks that they entail. In particular, the US regions are particularly susceptible to tornadoes and they are the focus and motivation of our statistical analysis. Tornado reports can be treated as spatiotemporal point patterns, and we develop some methods for the analysis of replicated spatiotemporal patterns to identify significant structural differences between cold and warm seasons along the years. We extend some existing spatial techniques to the spatiotemporal context to test the null hypothesis that two (or more) observed spatiotemporal point patterns with replications are realizations of point processes that have the same second-order descriptors. In particular, we develop a non-parametric test to approximate the null distribution of the test statistics. We present intensive simulation studies that demonstrate the validity and power of our test and apply our methods to the motivating problem of tornadoes.

Changes in the frequency and intensity of the prevailing northeast and east trade winds from 1973‐2009 are analyzed from four land stations in the Hawaiian Islands. A nonparametric robust trend analysis indicates a downward trend in northeast trade wind frequency since 1973. At the Honolulu International Airport, northeast trade wind days usually occurred 291 days per year 37 years ago are observed to occur only 210 days per year in 2009. In contrast, the frequency of the east trade winds has increased over the past 37 years. Comparison of observations from four ocean buoys with land stations for the last 26 years (1984–2009) is presented. The northeast trade frequency is found to decrease for all eight stations while the east trade winds are found to increase in frequency. These results are similar to the longer (1973–2009) data set. Most buoys revealed an increase in trade wind speeds since 1984. The NCEP/NCAR reanalysis II data are used to analyze surface winds and sea level pressure (SLP) over the north Pacific. A northeast to east shifting of winds and an increase in SLP is found to occur from the 1980s to the 2000s epoch. Linear trends in reanalysis II from 1980 to 2009 indicated a strengthening of northeast trade winds over the Hawaiian Islands and in the subtropical eastern North Pacific with an extension of increased northerlies off the California coast. Meanwhile, southeast trades in the eastern North Pacific reduced their strength. Changes in trades in the western Pacific are relatively small. Key Points Northeast trade winds over the Pacific have changed in frequency and strength Changes in wind patterns have major implications on future climate in Hawaii Comparison of land station wind trends versus surrounding ocean wind trends

We propose a non-parametric change-point test for long-range dependent data, which is based on the Wilcoxon two-sample test. We derive the asymptotic distribution of the test statistic under the null hypothesis that no change occurred. In a simulation study, we compare the power of our test with the power of a test which is based on differences of means. The results of the simulation study show that in the case of Gaussian data, our test has only slightly smaller power than the 'difference-of-means' test. For heavy-tailed data, our test outperforms the 'difference-of-means' test.

Background Data Envelopment Analysis (DEA) methodology is considered the most suitable approach for relative performance efficiency calculation for banks as it is believed to be superior to traditional ratio-based analysis and other conventional performance evaluations. This study provides statistical evidence on the sampling error that can creep into performance evaluation studies using the DEA methodology. Inferences are drawn based on samples, and various preventive measures must be taken to eliminate or avoid sampling errors and misleading results. This study demonstrates the possibility of sampling error in DEA with the secondary data available in financial statements and reports from a sample set of banks. Methods The samples included 15 public sectors and five leading private sector banks in India based on their market share, and the data for calculating efficiencies were retrieved from the published audited reports. The sample data was collected from 2014 to 2017 because the banking sector in India witnessed a series of mergers of public sector banks post-2017, and the data after that would be skewed and not comparable due to the demonetization policy implementation and merger process-related consolidation implemented by the Government of India. The efficiency measures thus computed are further analyzed using non-parametric statistical tests. Results We found statistically significant discrepancies in the efficiency score calculations using DEA approach when specific outlier values. Evidence is provided on statistically significant differences in the efficiencies due to the inclusion and exclusion of particular samples in the DEA. Conclusion The study offers a novel contribution along with statistical evidence on the possible sampling error that can creep into the performance evaluation of organizations while applying the DEA methodology.

Power system demand forecasting is a crucial task in the power system engineering field. This is due to the fact that most system planning and operation activities basically rely on proper forecasting models. Entire power infrastructures are built essentially to provide and serve the consumption of energy. Therefore, it is very necessary to construct robust and efficient predictive models in order to provide accurate load forecasting. In this paper, three techniques are utilized for short-term load forecasting. These techniques are deep neural network (DNN), multilayer perceptron-based artificial neural network (ANN), and decision tree-based prediction (DR). New predictive variables are included to enhance the overall forecasting and handle the difficulties caused by some categorical predictors. The comparison among these three techniques is executed based on coefficients of determination R2 and mean absolute error (MAE). Statistical tests are performed in order to verify the results and examine whether these models are statistically different or not. The results reveal that the DNN model outperformed the other models and was statistically different from them.

The paper proposes a new test for detecting the umbrella pattern under a general non-parametric scheme. The alternative asserts that the umbrella ordering holds while the hypothesis is its complement. The main focus is put on controlling the power function of the test outside the alternative. As a result, the asymptotic error of the first kind of the constructed solution is smaller than or equal to the fixed significance level α on the whole set where the umbrella ordering does not hold. Also, under finite sample sizes, this error is controlled to a satisfactory extent. A simulation study shows, among other things, that the new test improves upon the solution widely recommended in the literature of the subject. A routine, written in R, is attached as the Supporting Information file.

The present paper shows an experimental study on additive manufacturing for obtaining samples of polylactic acid (PLA). The process used for manufacturing these samples was fused deposition modeling (FDM). Little attention to the surface quality obtained in additive manufacturing processes has been paid by the research community. So, this paper aims at filling this gap. The goal of the study is the recognition of critical factors in FDM processes for reducing surface roughness. Two different types of experiments were carried out to analyze five printing parameters. The results were analyzed by means of Analysis of Variance, graphical methods, and non-parametric tests using Spearman’s ρ and Kendall’s τ correlation coefficients. The results showed how layer height and wall thickness are the most important factors for controlling surface roughness, while printing path, printing speed, and temperature showed no clear influence on surface roughness.

Background During the last 30 years, the median sample size of research studies published in high-impact medical journals has increased manyfold, while the use of non-parametric tests has increased at the expense of t-tests. This paper explores this paradoxical practice and illustrates its consequences. Methods A simulation study is used to compare the rejection rates of the Wilcoxon-Mann-Whitney (WMW) test and the two-sample t-test for increasing sample size. Samples are drawn from skewed distributions with equal means and medians but with a small difference in spread. A hypothetical case study is used for illustration and motivation. Results The WMW test produces, on average, smaller p -values than the t-test. This discrepancy increases with increasing sample size, skewness, and difference in spread. For heavily skewed data, the proportion of p <0.05 with the WMW test can be greater than 90% if the standard deviations differ by 10% and the number of observations is 1000 in each group. The high rejection rates of the WMW test should be interpreted as the power to detect that the probability that a random sample from one of the distributions is less than a random sample from the other distribution is greater than 50%. Conclusions Non-parametric tests are most useful for small studies. Using non-parametric tests in large studies may provide answers to the wrong question, thus confusing readers. For studies with a large sample size, t-tests and their corresponding confidence intervals can and should be used even for heavily skewed data.