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Journal articles on the topic 'Statistical inferences'

Author: Grafiati

Published: 25 January 2025

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1

Luo, Yu, and Jiaying Zhao. "Statistical Learning Creates Novel Object Associations via Transitive Relations." Psychological Science 29, no. 8 (May 22, 2018): 1207–20. http://dx.doi.org/10.1177/0956797618762400.

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A remarkable ability of the cognitive system is to make novel inferences on the basis of prior experiences. What mechanism supports such inferences? We propose that statistical learning is a process through which transitive inferences of new associations are made between objects that have never been directly associated. After viewing a continuous sequence containing two base pairs (e.g., A–B, B–C), participants automatically inferred a transitive pair (e.g., A–C) where the two objects had never co-occurred before (Experiment 1). This transitive inference occurred in the absence of explicit awareness of the base pairs. However, participants failed to infer the transitive pair from three base pairs (Experiment 2), showing the limits of the transitive inference (Experiment 3). We further demonstrated that this transitive inference can operate across the categorical hierarchy (Experiments 4–7). The findings revealed a novel consequence of statistical learning in which new transitive associations between objects are implicitly inferred.

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NIELSEN, RASMUS, and MARK A. BEAUMONT. "Statistical inferences in phylogeography." Molecular Ecology 18, no. 6 (March 2009): 1034–47. http://dx.doi.org/10.1111/j.1365-294x.2008.04059.x.

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3

Philip, G. M., and D. F. Watson. "Probabilism in Geological Data Analysis." Geological Magazine 124, no. 6 (November 1987): 577–83. http://dx.doi.org/10.1017/s0016756800017404.

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AbstractThe way in which probability can enter the interpretation of geological data is outlined. Probabilistic models are introduced in data synopses to allow statistical inferences about samples and population parameters. Inferences of this type are a special application of mathematical theory and have little to do with testing scientific generalizations. The logic of statistical inference, as used in operations research, is contrasted with that of geological inference. Geology is a cumulative science; its methodology is not that of experimentation with formal replication; inferences are developed from observations and tested and refined against new data, often by different investigators at different times and in different places. Because of the way in which inferences are drawn, sampling in geology is purposive. Random sampling, necessary for inferences based on sampling theory, is unattainable in most geological contexts. Different classes of geological measurements require careful consideration as to their appropriate form of synopsis, and, particularly, as to whether a parametric probability model is applicable.

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Zhang, Jin-Ting, and Jianwei Chen. "Statistical inferences for functional data." Annals of Statistics 35, no. 3 (July 2007): 1052–79. http://dx.doi.org/10.1214/009053606000001505.

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5

Watkins, A. J. "Statistical inferences for breakdown voltages." IEEE Transactions on Dielectrics and Electrical Insulation 7, no. 6 (2000): 869–71. http://dx.doi.org/10.1109/94.892002.

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6

Turner, Dana P., Hao Deng, and Timothy T. Houle. "Bayesian Approaches to Statistical Inferences." Headache: The Journal of Head and Face Pain 60, no. 9 (September 29, 2020): 1879–85. http://dx.doi.org/10.1111/head.13952.

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7

Kolokolov, Aleksey, Giulia Livieri, and Davide Pirino. "Statistical inferences for price staleness." Journal of Econometrics 218, no. 1 (September 2020): 32–81. http://dx.doi.org/10.1016/j.jeconom.2020.01.021.

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8

Raymond, Jean, and Tim E. Darsaut. "Understanding statistical populations and inferences." Neurochirurgie 71, no. 1 (January 2025): 101608. http://dx.doi.org/10.1016/j.neuchi.2024.101608.

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9

Wang, Yingxu. "Inference Algebra (IA)." International Journal of Cognitive Informatics and Natural Intelligence 6, no. 1 (January 2012): 21–47. http://dx.doi.org/10.4018/jcini.2012010102.

