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Topic Review
Six Stages to Choose Sampling Techniques
In order to answer the research questions, it is doubtful that researcher should be able to collect data from all cases. Thus, there is a need to select a sample. The entire set of cases from which researcher sample is drawn in called the population. Since, researchers neither have time nor the resources to analysis the entire population so they apply sampling technique to reduce the number of cases. There are six stages to choose sampling techniques.
  • 108.0K
  • 17 Jul 2023
Topic Review
Gompertz Function with R
The Gompertz function is a sigmoid curve being a special case of a logistic curve. Although it was originally designed to describe mortality, it is now used in biology. For example, it is useful to describe many  phenomena such as the growth of a cancerous tumor confined to an organ without metastasis, the growth of the number of individuals in a population, e.g. prey in a Volterra-Lotka model, the germination of seeds, etc. It also models as the logistic function the growth of a colony of bacteria or in an epidemic the spread of the number of infected people. However, despite its many applications, in many cases the fitting of experimental data to the Gompertz function is not always straightforward. In this article we present a protocol that will be useful when performing the data regression to this curve using the statistical package R.
  • 22.3K
  • 07 Apr 2021
Topic Review
Mobile Technology in Tourism
The influence of mobile technology on tourism is very significant. With the support of mobile-related devices (smartphones, glasses, or other wearable devices), technology, data and services, multiple travel concepts, and travel modes including mobile tourism, smart tourism, e-tourism, and sustainable tourism have emerged or developed further. Mobile technology is touted as the next technology wave that can fundamentally change tourism and hotels. Moreover, mobile technology is playing an increasing role in the travel experience, and increasing travel research is concentrated in this field. Research findings show that, first, the research of mobile technology in tourism can be divided into three phases and to a certain extent is synchronized with the development of mobile technology. Second, in the area of social sciences, the research of mobile technology in tourism needs further exploration, which must refer to related research in the areas of Transportation and IT to expand the perspective of research. Top journal analysis, journal co-citation analysis, author co-citation analysis, and collaboration network analysis reveal the most representative journals, authors, institutions, and countries/regions in this research field. This finding provides a valuable reference for scholars in this field. Additionally, this research also grasped the hot and cutting-edge topics in this field through the analysis of keywords in this field. Finally, the clustering of co-citation references presents the knowledge base of mobile technology research in the tourism field: mobile technology, travel mode, mobile instrument, travel behavior research, mobile applications, and geo-based technology.
  • 11.3K
  • 28 Sep 2020
Topic Review
Chi square statistic
The Chi-Square test is based on a series of assumptions frequently used in the statistical analysis of experimental data. The main weakness of the chi-square test is that is very accurate only in convergence (in large size samples), and for small sample sizes is exposed to errors of both types (type I and type II). On two scenarios of use - goodness of fit and contingencies assessment (2x2 tables of contingency) - here are discussed different aspects involving it. Further knowledge on the regard of the type of the error in contingencies assessment push further the analysis of the data, while in the same time opens the opportunity to devise a method for filling the gaps in contingencies (e.g. censored data), both scenarios being discussed here in detail. A program designed to fill the gaps in the assumption of the association is provided.
  • 4.1K
  • 24 Dec 2020
Topic Review
Heteroscedasticity
In statistics, a vector of random variables is heteroscedastic (or heteroskedastic; from Ancient Greek hetero "different" and skedasis "dispersion") if the variability of the random disturbance is different across elements of the vector. Here, variability could be quantified by the variance or any other measure of statistical dispersion. Thus heteroscedasticity is the absence of homoscedasticity. A typical example is the set of observations of income in different cities. The existence of heteroscedasticity is a major concern in regression analysis and the analysis of variance, as it invalidates statistical tests of significance that assume that the modelling errors all have the same variance. While the ordinary least squares estimator is still unbiased in the presence of heteroscedasticity, it is inefficient and generalized least squares should be used instead. Because heteroscedasticity concerns expectations of the second moment of the errors, its presence is referred to as misspecification of the second order. The econometrician Robert Engle was awarded the 2003 Nobel Memorial Prize for Economics for his studies on regression analysis in the presence of heteroscedasticity, which led to his formulation of the autoregressive conditional heteroscedasticity (ARCH) modeling technique.
