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Статті в журналах з теми "ANOVA test"

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Автор: Grafiati

Опубліковано: 6 вересня 2023

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1

Davison, Mark L., and Anu R. Sharma. "ANOVA and ANCOVA of pre- and post-test, ordinal data." Psychometrika 59, no. 4 (December 1994): 593–600. http://dx.doi.org/10.1007/bf02294394.

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2

Tarlow, Kevin R. "Teaching principles of inference with ANOVA." Teaching Statistics 38, no. 1 (July 24, 2015): 16–21. http://dx.doi.org/10.1111/test.12085.

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3

Cuevas, Antonio, Manuel Febrero, and Ricardo Fraiman. "An anova test for functional data." Computational Statistics & Data Analysis 47, no. 1 (August 2004): 111–22. http://dx.doi.org/10.1016/j.csda.2003.10.021.

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4

Maxwell, Scott E., Harold D. Delaney, and Jerry M. Manheimer. "Anova of Residuals and Ancova: Correcting an Illusion by Using Model Comparisons and Graphs." Journal of Educational Statistics 10, no. 3 (September 1985): 197–209. http://dx.doi.org/10.3102/10769986010003197.

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Анотація:

Analysis of covariance is often conceptualized as an analysis of variance of a single set of residual scores that are obtained by regressing the dependent variable on the covariate. Although this conceptualization of an equivalence between the two procedures may be intuitively appealing, it is mathematically incorrect. If residuals are obtained from the pooled within-groups regression coefficient ( bw), an analysis of variance on the residuals results in an inflated α-level. If the regression coefficient for the total sample combined into one group ( bT) is used, ANOVA on the residuals yields an inappropriately conservative test. In either case, analysis of variance of residuals fails to provide a correct test, because the significance test in analysis of covariance requires consideration of both bw and bT, unlike analysis of residuals. It is recommended that the significance test of treatment effects in analysis of covariance be conceptualized, not as an analysis of residuals, but as a comparison of models whose parameters are estimated by the principle of least squares. Focusing on model comparisons and their associated graphs can be used effectively here as in other cases to teach simply and correctly the logic of the statistical test.

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5

Chen, Tansheng, and Lukun Zheng. "One-Way High-Dimensional ANOVA." Journal of Mathematics 2023 (March 28, 2023): 1–11. http://dx.doi.org/10.1155/2023/9350523.

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Анотація:

ANOVA is one of the most important tools in comparing the treatment means among different groups in repeated measurements. The classical F test is routinely used to test if the treatment means are the same across different groups. However, it is inefficient when the number of groups or dimension gets large. We propose a smoothing truncation test to deal with this problem. It is shown theoretically and empirically that the proposed test works regardless of the dimension. The limiting null and alternative distributions of our test statistic are established for fixed and diverging number of treatments. Simulations demonstrate superior performance of the proposed test over the F test in different settings.

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6

Camilli, Gregory, and Lorrie A. Shepard. "The Inadequacy of ANOVA for Detecting Test Bias." Journal of Educational Statistics 12, no. 1 (March 1987): 87–99. http://dx.doi.org/10.3102/10769986012001087.

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Анотація:

The inadequacy of ANOVA for detecting bias in test items should already be well understood, yet it persists as a popular method. Here, previous arguments are extended to explain why ANOVA may obscure test bias when it exists, as well as create false impressions of bias. In fact, it is demonstrated in this paper that ANOVA will fail to detect even absurdly large amounts of bias. More specifically, it is shown that bias contributes relatively more to the group main effect than to the group-by-item interaction.

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7

Hecke, T. Van. "Power study of anova versus Kruskal-Wallis test." Journal of Statistics and Management Systems 15, no. 2-3 (May 2012): 241–47. http://dx.doi.org/10.1080/09720510.2012.10701623.

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8

Wetzels, Ruud, Raoul P. P. P. Grasman, and Eric-Jan Wagenmakers. "A Default Bayesian Hypothesis Test for ANOVA Designs." American Statistician 66, no. 2 (May 2012): 104–11. http://dx.doi.org/10.1080/00031305.2012.695956.

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9

Camilli, Gregory, and Lorrie A. Shepard. "The Inadequacy of ANOVA for Detecting Test Bias." Journal of Educational Statistics 12, no. 1 (1987): 87. http://dx.doi.org/10.2307/1164630.