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Inference as the basic mechanism of thought is abilities gifted to human beings, which is a cognitive process that creates rational causations between a pair of cause and effect based on empirical arguments, formal reasoning, and/or statistical norms. It’s recognized that a coherent theory and mathematical means are needed for dealing with formal causal inferences. Presented is a novel denotational mathematical means for formal inferences known as Inference Algebra (IA) and structured as a set of algebraic operators on a set of formal causations. The taxonomy and framework of formal causal inferences of IA are explored in three categories: a) Logical inferences; b) Analytic inferences; and c) Hybrid inferences. IA introduces the calculus of discrete causal differential and formal models of causations. IA enables artificial intelligence and computational intelligent systems to mimic human inference abilities by cognitive computing. A wide range of applications of IA are identified and demonstrated in cognitive informatics and computational intelligence towards novel theories and technologies for machine-enabled inferences and reasoning. This work is presented in two parts. The inference operators of IA as well as their extensions and applications will be presented in this paper; while the structure of formal inference, the framework of IA, and the mathematical models of formal causations has been published in the first part of the paper in IJCINI 5(4).

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10

Michalewicz, Zbigniew, and Anthony Yeo. "Multiranges and Multitrackers in Statistical Databases." Fundamenta Informaticae 11, no. 1 (January 1, 1988): 41–48. http://dx.doi.org/10.3233/fi-1988-11104.

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The goal of statistical databases is to provide statistics about groups of individuals while protecting their privacy. Sometimes. by correlating enough statistics, sensitive data about individual can be inferred. The problem of protecting against such indirect disclosures of confidential data is called the inference problem and a protecting mechanism – an inference control. A good inference control mechanism should be effective (it should provide security to a reasonable extent) and feasible (a practical way exists to enforce it). At the same time it should retain the richness of the information revealed to the users. During the last few years several techniques were developed for controlling inferences. One of the earliest inference controls for statistical databases restricts the responses computed over too small or too large query-sets. However, this technique is easily subverted. In this paper we propose a new query-set size inference control which is based on the idea of multiranges and has better performance then the original one.

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11

Umar Hussain and Farhad Ali Khattak. "Choosing Right Statistical Test for Data Analysis." Journal of Saidu Medical College, Swat 14, no. 3 (July 24, 2024): 263–65. http://dx.doi.org/10.52206/jsmc.2024.14.3.989.

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In scientific research, selecting the appropriate statistical test is crucial for accurate data analysis and valid inference. They allow researchers to make informed inferences about populations, quantify uncertainty, test hypotheses, identify relationships, and provide evidence-based support for decisions. By rigorously evaluating data, statistical tests enhance the credibility and generalizability of research findings. This process is guided by several key steps, including the type of data collected, the research design, and the assumptions underlying statistical tests.

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12

Sunder, Shyam. "Statistical studies of financial reports and stock markets." Journal of Capital Markets Studies 1, no. 1 (October 13, 2017): 5–9. http://dx.doi.org/10.1108/jcms-10-2017-006.

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Purpose The purpose of this paper is to examine the usefulness of statistical studies of financial reports and stock market data for improving corporate financial reports. Design/methodology/approach Analytical writing. Findings It is often claimed that statistical studies of co-variation between financial and stock market data can help set better financial reporting policy. Such co-variation, even when it can be estimated, tells us little about which financial reports help to make better financial decisions. A case in support of such claims remains to be made. Practical implications The readers are advised to be extremely careful in drawing inferences from studies of co-variation between accounting and stock market data for financial reporting policy. Social implications Inference from accounting empirical studies to policy needs better rationale to avoid bad policy consequences. Originality/value This paper raises original questions about policy inferences from a large class of empirical research in accounting.

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13

MANOR BRAHAM, HANA, and DANI BEN-ZVI. "STUDENTS’ EMERGENT ARTICULATIONS OF STATISTICAL MODELS AND MODELING IN MAKING INFORMAL STATISTICAL INFERENCES." STATISTICS EDUCATION RESEARCH JOURNAL 16, no. 2 (November 30, 2017): 116–43. http://dx.doi.org/10.52041/serj.v16i2.187.

