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Journal articles on the topic 'Chi square tests'

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Published: 4 June 2021
Last updated: 15 June 2025

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1

Ingster, Yu I. "Adaptive chi-square tests." Journal of Mathematical Sciences 99, no. 2 (2000): 1110–19. http://dx.doi.org/10.1007/bf02673632.

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2

Nihan, Sölpük Turhan. "Karl Pearsons chi-square tests." Educational Research and Reviews 15, no. 9 (2020): 575–80. http://dx.doi.org/10.5897/err2019.3817.

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3

Nowacki, Amy. "Chi-square and Fisher’s exact tests." Cleveland Clinic Journal of Medicine 84, no. 9 suppl 2 (2017): e20-e25. http://dx.doi.org/10.3949/ccjm.84.s2.04.

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4

Ermakov, M. S. "Asymptotic Minimaxity of Chi-Square Tests." Theory of Probability & Its Applications 42, no. 4 (1998): 589–610. http://dx.doi.org/10.1137/s0040585x97976441.

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5

Schober, Patrick, and Thomas R. Vetter. "Chi-square Tests in Medical Research." Anesthesia & Analgesia 129, no. 5 (2019): 1193. http://dx.doi.org/10.1213/ane.0000000000004410.

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6

MaCurdy, Thomas E., and Keunkwan Ryu. "Equivalence results in chi-square tests." Economics Letters 80, no. 3 (2003): 329–36. http://dx.doi.org/10.1016/s0165-1765(03)00124-1.

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7

Gagunashvili, N. D. "Chi-square tests for comparing weighted histograms." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 614, no. 2 (2010): 287–96. http://dx.doi.org/10.1016/j.nima.2009.12.037.

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8

Andrews, Donald W. K. "Chi-square diagnostic tests for econometric models." Journal of Econometrics 37, no. 1 (1988): 135–56. http://dx.doi.org/10.1016/0304-4076(88)90079-6.

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9

Greenwood, P., and M. S. Nikulin. "Application of tests of chi-square type." Journal of Soviet Mathematics 43, no. 6 (1988): 2776–91. http://dx.doi.org/10.1007/bf01129892.

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10

Robin, Jean-Marc, and Richard J. Smith. "TESTS OF RANK." Econometric Theory 16, no. 2 (2000): 151–75. http://dx.doi.org/10.1017/s0266466600162012.

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This paper considers tests for the rank of a matrix for which a root-T consistent estimator is available. However, in contrast to tests associated with the minimum chi-square and asymptotic least squares principles, the estimator's asymptotic variance matrix is not required to be either full or of known rank. Test statistics based on certain estimated characteristic roots are proposed whose limiting distributions are a weighted sum of independent chi-squared variables. These weights may be simply estimated, yielding convenient estimators for the limiting distributions of the proposed statistics. A sequential testing procedure is presented that yields a consistent estimator for the rank of a matrix. A simulation experiment is conducted comparing the characteristic root statistics advocated in this paper with statistics based on the Wald and asymptotic least squares principles.
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11

Andrews, Donald W. K. "Chi-Square Diagnostic Tests for Econometric Models: Theory." Econometrica 56, no. 6 (1988): 1419. http://dx.doi.org/10.2307/1913105.

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12

Oosterhoff, J. "THE CHOICE OF CELLS IN CHI–SQUARE TESTS." Statistica Neerlandica 39, no. 2 (1985): 115–28. http://dx.doi.org/10.1111/j.1467-9574.1985.tb01132.x.

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13

Lemeshko, B. Yu. "Chi-Square-Type Tests for Verification of Normality." Measurement Techniques 58, no. 6 (2015): 581–91. http://dx.doi.org/10.1007/s11018-015-0759-2.

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14

Wilson, Jeffrey R. "Chi-Square Tests for Overdispersion with Multiparameter Estimates." Applied Statistics 38, no. 3 (1989): 441. http://dx.doi.org/10.2307/2347732.

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15

S., Valarmathi, Hemapriya A.S, and Jasmine S. Sundar. "CHI-SQUARE TESTS: A QUICK GUIDE FOR HEALTH RESEARCHERS." International Journal of Advanced Research 12, no. 10 (2024): 1214–22. http://dx.doi.org/10.21474/ijar01/19746.

