Partitioning for Enhanced Statistical Power and Noise Reduction: Comparing One-Way and Repeated Measures Analysis of Variance (ANOVA)
Using simulated data with duplicate observational data points, this research aims to highlight the notable efficiency of repeated measures analysis of variance (ANOVA) compared to one-way ANOVA as a more powerful statistical model. One of the principal advantages of repeated measures ANOVA is its de...
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| Vydáno v: | Curēus (Palo Alto, CA) Ročník 16; číslo 12; s. e75322 |
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| Jazyk: | angličtina |
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Springer Nature B.V
08.12.2024
Cureus |
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| ISSN: | 2168-8184, 2168-8184 |
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| Abstract | Using simulated data with duplicate observational data points, this research aims to highlight the notable efficiency of repeated measures analysis of variance (ANOVA) compared to one-way ANOVA as a more powerful statistical model. One of the principal advantages of repeated measures ANOVA is its design, in which each subject acts as their own control. This methodology allows for the statistical mitigation of individual differences among subjects, thereby reducing extraneous variability (noise) that can obscure the effects of the experimental conditions under investigation. By employing identical simulated column values within this analysis, we observe that the F-statistic generated by the repeated measures ANOVA tends to be larger than that derived from the one-way ANOVA. A distinguishing feature of repeated measures ANOVA is its incorporation of an additional dimension of within-subject variation in its partitioning procedure. This acknowledges that measurements taken from the same subject are inherently correlated. This correlation introduces a separate source of partitioned variation, distinct from that attributable to between-subject differences. The term SS
encapsulates the residual variation that remains after accounting for both group differences and individual subject discrepancies. By explicitly recognizing the interrelatedness of measurements collected from the same subjects, repeated measures ANOVA effectively reduces the residual error variation contributing to the denominator in calculating the F-statistic. This reduction in error variation (noise) results in a more sensitive statistical test than one-way ANOVA, thus enhancing the power of the analysis. Consequently, the ability of repeated measures ANOVA to account for the correlated nature of repeated observations not only yields a more robust estimation of the treatment effects but also fortifies the statistical conclusions drawn from the data. |
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| AbstractList | Using simulated data with duplicate observational data points, this research aims to highlight the notable efficiency of repeated measures analysis of variance (ANOVA) compared to one-way ANOVA as a more powerful statistical model. One of the principal advantages of repeated measures ANOVA is its design, in which each subject acts as their own control. This methodology allows for the statistical mitigation of individual differences among subjects, thereby reducing extraneous variability (noise) that can obscure the effects of the experimental conditions under investigation. By employing identical simulated column values within this analysis, we observe that the F-statistic generated by the repeated measures ANOVA tends to be larger than that derived from the one-way ANOVA. A distinguishing feature of repeated measures ANOVA is its incorporation of an additional dimension of within-subject variation in its partitioning procedure. This acknowledges that measurements taken from the same subject are inherently correlated. This correlation introduces a separate source of partitioned variation, distinct from that attributable to between-subject differences. The term SS
encapsulates the residual variation that remains after accounting for both group differences and individual subject discrepancies. By explicitly recognizing the interrelatedness of measurements collected from the same subjects, repeated measures ANOVA effectively reduces the residual error variation contributing to the denominator in calculating the F-statistic. This reduction in error variation (noise) results in a more sensitive statistical test than one-way ANOVA, thus enhancing the power of the analysis. Consequently, the ability of repeated measures ANOVA to account for the correlated nature of repeated observations not only yields a more robust estimation of the treatment effects but also fortifies the statistical conclusions drawn from the data. Using simulated data with duplicate observational data points, this research aims to highlight the notable efficiency of repeated measures analysis of variance (ANOVA) compared to one-way ANOVA as a more powerful statistical model. One of the principal advantages of repeated measures ANOVA is its design, in which each subject acts as their own control. This methodology allows for the statistical mitigation of individual differences among subjects, thereby reducing extraneous variability (noise) that can obscure the effects of the experimental conditions under investigation. By employing identical simulated column values within this analysis, we observe that the F-statistic generated by the repeated measures ANOVA tends to be larger than that derived from the one-way ANOVA. A distinguishing feature of repeated measures ANOVA is its incorporation of an additional dimension of within-subject variation in its partitioning procedure. This acknowledges that measurements taken from the same subject are inherently correlated. This correlation introduces a separate source of partitioned variation, distinct from that attributable to between-subject differences. The term SSBetween x Within encapsulates the residual variation that remains after accounting for both group differences and individual subject discrepancies. By explicitly recognizing the interrelatedness of measurements collected from the same subjects, repeated measures ANOVA effectively reduces the residual error variation contributing to the denominator in calculating the F-statistic. This reduction in error variation (noise) results in a more sensitive statistical test than one-way ANOVA, thus enhancing the power of the analysis. Consequently, the ability of repeated measures ANOVA to account for the correlated nature of repeated observations not only yields a more robust estimation of the treatment effects but also fortifies the statistical conclusions drawn from the data.Using simulated data with duplicate observational data points, this research aims to highlight the notable efficiency of repeated measures analysis of variance (ANOVA) compared to one-way ANOVA as a more powerful statistical model. One of the principal advantages of repeated measures ANOVA is its design, in which each subject acts as their own control. This methodology allows for the statistical mitigation of individual differences among subjects, thereby reducing extraneous variability (noise) that can obscure the effects of the experimental conditions under investigation. By employing identical simulated column values within this analysis, we observe that the F-statistic generated by the repeated measures ANOVA tends to be larger than that derived from the one-way ANOVA. A distinguishing feature of repeated measures ANOVA is its incorporation of an additional dimension of within-subject variation in its partitioning procedure. This acknowledges that measurements taken from the same subject are inherently correlated. This correlation introduces a separate source of partitioned variation, distinct from that attributable to between-subject differences. The term SSBetween x Within encapsulates the residual variation that remains after accounting for both group differences and individual subject discrepancies. By explicitly recognizing the interrelatedness of measurements collected from the same subjects, repeated measures ANOVA effectively reduces the residual error variation contributing to the denominator in calculating the F-statistic. This reduction in error variation (noise) results in a more sensitive statistical test than one-way ANOVA, thus enhancing the power of the analysis. Consequently, the ability of repeated measures ANOVA to account for the correlated nature of repeated observations not only yields a more robust estimation of the treatment effects but also fortifies the statistical conclusions drawn from the data. Using simulated data with duplicate observational data points, this research aims to highlight the notable efficiency of repeated measures analysis of variance (ANOVA) compared to one-way ANOVA as a more powerful statistical model. One of the principal advantages of repeated measures ANOVA is its design, in which each subject acts as their own control. This methodology allows for the statistical mitigation of individual differences among subjects, thereby reducing extraneous variability (noise) that can obscure the effects of the experimental conditions under investigation. By employing identical simulated column values within this analysis, we observe that the F-statistic generated by the repeated measures ANOVA tends to be larger than that derived from the one-way ANOVA. A distinguishing feature of repeated measures ANOVA is its incorporation of an additional dimension of within-subject variation in its partitioning procedure. This acknowledges that measurements taken from the same subject are inherently correlated. This correlation introduces a separate source of partitioned variation, distinct from that attributable to between-subject differences. The term SSBetween x Within encapsulates the residual variation that remains after accounting for both group differences and individual subject discrepancies. By explicitly recognizing the interrelatedness of measurements collected from the same subjects, repeated measures ANOVA effectively reduces the residual error variation contributing to the denominator in calculating the F-statistic. This reduction in error variation (noise) results in a more sensitive statistical test than one-way ANOVA, thus enhancing the power of the analysis. Consequently, the ability of repeated measures ANOVA to account for the correlated nature of repeated observations not only yields a more robust estimation of the treatment effects but also