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A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students’ articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students understand the relationship between sample and population, as well as reasoning with models and modeling. We explore the articulations of a pair of primary school students, who had previously participated in the Connections Project exploratory data analysis (EDA) activities, and suggest an emergent conceptual framework for reasoning with statistical models and modeling. We shed light on ideas of statistical models and modeling that can emerge among primary students and how they articulate those ideas. Implications for teaching and research are discussed. First published November 2017 at Statistics Education Research Journal Archives

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14

Heckman, Jonathan J. "Statistical inference and string theory." International Journal of Modern Physics A 30, no. 26 (September 18, 2015): 1550160. http://dx.doi.org/10.1142/s0217751x15501602.

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In this paper, we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an [Formula: see text]-dimensional manifold of statistical fitting parameters. When the agents making nearby inferences align along a [Formula: see text]-dimensional grid, we find that the pooled probability that the collective reaches a correct inference is the partition function of a nonlinear sigma model in [Formula: see text] dimensions. Stability under perturbations to the original inference scheme requires the agents of the collective to distribute along two dimensions. Conformal invariance of the sigma model corresponds to the condition of a stable inference scheme, directly leading to the Einstein field equations for classical gravity. By summing over all possible arrangements of the agents in the collective, we reach a string theory. We also use this perspective to quantify how much an observer can hope to learn about the internal geometry of a superstring compactification. Finally, we present some brief speculative remarks on applications to the AdS/CFT correspondence and Lorentzian signature space–times.

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15

Biddle, Jeff. "Statistical Inference in Economics in the 1920s and 1930s." History of Political Economy 53, no. 6 (August 26, 2021): 53–80. http://dx.doi.org/10.1215/00182702-9414775.

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Statistical inference is the process of drawing conclusions from samples of statistical data about things not fully described or recorded in those samples. During the 1920s, economists in the United States articulated a general approach to statistical inference that downplayed the value of the inferential measures derived from probability theory that later came to be central to the idea of statistical inference in economics. This approach is illustrated by the practices of economists of the Bureau of Economic Analysis of the US Department of Agriculture, who regularly analyzed statistical samples to forecast supplies of various agricultural products. Forecasting represents an interesting case for studying the development of inferential methods, as analysts receive regular feedback on the effectiveness of their inferences when forecasts are compared with actual events.

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16

Zhang, Qi, and Lu Lin. "Terminal-Dependent Statistical Inferences for FBSDE." Stochastic Analysis and Applications 32, no. 1 (December 9, 2013): 128–51. http://dx.doi.org/10.1080/07362994.2013.852068.

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17

Pitowsky, Itamar. "On the status of statistical inferences." Synthese 63, no. 2 (May 1985): 233–47. http://dx.doi.org/10.1007/bf00485368.

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18

Zhu, Weimo. "Making Bootstrap Statistical Inferences: A Tutorial." Research Quarterly for Exercise and Sport 68, no. 1 (March 1997): 44–55. http://dx.doi.org/10.1080/02701367.1997.10608865.

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19

Damaraju, Lakshmi, and Damaraju Raghavarao. "Statistical inferences accounting for human behavior." Metrika 62, no. 1 (September 2005): 65–72. http://dx.doi.org/10.1007/s001840400356.

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20

Nakaya, Tomoki. "Statistical Inferences in Bidimensional Regression Models." Geographical Analysis 29, no. 2 (September 7, 2010): 169–86. http://dx.doi.org/10.1111/j.1538-4632.1997.tb00954.x.

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21

Golosnoy, Vasyl, Wolfgang Schmid, Miriam Isabel Seifert, and Taras Lazariv. "Statistical inferences for realized portfolio weights." Econometrics and Statistics 14 (April 2020): 49–62. http://dx.doi.org/10.1016/j.ecosta.2018.08.003.

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22

Khan, M. J. S., and Bushra Khatoon. "Statistical Inferences of $$R=P(X." Annals of Data Science 7, no. 3 (April 24, 2019): 525–45. http://dx.doi.org/10.1007/s40745-019-00207-6.

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23

Gui, Wenhao. "Statistical Inferences and Applications of the Half Exponential Power Distribution." Journal of Quality and Reliability Engineering 2013 (June 5, 2013): 1–9. http://dx.doi.org/10.1155/2013/219473.