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Pearsons chi-square (Χ²) tests are essential nonparametric statistical tools for analyzing associations among categorical data, making them crucial for research involving non-numeric variables. These tests are widely utilized in various research fields due to their independence from normal distribution assumptions. Chi-square tests are utilized to assess whether there is a significant association between groups, populations, or criteria, and to examine how closely observed data distributions align with expected ones. The three primary types of chi-square tests are: the Goodness-of-Fit test, which checks if the distribution of categorical data in a sample conforms to a predefined distribution the Test of Independence, which investigates whether there is a relationship between categorical variables within a single sample and the Test of Homogeneity, which compares the frequency counts of a categorical variable across multiple populations to see if their distributions are similar.For valid and reliable results, it is crucial to consider factors such as random sampling, adequate cell counts, sufficient sample size, and mutually exclusive variables. In healthcare research, chi-square tests are essential for analyzing risk factors, evaluating AYUSH treatments, assessing nursing interventions, and studying health behavior trends. This review underscores their importance in statistical analysis and evidence-based decision-making.
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16

Gorsuch, Richard L., and Curtis Lehmann. "Chi-square and F Ratio: Which should be used when?" Journal of Methods and Measurement in the Social Sciences 8, no. 2 (2018): 58–71. http://dx.doi.org/10.2458/v8i2.22990.

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Approximations for Chi-square and F distributions can both be computed to provide a p-value, or probability of Type I error, to evaluate statistical significance. Although Chi-square has been used traditionally for tests of count data and nominal or categorical criterion variables (such as contingency tables) and F ratios for tests of non-nominal or continuous criterion variables (such as regression and analysis of variance), we demonstrate that either statistic can be applied in both situations. We used data simulation studies to examine when one statistic may be more accurate than the other for estimating Type I error rates across different types of analysis (count data/contingencies, dichotomous, and non-nominal) and across sample sizes (Ns) ranging from 20 to 160 (using 25,000 replications for simulating p-value derived from either Chi-squares or F-ratios). Our results showed that those derived from F ratios were generally closer to nominal Type I error rates than those derived from Chi-squares. The p-values derived from F ratios were more consistent for contingency table count data than those derived from Chi-squares. The smaller than 100 the N was, the more discrepant p-values derived from Chi-squares were from the nominal p-value. Only when the N was greater than 80 did the p-values from Chi-square tests become as accurate as those derived from F ratios in reproducing the nominal p-values. Thus, there was no evidence of any need for special treatment of dichotomous dependent variables. The most accurate and/or consistent p's were derived from F ratios. We conclude that Chi-square should be replaced generally with the F ratio as the statistic of choice and that the Chi-square test should only be taught as history.
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17

Iglesias, José A., Agapito Ledezma, Araceli Sanchis, and Gal A. Kaminka. "A plan classifier based on Chi-square distribution tests." Intelligent Data Analysis 15, no. 2 (2011): 131–49. http://dx.doi.org/10.3233/ida-2010-0460.

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18

Vuong, Quang H., and Weiren Wang. "Minimum chi-square estimation and tests for model selection." Journal of Econometrics 56, no. 1-2 (1993): 141–68. http://dx.doi.org/10.1016/0304-4076(93)90104-d.

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19

Makambi, Kepher. "Weighted inverse chi-square method for correlated significance tests." Journal of Applied Statistics 30, no. 2 (2003): 225–34. http://dx.doi.org/10.1080/0266476022000023767.

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20

Cressie, Noel, and F. C. Drost. "Asymptotics for Generalized Chi-Square Goodness-of-Fit Tests." Journal of the Royal Statistical Society. Series A (Statistics in Society) 152, no. 2 (1989): 258. http://dx.doi.org/10.2307/2982927.

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21

Dunkl, E., O. Ludwig, and R. Lotz. "Tables of Bonferroni-limits for Simultaneous Chi-square Tests." Biometrical Journal 32, no. 5 (2007): 555–74. http://dx.doi.org/10.1002/bimj.4710320507.