fortifies the statistical conclusions drawn from the data. Within-groups sums of squares (SSW) represent the variation within each group due to individual differences or random error, analogous to the Standard Error of the Difference in the two independent sample t-test and paired t-test [5,7]. [...]this reduction in error variation (noise) leads to a more sensitive statistical test compared to one-way ANOVA, thereby enhancing the power of the analysis. Data collection This study compares two distinct statistical methodologies, one-way ANOVA and repeated measures ANOVA, by evaluating their performance using simulated datasets derived from identical observational data points. Through this comparative analysis, the present study seeks to elucidate the statistical power advantages inherent in repeated measures ANOVA, characterized by a larger F-statistic, with identical observational data points, as opposed to one-way ANOVA. |
| Author | Strale, Frederick |
| AuthorAffiliation | 1 Biostatistics, The Oxford Center, Brighton, USA |
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| Cites_doi | 10.1037/h0076767 10.1037/0033-2909.87.1.166 10.1037/0033-2909.83.2.314 10.4097/kjae.2017.70.1.22 10.5395/rde.2015.40.1.91 10.1007/978-1-4614-3725-3_8 10.1037/h0036937 10.1037/h0045186 10.1111/j.2044-8317.1979.tb00591.x 10.1348/000711001159357 10.1007/978-1-4419-0052-4_7 10.3343/kjlm.2009.29.1.1 |
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| Copyright | Copyright © 2024, Strale et al. Copyright © 2024, Strale et al. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. Copyright © 2024, Strale et al. 2024 Strale et al. |
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| Keywords | repeated measures analysis of variance (anova) one way analysis of variance (anova) f-statistic repeated-measures design partitioning sums of squares statistical power clinical trials experimental trials |
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| References | Kim HY (ref4) 2015; 40 Keppel G (ref5) 1990 Cohen J (ref8) 1962; 65 Ross A (ref14) 2017 Kim TK (ref13) 2017; 70 ref2 ref1 Rucci AJ (ref10) 1980; 87 Huck SW (ref18) 1975; 82 Keselman HJ (ref20) 2001; 54 Dwyer JH (ref9) 1974; 81 Park E (ref17) 2009; 29 ref3 Greenwald AG (ref6) 1976; 83 Heiberger R (ref15) 2009 Quirk T (ref16) 2012 Lovie A (ref7) 1979; 32 Stevens JP (ref11) 2009 Lix L (ref12) 2018 Girden E (ref19) 1992 |
| References_xml | – ident: ref1 – year: 2017 ident: ref14 article-title: Basic and Advanced Statistical Tests: Writing Results Sections and Creating Tables and Figures – volume: 82 year: 1975 ident: ref18 article-title: Using a repeated measures ANOVA to analyze the data from a pretest-posttest design: A potentially confusing task publication-title: Psychol. Bull doi: 10.1037/h0076767 – ident: ref2 – ident: ref3 – volume: 87 year: 1980 ident: ref10 article-title: Analysis of variance and the "second discipline" of scientific psychology: A historical account publication-title: Psychol Bull doi: 10.1037/0033-2909.87.1.166 – year: 2009 ident: ref11 article-title: Applied Multivariate Statistics for the Social Sciences. 5th Edition – year: 2018 ident: ref12 article-title: Analysis of variance: Repeated-measures designs – volume: 83 year: 1976 ident: ref6 article-title: Within-subjects designs: To use or not to use? publication-title: Psychol Bull doi: 10.1037/0033-2909.83.2.314 – volume: 70 year: 2017 ident: ref13 article-title: Understanding one-way ANOVA using conceptual figures publication-title: Korean J Anesthesiol doi: 10.4097/kjae.2017.70.1.22 – year: 1992 ident: ref19 – volume: 40 year: 2015 ident: ref4 article-title: Statistical notes for clinical researchers: A one-way repeated measures ANOVA for data with repeated observations publication-title: Restor Dent Endod doi: 10.5395/rde.2015.40.1.91 – year: 2012 ident: ref16 article-title: One-way analysis of variance (ANOVA) doi: 10.1007/978-1-4614-3725-3_8 – volume: 81 year: 1974 ident: ref9 article-title: Analysis of variance and the magnitude of effects: A general approach publication-title: Psychol Bull doi: 10.1037/h0036937 – volume: 65 year: 1962 ident: ref8 article-title: The statistical power of abnormal-social psychological research: A review publication-title: J Abnorm Soc Psychol doi: 10.1037/h0045186 – year: 1990 ident: ref5 article-title: Data Analysis for Research Designs: Analysis of Variance and Multiple Regression/Correlation Approaches – volume: 32 year: 1979 ident: ref7 article-title: The analysis of variance in experimental psychology: 1934-1945 publication-title: Br J Math Stat Psychol doi: 10.1111/j.2044-8317.1979.tb00591.x – volume: 54 year: 2001 ident: ref20 article-title: The analysis of repeated measures designs: A review publication-title: Br J Math Stat Psychol doi: 10.1348/000711001159357 – year: 2009 ident: ref15 article-title: One-way anova doi: 10.1007/978-1-4419-0052-4_7 – volume: 29 year: 2009 ident: ref17 article-title: Correct use of repeated measures analysis of variance publication-title: Korean J Lab Med doi: 10.3343/kjlm.2009.29.1.1 |
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| Title | Partitioning for Enhanced Statistical Power and Noise Reduction: Comparing One-Way and Repeated Measures Analysis of Variance (ANOVA) |
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