  • 3.5K
  • 14 Oct 2022
Topic Review
Markov Chain Applications to Education
The theory of Markov chains is a smart combination of Linear Algebra and Probability theory offering ideal conditions for modelling situations depending on random variables. Markov chains have found important applications to many sectors of the human activity. In this work a finite Markov chain is introduced representing mathematically the teaching process which is based on the ideas of constructivism for learning. Interesting conclusions are derived and a measure is obtained for the teaching effectiveness. An example on teaching the derivative to fresher university students is also presented illustrating our results.
  • 2.7K
  • 03 Dec 2020
Topic Review
Forensic Statistics
Forensic statistics is the application of probability models and statistical techniques to scientific evidence, such as DNA evidence, and the law. In contrast to "everyday" statistics, to not engender bias or unduly draw conclusions, forensic statisticians report likelihoods as likelihood ratios (LR). This ratio of probabilities is then used by juries or judges to draw inferences or conclusions and decide legal matters. Jurors and judges rely on the strength of a DNA match, given by statistics, to make conclusions and determine guilt or innocence in legal matters. In forensic science, the DNA evidence received for DNA profiling often contains a mixture of more than one person's DNA. DNA profiles are generated using a set procedure, however, the interpretation of a DNA profile becomes more complicated when the sample contains a mixture of DNA. Regardless of the number of contributors to the forensic sample, statistics and probabilities must be used to provide weight to the evidence and to describe what the results of the DNA evidence mean. In a single-source DNA profile, the statistic used is termed a random match probability (RMP). RMPs can also be used in certain situations to describe the results of the interpretation of a DNA mixture. Other statistical tools to describe DNA mixture profiles include likelihood ratios (LR) and combined probability of inclusion (CPI), also known as random man not excluded (RMNE). Computer programs have been implemented with forensic DNA statistics for assessing the biological relationships between two or more people. Forensic science uses several approaches for DNA statistics with computer programs such as; match probability, exclusion probability, likelihood ratios, Bayesian approaches, and paternity and kinship testing. Although the precise origin of this term remains unclear, it is apparent that the term was used in the 1980s and 1990s. Among the first forensic statistics conferences were two held in 1991 and 1993.
  • 2.5K
  • 12 Oct 2022
Topic Review
Digital Marketing Utilization Index in Digital Marketing Capability
The digital marketing utilization index (DMUI) measures an organization’s ability to utilize digital marketing to create value for the company through the utilization of the readiness of the innovation ecosystem, digital marketing technology, and digital transformation.
  • 2.1K
  • 06 Sep 2022
Topic Review
Media Pluralism
Media pluralism defines the state of having a plurality of voices, opinions and analyses on media system (internal pluralism) or the coexistence of different and diverse types of medias and media support (external pluralism). Media pluralism is often recognized by international organizations and non-governmental organizations as being an essential part of a democratic state, Reporters Without Borders considers "access to a plurality of editorial lines and analyses [as] essential for citizens to be able to confront ideas, to make their own informed choices and to conduct their life freely". Expanded access to the Internet and the digital switch-over has enabled an increased availability of media content, largely through sharing and user-generated content on social media, in addition to the digital channels to which individuals have access across television and radio. The diversity of content is however accompanied by what Hallin and Mancini call polarized pluralism in a media system. According to the World Trends Report, a sharper division in the way we use news is coming up due to the interaction between consumption habits, changing economic models and technical systems. This signifies that even if multiple kinds of information and programming are available, each segmented group may only ingest one branch of the whole. The increase of Internet penetration and reliance on online sources for news is thought of to producing siloed debates. At the infrastructural level, ‘zero rating’— in which Internet or mobile service providers allow users to access specific content or applications without counting towards the user’s data ‘cap’— expands in parallel to mobile uptakes, particularly in emerging countries. Traditional business models for the news media continue to be disrupted, leading to vertical and horizontal concentration and introduction of new types of ownership. Challenges to media funding introduce new types of economic models such as pay-walls and crowd-funding initiatives. Gender is a part of media pluralism and is characterized by the under-representation of women in the media workforce, in decision-making and in media content. People with disabilities are also under-represented in the media system.