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We investigate the statistical inferences and applications of the half exponential power distribution for the first time. The proposed model defined on the nonnegative reals extends the half normal distribution and is more flexible. The characterizations and properties involving moments and some measures based on moments of this distribution are derived. The inference aspects using methods of moment and maximum likelihood are presented. We also study the performance of the estimators using the Monte Carlo simulation. Finally, we illustrate it with two real applications.

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24

Robinson, Geoffrey K. "What Properties Might Statistical Inferences Reasonably be Expected to Have?—Crisis and Resolution in Statistical Inference." American Statistician 73, no. 3 (June 4, 2018): 243–52. http://dx.doi.org/10.1080/00031305.2017.1415971.

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25

Morstyn, Ron. "Some Fallacies of Statistical Inferences about Psychotherapy." Australian & New Zealand Journal of Psychiatry 27, no. 1 (March 1993): 101–7. http://dx.doi.org/10.3109/00048679309072128.

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Statistical methodology does not provide an effective, impartial, or objective way to determine the validity of theories of psychotherapy. Furthermore, the correlations revealed by statistical studies of psychotherapy are clinically irrelevant. Nevertheless there is a growing trend to recognise only statistically “proven” techniques of psychotherapy as legitimate medical treatment. The replacement of established medical standards for psychotherapy with this bogus new scientism is likely to lead to iniquitous clinical and administrative restrictions upon psychotherapists which will cause unnecessary suffering to patients.

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26

Scales, John A., and Roel Snieder. "To Bayes or not to Bayes?" GEOPHYSICS 62, no. 4 (July 1, 1997): 1045–46. http://dx.doi.org/10.1190/1.6241045.1.

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The goal of geophysical inversion is to make quantitative inferences about the Earth from noisy, finite data. The limitations of noise and the inadequacy of the data mean that geophysical inversion problems are fundamentally problems of statistical inference. We do not invert data to find “models.” as much as we might like to; we invert data to make inferences about models. There will usually be an infinity of models that fit the data. Thus we must look to probability theory for help.

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27

Morgan, Mary S. "Narrative Inference with and without Statistics." History of Political Economy 53, no. 6 (August 26, 2021): 113–38. http://dx.doi.org/10.1215/00182702-9414803.

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This article investigates the role played by narrative in drawing inferences from statistics before the adoption of formal inference regimes in economics. Two well-known, and exemplary, cases of informal inference provide the materials. Nikolai Kondratiev’s struggles to make inferences about the existence of his “long waves” from heaps of statistics in the 1920s contrast sharply with Thomas Robert Malthus’s confident account of demographic-economic oscillations made on the basis of the limited numbers available in the late eighteenth century. Comparison of their inferential reasoning, using detailed textual analysis, casts attention on the important role of narrative. These cases prompt the notion of “narrative inference”: where informal statistical inference depends on narrative accounts—used to make sense of the numbers by Malthus or to add sense onto the numbers by Kondratiev.

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28

Frank, Kenneth, and Kyung-Seok Min. "10. Indices of Robustness for Sample Representation." Sociological Methodology 37, no. 1 (August 2007): 349–92. http://dx.doi.org/10.1111/j.1467-9531.2007.00186.x.

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Social scientists are rarely able to gather data from the full range of contexts to which they hope to generalize (Shadish, Cook, and Campbell 2002). Here we suggest that debates about the generality of causal inferences in the social sciences can be informed by quantifying the conditions necessary to invalidate an inference. We begin by differentiating the target population into two sub-populations: a potentially observed subpopulation from which all of a sample is drawn and a potentially unobserved subpopulation from which no members of the sample are drawn but which is part of the population to which policymakers seek to generalize. We then quantify the robustness of an inference in terms of the conditions necessary to invalidate an inference if cases from the potentially unobserved subpopulation were included in the sample. We apply the indices to inferences regarding the positive effect of small classes on achievement from the Tennessee class size study and then consider the breadth of external validity. We use the statistical test for whether there is a difference in effects between two subpopulations as a baseline to evaluate robustness, and we consider a Bayesian motivation for the indices and compare the use of the indices with other procedures. In the discussion we emphasize the value of quantifying robustness, consider the value of different quantitative thresholds, and conclude by extending a metaphor linking statistical and causal inferences.