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22

Berry, Kenneth J., and Paul W. Mielke. "Monte Carlo comparisons of the asymptotic chi-square and likelihood-ratio tests with the nonasymptotic chi-square tests for sparse r × c tables." Psychological Bulletin 103, no. 2 (1988): 256–64. http://dx.doi.org/10.1037/0033-2909.103.2.256.

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23

García-Pérez, A. "Chi-Square Tests Under Models Close to the Normal Distribution." Metrika 63, no. 3 (2006): 343–54. http://dx.doi.org/10.1007/s00184-005-0024-9.

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24

Kim, Joo Han. "Chi-Square Goodness-of-Fit Tests for Randomly Censored Data." Annals of Statistics 21, no. 3 (1993): 1621–39. http://dx.doi.org/10.1214/aos/1176349275.

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25

Habib, M. G., and D. R. Thomas. "Chi-Square Goodness-if-Fit Tests for Randomly Censored Data." Annals of Statistics 14, no. 2 (1986): 759–65. http://dx.doi.org/10.1214/aos/1176349953.

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26

Voloshko, Valeriy A., and Egor V. Vecherko. "New upper bounds for noncentral chi-square cdf." Journal of the Belarusian State University. Mathematics and Informatics, no. 1 (March 31, 2020): 70–74. http://dx.doi.org/10.33581/2520-6508-2020-1-70-74.

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Some new upper bounds for noncentral chi-square cumulative density function are derived from the basic symmetries of the multidimensional standard Gaussian distribution: unitary invariance, components independence in both polar and Cartesian coordinate systems. The proposed new bounds have analytically simple form compared to analogues available in the literature: they are based on combination of exponents, direct and inverse trigonometric functions, including hyperbolic ones, and the cdf of the one dimensional standard Gaussian law. These new bounds may be useful both in theory and in applications: for proving inequalities related to noncentral chi-square cumulative density function, and for bounding powers of Pearson’s chi-squared tests.
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27

Berry, Kenneth J., and Paul W. Mielke. "Subroutines for Computing Exact CHI-Square and Fisher's Exact Probability Tests." Educational and Psychological Measurement 45, no. 1 (1985): 153–59. http://dx.doi.org/10.1177/0013164485451016.

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28

Quine, M. P., and J. Robinson. "Efficiencies of Chi-Square and Likelihood Ratio Goodness-of-Fit Tests." Annals of Statistics 13, no. 2 (1985): 727–42. http://dx.doi.org/10.1214/aos/1176349550.

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29

Rao, J. N. K., and A. J. Scott. "On Simple Adjustments to Chi-Square Tests with Sample Survey Data." Annals of Statistics 15, no. 1 (1987): 385–97. http://dx.doi.org/10.1214/aos/1176350273.

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30

Winterstein, Scott R. "Chi-Square Tests for Intrabrood Independence When Using the Mayfield Method." Journal of Wildlife Management 56, no. 2 (1992): 398. http://dx.doi.org/10.2307/3808842.

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31

Sutrick, Kenneth H. "Asymptotic power comparison of the chi-square and likelihood ratio tests." Annals of the Institute of Statistical Mathematics 38, no. 3 (1986): 503–11. http://dx.doi.org/10.1007/bf02482537.

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32

Boldin, M. V. "On Symmetrized Chi-Square Tests in Autoregression with Outliers in Data." Theory of Probability & Its Applications 68, no. 4 (2024): 559–69. http://dx.doi.org/10.1137/s0040585x97t991623.

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33

Berry, Mari, Brian Peacock, Bobbie Foote, and Lawrence Leemis. "Visual Assessment vs. Statistical Goodness of Fit Tests for Identifying Parent Population." Proceedings of the Human Factors Society Annual Meeting 32, no. 7 (1988): 460–64. http://dx.doi.org/10.1177/154193128803200701.