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10

Jung, Byoung Cheol, Myoungshic Jhun, and Seuck Heun Song. "A new random permutation test in ANOVA models." Statistical Papers 48, no. 1 (January 2007): 47–62. http://dx.doi.org/10.1007/s00362-006-0315-x.

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11

Al-Kandari, Noriah M., and Emad-Eldin A. A. Aly. "An ANOVA-type test for multiple change points." Statistical Papers 55, no. 4 (October 1, 2013): 1159–78. http://dx.doi.org/10.1007/s00362-013-0559-1.

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12

Park, Hyo-Il. "Simultaneous Test Procedure for ANOVA with Possibly Unequal Variances." Korean Data Analysis Society 20, no. 3 (June 30, 2018): 1099–106. http://dx.doi.org/10.37727/jkdas.2018.20.3.1099.

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13

Kucuk, Ugur, Mehmet Eyuboglu, Hilal Olgun Kucuk, and Gokhan Degirmencioglu. "Importance of using proper post hoc test with ANOVA." International Journal of Cardiology 209 (April 2016): 346. http://dx.doi.org/10.1016/j.ijcard.2015.11.061.

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14

Karagoz, Derya. "Modified Welch Test Statistic for ANOVA under Weibull Distribution." Hacettepe Journal of Mathematics and Statistics 45, no. 56 (March 10, 2015): 1. http://dx.doi.org/10.15672/hjms.2015569632.

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15

Wang, Lan, Michael G. Akritas, and Ingrid Van Keilegom. "An ANOVA-type nonparametric diagnostic test for heteroscedastic regression models." Journal of Nonparametric Statistics 20, no. 5 (July 2008): 365–82. http://dx.doi.org/10.1080/10485250802066112.

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16

Bilker, Warren B., Colleen Brensinger, and Ruben C. Gur. "A Two Factor ANOVA-like Test for Correlated Correlations: CORANOVA." Multivariate Behavioral Research 39, no. 4 (October 2004): 565–94. http://dx.doi.org/10.1207/s15327906mbr3904_1.

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17

Ning, Wei, and Hyune-Ju Kim. "Residual Pattern Based Test for Interactions in Two-Way ANOVA." Biometrical Journal 50, no. 3 (June 2008): 431–45. http://dx.doi.org/10.1002/bimj.200710427.

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18

Hegazy, R., M. I. Mohamed, and A. Abu-Sinna. "Proposed the ANOVA Method for Analysis of Proficiency Test Result." MAPAN 31, no. 2 (February 1, 2016): 115–18. http://dx.doi.org/10.1007/s12647-015-0163-z.

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19

Celik, Nuri. "One-way ANOVA with Bimodal Error Terms." Journal of Advances in Mathematics and Computer Science 38, no. 8 (July 9, 2023): 168–73. http://dx.doi.org/10.9734/jamcs/2023/v38i81798.

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Анотація:

In this paper, we assume the error distribution of one-way ANOVA as alpha-skew normal distribution. Alpha-skew normal distribution gives us exibility for modelling the data which has heavy tailness, skewness, bimodality and also symmetricity. We obtain the maximum likelihood estimator of the model parameters and the test statistics based on these estimators. Monte Carlo simulation study states that the maximum likelihood estimators of the parameters of interest are more efficient than the corresponding traditional estimators based on normality. Additionally, the test statistics based on maximum likelihood estimators is much more powerful than the test statistics based on traditional normal theory. At the end of this study, a real-life example is made just for illustration of the proposed methodology.

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20

Xiao, Li. "ANOVA on College Students' Physical Fitness." MATEC Web of Conferences 365 (2022): 01034. http://dx.doi.org/10.1051/matecconf/202236501034.

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Анотація:

Through a sampling survey of the results of the physical fitness test of the students of Guilin Institute of Aerospace Industry in 2018, using the analysis of variance research method, the five variable indicators of the physical fitness of the surveyed students were analyzed, and the changes in the physical fitness of the students during the three years of university were studied. The test results show that during college, the physical fitness of students has been increasing year by year, but the growth rate has been declining, and the difference in physical fitness is mainly due to the changes in their own high body mass index and vital capacity body mass index, and the endurance quality of students has not improved much. The analysis results show that the improvement of college students' physical fitness can be regarded as a recovery from poor physical fitness in high school. Therefore, there is still greater potential and room for improving the physical fitness of college students.

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21

Shen, Juan, and Xuming He. "Generalized F Test and Generalized Deviance Test in Two-Way ANOVA Models for Randomized Trials." Journal of Biopharmaceutical Statistics 24, no. 3 (April 15, 2014): 523–34. http://dx.doi.org/10.1080/10543406.2014.888435.