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29

Goodwin, Chris, and Enrique Ortiz. "It's a Girl! Random Numbers, Simulations, and the Law of Large Numbers." Mathematics Teaching in the Middle School 20, no. 9 (May 2015): 561–64. http://dx.doi.org/10.5951/mathteacmiddscho.20.9.0561.

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Modeling using mathematics and making inferences about mathematical situations are becoming more and more prevalent in most fields of study. When we want to generalize about a population or make predictions of what could occur, we cannot use descriptive statistics. Instead, we turn to inference. Simulation and sampling are essential in building a foundation for statistical inference.

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Li, Zhang Miao, Xin Jian Kou, and Jian Yong Huang. "The Interval Estimation about Confidence of the Reliability Index." Applied Mechanics and Materials 166-169 (May 2012): 1854–58. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.1854.

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The theory of statistical inferences is the base of the reliability analysis. The results of inferences can not be believed unquestionably because the data sample could not involve whole information about the parent distribution. In engineering, it is reasonable to estimate the precision of inference results concerning the reliability index. Therefore, the randomness of reliability index is discussed in this paper. The confidence interval, which is one of the most important concepts in statistics, is employed to express the precision of the reliability index.

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31

Kvålseth, Tarald O. "Range Measure of Qualitative Variation: Statistical Inferences." Perceptual and Motor Skills 70, no. 1 (February 1990): 82. http://dx.doi.org/10.2466/pms.1990.70.1.82.

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32

Simushkin, S. V. "Exact statistical inferences and Monte Carlo method." Lobachevskii Journal of Mathematics 35, no. 4 (October 2014): 360–70. http://dx.doi.org/10.1134/s1995080214040210.

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33

Guenther, William C. "Statistical Inferences for Two One-Parameter Families." American Statistician 41, no. 1 (February 1987): 50. http://dx.doi.org/10.2307/2684320.

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34

Rahardja, Dewi, Yan D. Zhao, and Han Wu. "Statistical inferences for two-dimensional workpiece localisation." International Journal of Manufacturing Research 2, no. 1 (2007): 88. http://dx.doi.org/10.1504/ijmr.2007.013428.

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35

Guenther, William C. "Statistical Inferences for Two One-Parameter Families." American Statistician 41, no. 1 (February 1987): 50–52. http://dx.doi.org/10.1080/00031305.1987.10475442.

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36

Stienstra, D., T. L. Anderson, and L. J. Ringer. "Statistical Inferences on Cleavage Fracture Toughness Data." Journal of Engineering Materials and Technology 112, no. 1 (January 1, 1990): 31–37. http://dx.doi.org/10.1115/1.2903183.

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A method to predict lower bound cleavage fracture toughness values from small data sets is presented. The method is derived from a Weibull statistic based micromechanical analysis and can be applied in the ductile-brittle transition region. Lower bound predictions can compare well with the ASME KIR and KIC design curves. Difficulties in comparing Weibull shape parameters calculated by different methods are also discussed and several calculation methods are compared with a Monte Carlo simulation. The preferred methods are the maximum likelihood estimators (MLEs), least squares with the (i−.5)/n centralizing approach, or a simple estimation scheme which gives a “Good Linear Unbiased Estimator.”

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37

Evans, J. St B. T., and P. Pollard. "Intuitive statistical inferences about normally distributed data." Acta Psychologica 60, no. 1 (September 1985): 57–71. http://dx.doi.org/10.1016/0001-6918(85)90013-7.

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38

Shunian, Yang, Li Zhu, and Li Guangying. "Statistical inferences of form error distribution function." Precision Engineering 10, no. 2 (April 1988): 97–99. http://dx.doi.org/10.1016/0141-6359(88)90007-4.

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39

Muralidharan, K., and Arti Khabia. "Some statistical inferences on Inlier(s) models." International Journal of System Assurance Engineering and Management 8, S1 (July 25, 2014): 18–25. http://dx.doi.org/10.1007/s13198-014-0284-8.