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Statistical tests are used to identify the parent distribution corresponding to a data set. A human observer looking at a histogram can also identify a probability distribution that models the parent distribution. The accuracy of a human observer was compared to the chi-square test for discrete data and the Kolmogorov-Smirnov and chi-square tests for continuous data. The human observer proved more accurate in identifying continuous distributions and the chi-square test proved to be superior in identifying discrete distributions. The effect of sample size and number of intervals in the histogram was included in the experimental design.
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34

Brown, Mark, and Marcia H. Flicker. "Chi-Square Goodness of Fit: A Failure Rate Perspective." Probability in the Engineering and Informational Sciences 5, no. 3 (1991): 273–84. http://dx.doi.org/10.1017/s0269964800002084.

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Employing a failure rate approach, we propose a test statistic, , for the classic goodness-of-fit problem. It is then shown that a variation of , obtained by replacing observed variances by expected variances (an unwise change in our point of view), leads to the classical test statistic, x2. We argue that should be better approximated by a chi-square distribution, and thus employing , the true p−values should be closer to the nominal p−values than under x2 Various other comparisons of the two tests are made.
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35

Gning, Gorgui, Aladji Babacar Niang, Modou Ngom, and Gane Lo. "Moments estimators and omnibus chi-square tests for some usual probability laws." Afrika Statistika 16, no. 4 (2021): 3061–94. http://dx.doi.org/10.16929/as/2021.3061.195.

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For many probability laws, in parametric models, the estimation of the parameters can be done in the frame of the maximum likelihood method, or in the frame of moment estimation methods, or by using the plug-in method, etc. Usually, for estimating more than one parameter, the same frame is used. We focus on the moment estimation method in this paper. We use the instrumental tool of the functional empirical process (fep) in Lo (2016) to show how it is practical to derive, almost algebraically, the joint distribution Gaussian law and to derive omnibus chi-square asymptotic laws from it. We choose four distributions to illustrate the method (Gamma law, beta law, Uniform law and Fisher law) and completely describe the asymptotic laws of the moment estimators whenever possible. Simulations studies are performed to investigate for each case the smallest sizes for which the obtained statistical tests are recommendable. Generally, the omnibus chi-square test proposed here work fine with sample sizes around fifty.
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36

Koehler, Kenneth J., and Jeffrey R. Wilson. "Chi–square tests for comparing vectors of proportions for several cluster samples." Communications in Statistics - Theory and Methods 15, no. 10 (1986): 2977–90. http://dx.doi.org/10.1080/03610928608829290.

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37

Gagunashvili, N. D. "Chi-square goodness of fit tests for weighted histograms. Review and improvements." Journal of Instrumentation 10, no. 05 (2015): P05004. http://dx.doi.org/10.1088/1748-0221/10/05/p05004.

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38

Zhang, Qingbua, and Michèle Basseville. "Advanced numerical computation of chi-square tests for fault detection and isolation." IFAC Proceedings Volumes 36, no. 5 (2003): 209–14. http://dx.doi.org/10.1016/s1474-6670(17)36495-9.

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39

Dow, Malcolm M. "Saving the Theory: On Chi-Square Tests With Cross-Cultural Survey Data." Cross-Cultural Research 27, no. 3-4 (1993): 247–76. http://dx.doi.org/10.1177/106939719302700305.

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40

Quessy, Jean-François, Louis-Paul Rivest, and Marie-Hélène Toupin. "Goodness-of-fit tests for the family of multivariate chi-square copulas." Computational Statistics & Data Analysis 140 (December 2019): 21–40. http://dx.doi.org/10.1016/j.csda.2019.04.008.

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41

Amemiya, Yasuo, and T. W. Anderson. "Asymptotic Chi-Square Tests for a Large Class of Factor Analysis Models." Annals of Statistics 18, no. 3 (1990): 1453–63. http://dx.doi.org/10.1214/aos/1176347760.

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42

Wright, Bryan E. "Use of chi-square tests to analyze scat-derived diet composition data." Marine Mammal Science 26, no. 2 (2010): 395–401. http://dx.doi.org/10.1111/j.1748-7692.2009.00308.x.

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43

Markowski, Edward P., and Carol A. Markowski. "A Systematic Method for Teaching Post Hoc Analysis of Chi-Square Tests." Decision Sciences Journal of Innovative Education 7, no. 1 (2009): 59–65. http://dx.doi.org/10.1111/j.1540-4609.2008.00202.x.