  • 1.8K
  • 09 Oct 2022
Topic Review Peer Reviewed
Spatial Hurst–Kolmogorov Clustering
The stochastic analysis in the scale domain (instead of the traditional lag or frequency domains) is introduced as a robust means to identify, model and simulate the Hurst–Kolmogorov (HK) dynamics, ranging from small (fractal) to large scales exhibiting the clustering behavior (else known as the Hurst phenomenon or long-range dependence). The HK clustering is an attribute of a multidimensional (1D, 2D, etc.) spatio-temporal stationary stochastic process with an arbitrary marginal distribution function, and a fractal behavior on small spatio-temporal scales of the dependence structure and a power-type on large scales, yielding a high probability of low- or high-magnitude events to group together in space and time. This behavior is preferably analyzed through the second-order statistics, and in the scale domain, by the stochastic metric of the climacogram, i.e., the variance of the averaged spatio-temporal process vs. spatio-temporal scale.
  • 1.4K
  • 14 Apr 2022
Topic Review
Statistical Methods for Food Composition Database Analysis
A food composition database (FCDB) or nutrient database is a compilation of the chemical composition of food and beverage items, obtained from chemical analyses, estimations from published literature, or unpublished laboratory reports. A summary of the statistical methods that have been directly applied to food composition databases and datasets is described here.
  • 1.4K
  • 08 Jun 2022
Topic Review
Bayesian Analysis in Social Sciences
Given the reproducibility crisis (or replication crisis), more psychologists and social-cultural scientists are getting involved with Bayesian inference. Therefore, the current article provides a brief overview of programs (or software) and steps to conduct Bayesian data analysis in social sciences. 
  • 1.3K
  • 23 Jul 2021
Topic Review
Sports Analytics
Sports analytics are a collection of relevant, historical, statistics that can provide a competitive advantage to a team or individual. Through the collection and analyzation of these data, sports analytics inform players, coaches and other staff in order to facilitate decision making both during and prior to sporting events. The term "sports analytics" was popularized in mainstream sports culture following the release of the 2011 film, Moneyball, in which Oakland Athletics General Manager Billy Beane (played by Brad Pitt) relies heavily on the use of analytics to build a competitive team on a minimal budget. There are two key aspects of sports analytics — on-field and off-field analytics. On-field analytics deals with improving the on-field performance of teams and players, including questions such as "which player on the Red Sox contributed most to the team's offense?" or "who is the best wing player in the NBA?", etc. Off-field analytics deals with the business side of sports. Off-field analytics focuses on helping a sport organization or body surface patterns and insights through data that would help increase ticket and merchandise sales, improve fan engagement, etc. Off-field analytics essentially uses data to help rightsholders take decisions that would lead to higher growth and increased profitability. As technology has advanced over the last number of years data collection has become more in-depth and can be conducted with relative ease. Advancements in data collection have allowed for sports analytics to grow as well, leading to the development of advanced statistics and machine learning, as well as sport specific technologies that allow for things like game simulations to be conducted by teams prior to play, improve fan acquisition and marketing strategies, and even understand the impact of sponsorship on each team as well as its fans. Another significant impact sports analytics have had on professional sports is in relation to sport gambling. In depth sports analytics have taken sports gambling to new levels, whether it be fantasy sports leagues or nightly wagers, bettors now have more information at their disposal to help aid decision making. A number of companies and webpages have been developed to help provide fans with up to the minute information for their betting needs.
  • 1.3K
  • 14 Nov 2022
Topic Review
Extreme values statistic
One of the pillars of experimental sciences is sampling. Based on analysis conducted on samples the estimations for the populations are made. The distributions are split in two main groups: continuous and discrete and the present study applies for the continuous ones. One of the challenges of the sampling is the accuracy of it, or, in other words how representative is the sample for the population from which was drawn. Another challenge, connected with this one, is the presence of the outliers - observations wrongly collected, not actually belonging to the population subjected to study. The present study proposes a statistic (and a test) intended to be used for any continuous distribution to detect the outliers, by constructing the confidence interval for the extreme value in the sample, at certain (preselected) risk of being in error, and depending on the sample size. The proposed statistic is operational for known distributions (having known their probability density function) and is dependent too on the statistical parameters of the population.