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40

Maua, D. D., C. P. De Campos, A. Benavoli, and A. Antonucci. "Probabilistic Inference in Credal Networks: New Complexity Results." Journal of Artificial Intelligence Research 50 (July 28, 2014): 603–37. http://dx.doi.org/10.1613/jair.4355.

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Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove a similar result for inference in naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and naive Bayes structures are used in real applications of imprecise probability.

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41

Shellman, Stephen M. "Time Series Intervals and Statistical Inference: The Effects of Temporal Aggregation on Event Data Analysis." Political Analysis 12, no. 1 (2004): 97–104. http://dx.doi.org/10.1093/pan/mpg017.

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While many areas of research in political science draw inferences from temporally aggregated data, rarely have researchers explored how temporal aggregation biases parameter estimates. With some notable exceptions (Freeman 1989, Political Analysis 1:61–98; Alt et al. 2001, Political Analysis 9:21–44; Thomas 2002, “Event Data Analysis and Threats from Temporal Aggregation”) political science studies largely ignore how temporal aggregation affects our inferences. This article expands upon others' work on this issue by assessing the effect of temporal aggregation decisions on vector autoregressive (VAR) parameter estimates, significance levels, Granger causality tests, and impulse response functions. While the study is relevant to all fields in political science, the results directly apply to event data studies of conflict and cooperation. The findings imply that political scientists should be wary of the impact that temporal aggregation has on statistical inference.

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Eklund, Anders, Thomas E. Nichols, and Hans Knutsson. "Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates." Proceedings of the National Academy of Sciences 113, no. 28 (June 28, 2016): 7900–7905. http://dx.doi.org/10.1073/pnas.1602413113.

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The most widely used task functional magnetic resonance imaging (fMRI) analyses use parametric statistical methods that depend on a variety of assumptions. In this work, we use real resting-state data and a total of 3 million random task group analyses to compute empirical familywise error rates for the fMRI software packages SPM, FSL, and AFNI, as well as a nonparametric permutation method. For a nominal familywise error rate of 5%, the parametric statistical methods are shown to be conservative for voxelwise inference and invalid for clusterwise inference. Our results suggest that the principal cause of the invalid cluster inferences is spatial autocorrelation functions that do not follow the assumed Gaussian shape. By comparison, the nonparametric permutation test is found to produce nominal results for voxelwise as well as clusterwise inference. These findings speak to the need of validating the statistical methods being used in the field of neuroimaging.

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43

Jones, Ryan Seth, Zhigang Jia, and Joel Bezaire. "Giving Birth to Inferential Reasoning." Mathematics Teacher: Learning and Teaching PK-12 113, no. 4 (April 2020): 287–92. http://dx.doi.org/10.5951/mtlt.2019.0152.

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Too often, statistical inference and probability are treated in schools like they are unrelated. In this paper, we describe how we supported students to learn about the role of probability in making inferences with variable data by building models of real world events and using them to simulate repeated samples.

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44

Clark, Oliver. "Improve your statistical inferences with this one neat trick: A brief review of the Improving your statistical inferences MOOC." PsyPag Quarterly 1, no. 111 (June 2019): 44–46. http://dx.doi.org/10.53841/bpspag.2019.1.111.44.

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This article is a brief review of an excellent free Massive Open Online Course that guides students through the various ways that they can improve research questions and make more informed choices about their choices of statistical tests. The MOOC includes an introduction to simulation and data-analysis using the R programming language, meta-science, open practices, and alternative statistical frameworks (e.g. Likelihood Principal, Bayes Theorem). Although it is predominantly aimed at those using quantitative methodology, it has useful modules on philosophy of science and theory building which may be interesting for qualitative researchers.

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McCabe, Connor J., Dale S. Kim, and Kevin M. King. "Improving Present Practices in the Visual Display of Interactions." Advances in Methods and Practices in Psychological Science 1, no. 2 (March 28, 2018): 147–65. http://dx.doi.org/10.1177/2515245917746792.