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44

Hosmane, B. S. "Improved likelihood ratio tests and pearson chi-square tests for independence in two dimensional contingency tables." Communications in Statistics - Theory and Methods 15, no. 6 (1986): 1875–88. http://dx.doi.org/10.1080/03610928608829224.

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45

York, Kenneth M. "Disparate Results in Adverse Impact Tests: The 4/5ths Rule and the Chi Square Test." Public Personnel Management 31, no. 2 (2002): 253–62. http://dx.doi.org/10.1177/009102600203100210.

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The Uniform Guidelines on Employee Selection Procedures suggests the “4/5ths rule” for testing the outcome of selection procedures for adverse impact. The appropriate statistical test is a Chi Square testing for a significant difference between the selection ratios of the minority and majority applicants. However, the 4/5ths rule and Chi Square test do not agree 10–40% of the time depending on sample size, making it difficult for personnel managers to monitor their organization's Equal Employment Opportunity compliance. The extent of disagreement between the two tests is described, and recommendations are given for how personnel managers should use the 4/5ths rule and the Chi Square test to determine whether a selection procedure has adverse impact.
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46

Jolliffe, Ian T., and Cristina Primo. "Evaluating Rank Histograms Using Decompositions of the Chi-Square Test Statistic." Monthly Weather Review 136, no. 6 (2008): 2133–39. http://dx.doi.org/10.1175/2007mwr2219.1.

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Abstract Rank histograms are often plotted to evaluate the forecasts produced by an ensemble forecasting system—an ideal rank histogram is “flat” or uniform. It has been noted previously that the obvious test of “flatness,” the well-known χ2 goodness-of-fit test, spreads its power thinly and hence is not good at detecting specific alternatives to flatness, such as bias or over- or underdispersion. Members of the Cramér–von Mises family of tests do much better in this respect. An alternative to using the Cramér–von Mises family is to decompose the χ2 test statistic into components that correspond to specific alternatives. This approach is described in the present paper. It is arguably easier to use and more flexible than the Cramér–von Mises family of tests, and does at least as well as it in detecting alternatives corresponding to bias and over- or underdispersion.
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47

Yuan, Ke-Hai, and Wai Chan. "Measurement invariance via multigroup SEM: Issues and solutions with chi-square-difference tests." Psychological Methods 21, no. 3 (2016): 405–26. http://dx.doi.org/10.1037/met0000080.

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48

Mirvaliev, M. "Chi-Square Goodness-of-Fit Tests for a Family of Multidimensional Discrete Distributions." Theory of Probability & Its Applications 34, no. 4 (1990): 728–32. http://dx.doi.org/10.1137/1134094.

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49

Suh, Youngsuk, and Sun-Joo Cho. "Chi-Square Difference Tests for Detecting Differential Functioning in a Multidimensional IRT Model." Applied Psychological Measurement 38, no. 5 (2014): 359–75. http://dx.doi.org/10.1177/0146621614523116.

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50

Akshay Raj, I., and C. Saraswathy. "A Study on Paternalistic Leadership Style and its Implication on Workplace Relationship." ComFin Research 12, S1-May (2024): 7–13. http://dx.doi.org/10.34293/commerce.v12is1-may.7800.

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This study looks into how relationships at work are affected by a paternalistic leadership style. A thorough examination using regression, correlation, and chi-square tests yields a number of important conclusions. First, it has been illustrated that paternalistic authority significantly advances positive working environment connections by factually noteworthy Pearson chi-square, probability proportion chi-square, and linear-by-linear affiliation chi-square tests. Furthermore, a Spearman’s rho coefficient of 0.538 and a p-value underneath 0.001 bolster the momentous positive affiliation between judgments of supervisors’ paternalistic authority properties and the certainty in its positive impact on collaborative adequacy. The regression analysis’s findings clarified the residuals and expected values, displaying accurate forecasts and an average of 3.81 for the mean predicted value. These results highlight the value of paternalistic leadership in creating a favourable work environment and indicate that it is still applicable in project-based organizational contexts.
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