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22

Zimmerman, Donald W., and Bruno D. Zumbo. "Relative Power of the Wilcoxon Test, the Friedman Test, and Repeated-Measures ANOVA on Ranks." Journal of Experimental Education 62, no. 1 (July 1993): 75–86. http://dx.doi.org/10.1080/00220973.1993.9943832.

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23

Saleh, A. K. Md Ehsanes, M. Arashi, M. Norouzirad, and B. M. Goalm Kibria. "On shrinkage and selection: ANOVA model." Journal of Statistical Research 51, no. 2 (February 1, 2018): 165–91. http://dx.doi.org/10.47302/jsr.2017510205.

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Анотація:

This paper considers the estimation of the parameters of an ANOVA model when sparsity is suspected. Accordingly, we consider the least square estimator (LSE), restricted LSE, preliminary test and Stein-type estimators, together with three penalty estimators, namely, the ridge estimator, subset selection rules (hard threshold estimator) and the LASSO (soft threshold estimator). We compare and contrast the L2-risk of all the estimators with the lower bound of L2-risk of LASSO in a family of diagonal projection scheme which is also the lower bound of the exact L2-risk of LASSO. The result of this comparison is that neither LASSO nor the LSE, preliminary test, and Stein-type estimators outperform each other uniformly. However, when the model is sparse, LASSO outperforms all estimators except “ridge” estimator since both LASSO and ridge are L2-risk equivalent under sparsity. We also find that LASSO and the restricted LSE are L2-risk equivalent and both outperform all estimators (except ridge) depending on the dimension of sparsity. Finally, ridge estimator outperforms all estimators uniformly. Our finding are based on L2-risk of estimators and lower bound of the risk of LASSO together with tables of efficiency and graphical display of efficiency and not based on simulation.

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24

Mu, Weiyan, and Xiaojing Wang. "Inference for One-Way ANOVA with Equicorrelation Error Structure." Scientific World Journal 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/341617.

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Анотація:

We consider inferences in a one-way ANOVA model with equicorrelation error structures. Hypotheses of the equality of the means are discussed. A generalizedF-test has been proposed by in the literature to compare the means of all populations. However, they did not discuss the performance of that test. We propose two methods, a generalized pivotal quantities-based method and a parametric bootstrap method, to test the hypotheses of equality of the means. We compare the empirical performance of the proposed tests with the generalizedF-test. It can be seen from the simulation results that the generalizedF-test does not perform well in terms of Type I error rate, and the proposed tests perform much better. We also provide corresponding simultaneous confidence intervals for all pair-wise differences of the means, whose coverage probabilities are close to the confidence level.

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25

Nyaga, Victoria N., Marc Aerts, and Marc Arbyn. "ANOVA model for network meta-analysis of diagnostic test accuracy data." Statistical Methods in Medical Research 27, no. 6 (September 20, 2016): 1766–84. http://dx.doi.org/10.1177/0962280216669182.

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Анотація:

Procedures combining and summarising direct and indirect evidence from independent studies assessing the diagnostic accuracy of different tests for the same disease are referred to network meta-analysis. Network meta-analysis provides a unified inference framework and uses the data more efficiently. Nonetheless, handling the inherent correlation between sensitivity and specificity continues to be a statistical challenge. We developed an arm-based hierarchical model which expresses the logit transformed sensitivity and specificity as the sum of fixed effects for test, correlated study-effects to model the inherent correlation between sensitivity and specificity and a random error associated with various tests evaluated in a given study. We present the accuracy of 11 tests used to triage women with minor cervical lesions to detect cervical precancer. Finally, we compare the results with those from a contrast-based model which expresses the linear predictor as a contrast to a comparator test. The proposed arm-based model is more appealing than the contrast-based model since the former permits more straightforward interpretation of the parameters, makes use of all available data yielding shorter credible intervals, and models more natural variance–covariance matrix structures.

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26

Brady, Siobhan M., Meike Burow, Wolfgang Busch, Örjan Carlborg, Katherine J. Denby, Jane Glazebrook, Eric S. Hamilton, et al. "Reassess the t Test: Interact with All Your Data via ANOVA." Plant Cell 27, no. 8 (July 28, 2015): 2088–94. http://dx.doi.org/10.1105/tpc.15.00238.