  • 1.3K
  • 29 Oct 2020
Topic Review
Partial Area Under the ROC Curve (PAUC)
The Partial Area Under the ROC Curve (pAUC) is a metric for the performance of binary classifier. It is computed based on the receiver operating characteristic (ROC) curve that illustrates the diagnostic ability of a given binary classifier system as its discrimination threshold is varied. The ROC curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings.The area under the ROC curve (AUC) is often used to summarize in a single number the diagnostic ability of the classifier. The AUC is simply defined as the area of the ROC space that lies below the ROC curve. However, in the ROC space there are regions where the values of FPR or TPR are unacceptable or not viable in practice. For instance, the region where FPR is greater than 0.8 involves that more than 80% of negative subjects are incorrectly classified as positives: this is unacceptable in many real cases. As a consequence, the AUC computed in the entire ROC space (i.e., with both FPR and TPR ranging from 0 to 1) can provide misleading indications. To overcome this limitation of AUC, it was proposed to compute the area under the ROC curve in the area of the ROC space that corresponds to interesting (i.e., practically viable or acceptable) values of FPR and TPR.
  • 1.3K
  • 21 Oct 2022
Topic Review
Aesthetical Evaluation with Stochastic Analysis
Stochastic calculus is used for the objective evaluation of the variability present in aesthetic attributes of paintings and landscapes.
  • 1.2K
  • 24 Nov 2020
Topic Review
Application of Biological Domain Knowledge
Integrative approaches that utilize the biological knowledge while performing feature selection are necessary for this kind of data. The main idea behind the integrative gene selection process is to generate a ranked list of genes considering both the statistical metrics that are applied to the gene expression data, and the biological background information which is provided as external datasets. 
  • 1.2K
  • 19 Feb 2021
Topic Review
Diffusion of Solar PV Energy
Solar photovoltaic energy (solar PV) is considered a very attractive solution among renewable energy sources (RES), especially for households. According to the most recent IEA report on renewables, the growth of renewable power capacity at the world level has reached another record in 2021, driven by solar photovoltaic energy; solar PV alone has accounted for more than half of all renewable power expansion in 2021, followed by wind and hydropower.
  • 1.2K
  • 28 Apr 2022
Topic Review
Bayesian Nonlinear Mixed Effects Models
Nonlinear mixed effects models have become a standard platform for analysis when data is in the form of continuous and repeated measurements of subjects from a population of interest, while temporal profiles of subjects commonly follow a nonlinear tendency. While frequentist analysis of nonlinear mixed effects models has a long history, Bayesian analysis of the models has received comparatively little attention until the late 1980s, primarily due to the time-consuming nature of Bayesian computation. Since the early 1990s, Bayesian approaches for the models began to emerge to leverage rapid developments in computing power, and have recently received significant attention due to (1) superiority to quantify the uncertainty of parameter estimation; (2) utility to incorporate prior knowledge into the models; and (3) flexibility to match exactly the increasing complexity of scientific research arising from diverse industrial and academic fields. 
  • 1.1K
  • 23 Mar 2022
Topic Review
Homoscedasticity
In statistics, a sequence (or a vector) of random variables is homoscedastic/ˌhoʊmoʊskəˈdæstɪk/ if all its random variables have the same finite variance. This is also known as homogeneity of variance. The complementary notion is called heteroscedasticity. The spellings homoskedasticity and heteroskedasticity are also frequently used. Assuming a variable is homoscedastic when in reality it is heteroscedastic (/ˌhɛtəroʊskəˈdæstɪk/) results in unbiased but inefficient point estimates and in biased estimates of standard errors, and may result in overestimating the goodness of fit as measured by the Pearson coefficient.
  • 1.1K
  • 31 Oct 2022
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