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Interaction plots are used frequently in psychology research to make inferences about moderation hypotheses. A common method of analyzing and displaying interactions is to create simple-slopes or marginal-effects plots using standard software programs. However, these plots omit features that are essential to both graphic integrity and statistical inference. For example, they often do not display all quantities of interest, omit information about uncertainty, or do not show the observed data underlying an interaction, and failure to include these features undermines the strength of the inferences that may be drawn from such displays. Here, we review the strengths and limitations of present practices in analyzing and visualizing interaction effects in psychology. We provide simulated examples of the conditions under which visual displays may lead to inappropriate inferences and introduce open-source software that provides optimized utilities for analyzing and visualizing interactions.

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46

Sileshi, G. "Selecting the right statistical model for analysis of insect count data by using information theoretic measures." Bulletin of Entomological Research 96, no. 5 (October 2006): 479–88. http://dx.doi.org/10.1079/ber2006449.

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AbstractResearchers and regulatory agencies often make statistical inferences from insect count data using modelling approaches that assume homogeneous variance. Such models do not allow for formal appraisal of variability which in its different forms is the subject of interest in ecology. Therefore, the objectives of this paper were to (i) compare models suitable for handling variance heterogeneity and (ii) select optimal models to ensure valid statistical inferences from insect count data. The log-normal, standard Poisson, Poisson corrected for overdispersion, zero-inflated Poisson, the negative binomial distribution and zero-inflated negative binomial models were compared using six count datasets on foliage-dwelling insects and five families of soil-dwelling insects. Akaike's and Schwarz Bayesian information criteria were used for comparing the various models. Over 50% of the counts were zeros even in locally abundant species such as Ootheca bennigseni Weise, Mesoplatys ochroptera Stål and Diaecoderus spp. The Poisson model after correction for overdispersion and the standard negative binomial distribution model provided better description of the probability distribution of seven out of the 11 insects than the log-normal, standard Poisson, zero-inflated Poisson or zero-inflated negative binomial models. It is concluded that excess zeros and variance heterogeneity are common data phenomena in insect counts. If not properly modelled, these properties can invalidate the normal distribution assumptions resulting in biased estimation of ecological effects and jeopardizing the integrity of the scientific inferences. Therefore, it is recommended that statistical models appropriate for handling these data properties be selected using objective criteria to ensure efficient statistical inference.

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HENRIQUES, ANA, and HÉLIA OLIVEIRA. "STUDENTS’ EXPRESSIONS OF UNCERTAINTY IN MAKING INFORMAL INFERENCE WHEN ENGAGED IN A STATISTICAL INVESTIGATION USING TINKERPLOTS." STATISTICS EDUCATION RESEARCH JOURNAL 15, no. 2 (November 30, 2016): 62–80. http://dx.doi.org/10.52041/serj.v15i2.241.

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This paper reports on the results of a study investigating the potential to embed Informal Statistical Inference in statistical investigations, using TinkerPlots, for assisting 8th grade students’ informal inferential reasoning to emerge, particularly their articulations of uncertainty. Data collection included students’ written work on a statistical investigation as well as audio and screen records. Results show students’ ability to draw conclusions based on data, recognizing that these are constrained by uncertainty, and to use them to make inferences. However, few students used probabilistic language for describing their generalizations. These results highlight the need for working on probabilistic ideas within statistics, helping students to evolve from a deterministic perspective of inference to include uncertainty in their statements. First published November 2016 at Statistics Education Research Journal Archives

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Zhang, Jin-Ting. "Statistical inferences for linear models with functional responses." Statistica Sinica 21, no. 3 (June 1, 2011): 1431–51. http://dx.doi.org/10.5705/ss.2009.302.

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Piegorsch, Walter W., R. Webster West, Wei Pan, and Ralph L. Kodell. "Low dose risk estimation via simultaneous statistical inferences." Journal of the Royal Statistical Society: Series C (Applied Statistics) 54, no. 1 (January 2005): 245–58. http://dx.doi.org/10.1111/j.1467-9876.2005.00481.x.

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Katz, Richard W. "Statistical Procedures for Making Inferences about Climate Variability." Journal of Climate 1, no. 11 (November 1988): 1057–64. http://dx.doi.org/10.1175/1520-0442(1988)001<1057:spfmia>2.0.co;2.

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