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27

Chen, Shun-Yi, Hubert J. Chen, and Cherng G. Ding. "An ANOVA test for the equivalency of means under unequal variances." Computational Statistics & Data Analysis 33, no. 2 (April 2000): 151–75. http://dx.doi.org/10.1016/s0167-9473(99)00053-5.

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28

Zhang, Jin-Ting. "An approximate degrees of freedom test for heteroscedastic two-way ANOVA." Journal of Statistical Planning and Inference 142, no. 1 (January 2012): 336–46. http://dx.doi.org/10.1016/j.jspi.2011.07.023.

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29

Jan, Show-Li, and Gwowen Shieh. "Sample size determinations for Welch's test in one-way heteroscedastic ANOVA." British Journal of Mathematical and Statistical Psychology 67, no. 1 (January 14, 2013): 72–93. http://dx.doi.org/10.1111/bmsp.12006.

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30

Mutlu, Hakan Tahiri, Fikri Gökpinar, Esra Gökpinar, Hasan Hüseyin Gül, and Gamze Güven. "A new computational approach test for one-way ANOVA under heteroscedasticity." Communications in Statistics - Theory and Methods 46, no. 16 (August 5, 2016): 8236–56. http://dx.doi.org/10.1080/03610926.2016.1177082.

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31

Fan, Chunpeng, and Donghui Zhang. "On power and sample size of the ANOVA-type rank test." Communications in Statistics - Simulation and Computation 46, no. 4 (December 28, 2016): 3224–41. http://dx.doi.org/10.1080/03610918.2015.1082585.

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32

Grund, Simon, Oliver Lüdtke, and Alexander Robitzsch. "Pooling ANOVA Results From Multiply Imputed Datasets." Methodology 12, no. 3 (July 2016): 75–88. http://dx.doi.org/10.1027/1614-2241/a000111.

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Анотація:

Abstract. The analysis of variance (ANOVA) is frequently used to examine whether a number of groups differ on a variable of interest. The global hypothesis test of the ANOVA can be reformulated as a regression model in which all group differences are simultaneously tested against zero. Multiple imputation offers reliable and effective treatment of missing data; however, recommendations differ with regard to what procedures are suitable for pooling ANOVA results from multiply imputed datasets. In this article, we compared several procedures (known as D1, D2, and D3) using Monte Carlo simulations. Even though previous recommendations have advocated that D2 should be avoided in favor of D1 or D3, our results suggest that all procedures provide a suitable test of the ANOVA’s global null hypothesis in many plausible research scenarios. In more extreme settings, D1 was most reliable, whereas D2 and D3 suffered from different limitations. We provide guidelines on how the different methods can be applied in one- and two-factorial ANOVA designs and information about the conditions under which some procedures may perform better than others. Computer code is supplied for each method to be used in freely available statistical software.

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33

England, Ashley D., Sosthene Musigwa, Alip Kumar, Ali Daneshmand, Kosar Gharib-Naseri, Sarbast K. Kheravii, Gene Pesti, and Shu-Biao Wu. "Sex proportion as a covariate increases the statistical test power in growth performance based experiments using as-hatched broilers." PLOS ONE 18, no. 1 (January 20, 2023): e0280040. http://dx.doi.org/10.1371/journal.pone.0280040.

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Анотація:

The availability of sexed day-old broiler chicks is becoming an issue as feather sexing is no longer possible. This has great implications for broiler researchers as the use of randomly distributed mixed-sex birds may result in a greater between-pen variation and thus less statistical power than the use of single-sex birds. The objective of this study was to evaluate the effect of including sex proportion as a covariate in an analysis of covariance (ANCOVA) on the statistical power compared to analysis of variance (ANOVA) where sex was not considered. The statistical parameters examined include mean square error (MSE), the F-statistic, model fit, model significance and observed power. A total of 4 separate experiments that used mixed-sex broilers with unequal numbers of male and female birds per pen were conducted during which performance of the birds was measured. The male % in each pen was recorded during each experiment and corrected for mortality. The performance results were analysed by ANOVA and the statistical parameters were then compared to ANCOVA where sex proportion was included as a covariate. The results showed that a set of assumptions first needed to be met to run ANCOVA. In addition, if the ANOVA results show a high level of model significance and power, then ANCOVA may not be necessary. In other circumstances where the assumptions are met and model significance and observed power are low, the inclusion of sex proportion as a covariate in the analysis will help to reduce MSE, increase the F-statistic value and improve the model significance, model fit and observed power. Therefore, it is suggested that sex proportion should be considered as a covariate in ANCOVA to improve statistical power in nutritional experiments when male and female broilers are unequally and randomly distributed in pens.

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34

Siraj, Muhammad. "Analyzing ANOVA F-test and Sequential Feature Selection for Intrusion Detection Systems." International Journal of Advances in Soft Computing and its Applications 14, no. 2 (July 20, 2022): 186–94. http://dx.doi.org/10.15849/ijasca.220720.13.

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Анотація:

An Intrusion Detection System (IDS) helps the computer system notify an admin when an attack is coming to a network. However, some problems may delay this process, such as a long time caused by several features in the captured data to classify. One of the optimization approaches is to select those critical features. It is intended to increase performance and reduce computational time. This research evaluates feature selection methods using the ANOVA F-test and Sequential Feature Selection (SFS), whose performance is measured using some metrics: accuracy, specificity, and sensitivity over NSLKDD, Kyoto2006, and UNSW_NB15 datasets. Using that approach, the performance increases, on average, by more than 10% for multiclass; and about 5% for binary class. It can be inferred that an optimal number of features can be obtained, where the best features are selected by SFS. Nevertheless, this method still needs to be improved before being implemented in a real system. Keywords: Network security, Network infrastructure, Intrusion Detection System, Data Security, Information Security.

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35

Liu, Xuefeng, and Jin-Ting Zhang. "A modified Bartlett test for linear hypotheses in heteroscedastic one-way ANOVA." Statistics and Its Interface 5, no. 2 (2012): 253–62. http://dx.doi.org/10.4310/sii.2012.v5.n2.a9.

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36

De Beuckelaer, A. "A closer examination on some parametric alternatives to the ANOVA F-test." Statistical Papers 37, no. 4 (December 1996): 291–305. http://dx.doi.org/10.1007/bf02926110.

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37

Aenab, Allaa M., S. K. Singh, and Ali Jabir Lafta. "Critical assessment of air pollution by ANOVA test and human health effects." Atmospheric Environment 71 (June 2013): 84–91. http://dx.doi.org/10.1016/j.atmosenv.2013.01.039.

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38

Shieh, Gwowen, and Show-Li Jan. "Optimal sample size allocation for Welch’s test in one-way heteroscedastic ANOVA." Behavior Research Methods 47, no. 2 (June 6, 2014): 374–83. http://dx.doi.org/10.3758/s13428-014-0477-8.

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39

González-Rodríguez, Gil, Ana Colubi, and María Ángeles Gil. "Fuzzy data treated as functional data: A one-way ANOVA test approach." Computational Statistics & Data Analysis 56, no. 4 (April 2012): 943–55. http://dx.doi.org/10.1016/j.csda.2010.06.013.

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40

Chatterjee, Shoutir Kishore, and Sisir Kumar Samanta. "An Alternative Approach to the Anova Problem." Calcutta Statistical Association Bulletin 45, no. 3-4 (September 1995): 179–94. http://dx.doi.org/10.1177/0008068319950305.

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Анотація:

When the hypothesis of equality of means of several univariate homoscedastic normal populations from which independent samples are available, is rejected on the basis of the ANOV A F-test, the populations have to be divided into disjoint groups such that within each group the populations are all same. For any such division a natural index of correctness of the grouping is defined and a procedure is proposed such that it leads to the choice of a division for which the true index does not fall below a stipulated threshold at a given level of confidence. The procedure is illustrated through some numerical examples.

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41

Zhou, Yuanyuan, and Susan Troncoso Skidmore. "A Reassessment of ANOVA Reporting Practices: A Review of Three APA Journals." Journal of Methods and Measurement in the Social Sciences 8, no. 1 (February 28, 2018): 3–19. http://dx.doi.org/10.2458/v8i1.22019.

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Анотація:

Historically, ANOVA has been the most prevalent statistical method used in educational and psychological research and today ANOVA continues to be widely used. A comprehensive review published in 1998 examined several APA journals and discovered persistent concerns in ANOVA reporting practices. The present authors examined all articles published in 2012 in three APA journals (Journal of Applied Psychology, Journal of Counseling Psychology, and Journal of Personality and Social Psychology) to review ANOVA reporting practices including p values and effect sizes. Results indicated that ANOVA continues to be prevalent in the reviewed journals as a test of the primary research question, as well as to test conditional assumptions prior to the primary analysis. Still, ANOVA reporting practices are essentially unchanged from what was previously reported. However, effect size reporting has improved.

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42

Febriani, Suci, Astuti, Kasman Ediputra, and Zulfah. "Anova dan Tukey HSD Analisis Kesalahan Siswa dalam Menjawab Soal Cerita Matematika Berdasarkan Kriteria Watson." Jurnal Pengabdian Masyarakat dan Riset Pendidikan 2, no. 1 (August 1, 2023): 183–88. http://dx.doi.org/10.31004/jerkin.v2i1.139.

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Анотація:

Error Analysis is a technique to identify, classify and interpret systematically the mistakes made by students who are learning to find out the circumstances, causes and various other aspects that are in it. This study analyzes the types of errors made by students in working on mathematics story problems based on Watson's criteria in class IX students of SMP Negeri 1 Bangkinang Kota. The purpose of this study was to see if there was a significant comparison of the results of the 9th grade Mathematics daily test. Before conducting the ANOVA test, first the data normalization test is carried out, then the homogeneity test and then conduct the ANOVA test. The ANOVA test used in this study is a one-way ANOVA test. After testing the data on the results of the daily test scores of Mathematics class IX SMP Negeri 1 Bangkinang Kota, the data obtained from the daily test scores of class IX B, class IX I, class IX J which means that the average daily test scores of the five classes do not have significant differences. In other words, the average daily test scores of class IX B, class IX I, class IX H are the same. There is data on the daily test scores of class IX I, class IX H, class IX F which means that the average daily test scores of the three classes are the same.

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43

Ma, Ming Lei, Gui Ling Wang, Dong Mei Miao, and Bao Yu Lian. "Strength Analysis of BFRP Rebar Based on Kolmogorov–Smirnov Test and ANOVA Method." Advanced Materials Research 598 (November 2012): 492–96. http://dx.doi.org/10.4028/www.scientific.net/amr.598.492.

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Анотація:

A very triditional and comprehensive understanding of the rebars’ static strength is that the strenth followes a normal distribution, no evidence or mathmatic test have adopted to prove that. This paper wants to bring a new idea to analyze the real true result to the former understanding. And finally a six more general distribution forms are used to give a provement which ignored in many strength analyis in China engineering community.During the provement, Fisher test and ANOVA method are studied carefully to suport the KS test.

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44

Johnson, Roger W. "Alternate Forms of the One-Way ANOVA F and Kruskal–Wallis Test Statistics." Journal of Statistics and Data Science Education 30, no. 1 (January 2, 2022): 82–85. http://dx.doi.org/10.1080/26939169.2021.2025177.

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45

Petersen, DR, RE Link, IA Golinkin, DD Ruff, EP Kvam, GP McCabe, and AF Grandt. "Application of Analysis of Variance (ANOVA) Statistical Methods to Breaking Load Corrosion Test." Journal of Testing and Evaluation 25, no. 6 (1997): 565. http://dx.doi.org/10.1520/jte11496j.

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46

Rojewski, Jay W., In Heok Lee, and Sinan Gemici. "Use of t-test and ANOVA in Career-Technical Education Research." Career and Technical Education Research 37, no. 3 (January 1, 2012): 263–75. http://dx.doi.org/10.5328/cter37.3.263.

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47

Gumus, Kutalmis, Mahmut Oguz Selbesoglu, and Cahit Tagi Celik. "Accuracy investigation of height obtained from Classical and Network RTK with ANOVA test." Measurement 90 (August 2016): 135–43. http://dx.doi.org/10.1016/j.measurement.2016.04.045.

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48

Lee, Jinkun, Inyoung Yang, Sooseok Yang, and Jae Su Kwak. "Uncertainty analysis and ANOVA for the measurement reliability estimation of altitude engine test." Journal of Mechanical Science and Technology 21, no. 4 (April 2007): 664–71. http://dx.doi.org/10.1007/bf03026971.

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49

Yusof, Zahayu Md, Suhaida Abdullah, and Sharipah Soaad Syed Yahaya. "Comparing the performance of modified Ft statistic with ANOVA and Kruskal Wallis test." Applied Mathematics & Information Sciences 7, no. 2L (June 1, 2013): 403–8. http://dx.doi.org/10.12785/amis/072l04.

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50

Xu, Liwen, Fangqin Yang, Ranran Chen, and Shenghua Yu. "A Parametric Bootstrap Test for Two-Way ANOVA Model Without Interaction Under Heteroscedasticity." Communications in Statistics - Simulation and Computation 44, no. 5 (October 23, 2014): 1264–72. http://dx.doi.org/10.1080/03610918.2013.818689.

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