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The results of a NASA investigation of a claimed Overlap between two gust response analysis methods: the Statistical Discrete Gust (SDG) Method and the Power Spectral Density (PSD) Method are presented. The claim is that the ratio of an SDG response to the corresponding PSD response is 10.4. Analytical results presented for several different airplanes at several different flight conditions indicate that such an Overlap does appear to exist. However, the claim was not met precisely: a scatter of up to about 10 percent about the 10.4 factor can be expected.

Present methods of analysis of the structural response and the structure-borne transmission of vibrational energy use either finite element (FE) techniques or statistical energy analysis (SEA) methods. The FE methods are a very useful tool at low frequencies where the number of resonances involved in the analysis is rather small. On the other hand SEA methods can predict with acceptable accuracy the response and energy transmission between coupled structures at relatively high frequencies where the structural modal density is high and a statistical approach is the appropriate solution. In the mid-frequency range, a relatively large number of resonances exist which make finite element method too costly. On the other hand SEA methods can only predict an average level form. In this mid-frequency range a possible alternative is to use power flow techniques, where the input and flow of vibrational energy to excited and coupled structural components can be expressed in terms of input and transfer mobilities. This power flow technique can be extended from low to high frequencies and this can be integrated with established FE models at low frequencies and SEA models at high frequencies to form a verification of the method. This method of structural analysis using power flo and mobility methods, and its integration with SEA and FE analysis is applied to the case of two thin beams joined together at right angles.

This paper begins with a general discussion of statistical significance, effect size, and power analysis; and concludes by extending the discussion to the multivariate case (MANOVA). Historically, traditional statistical significance testing has guided researchers' thinking about the meaningfulness of their data. The use of significance testing alone in making these decisions has proved problematic. It is likely that less reliance on statistical significance testing, and an increased use of power analysis and effect size estimates in combination could contribute to an overall improvement in the quality of new research produced. The more informed researchers are about the benefits and limitations of statistical significance, effect size, and power analysis, the more likely it is that they will be able to make more sophisticated and useful interpretations about the meaningfulness of research results. One table illustrates the discussion. (Contains 37 references.) (SLD)

Statistical power in music education was examined by taking an in-depth look at quantitative articles published in the "Journal of Research in Music Education" between 1987 and 1991, inclusive. Of the 109 articles of the period, 78 were quantitative, with both parametric and nonparametric procedures considered. Sample sizes were those reported by the authors. Effect sizes were estimated according to the guidelines developed by J. Cohen (1988), and his power analysis tables were used. The overall median power for the articles was 0.13 for detecting small effects, 0.64 for detecting medium effects, and 0.97 for detecting large effects. Implications of these findings, limitations of the study, and suggestions for future music-education research are discussed. In general, more attention should be placed on a priori power analyses of research designs. Adequate sample sizes should be chosen and a greater understanding and application of the concept of effect size is needed in music education research. Six tables are included. (Contains 18 references.) (SLD)

Statistical power in music education was examined by taking an in-depth look at quantitative articles published in the "Journal of Research in Music Education" between 1987 and 1991, inclusive. Of the 109 articles of the period, 78 were quantitative, with both parametric and nonparametric procedures considered. Sample sizes were those reported by the authors. Effect sizes were estimated according to the guidelines developed by J. Cohen (1988), and his power analysis tables were used. The overall median power for the articles was 0.13 for detecting small effects, 0.64 for detecting medium effects, and 0.97 for detecting large effects. Implications of these findings, limitations of the study, and suggestions for future music-education research are discussed. In general, more attention should be placed on a priori power analyses of research designs. Adequate sample sizes should be chosen and a greater understanding and application of the concept of effect size is needed in music education research. Six tables are included. (Contains 18 references.) (SLD)

Electric vehicles (EVs) and particularly plug-in hybrid electric vehicles (PHEVs) are foreseen to become popular in the near future. Not only are they much more environmentally friendly than conventional internal combustion engine (ICE) vehicles, their fuel can also be catered from diverse energy sources and resources. However, they add significant load on the power grid as they become widespread. The characteristics of this extra load follow the patterns of people's driving behaviours. In particular, random parameters such as arrival time and driven distance of the vehicles determine their expected demand profile from the power grid. In this paper, we first present a model for uncoordinated charging power demand of PHEVs based on a stochastic process and accordingly we characterize the EV's expected daily power demand profile. Next, we adopt different distributions for the EV's charging time following some available empirical research data in the literature. Simulation results show that the EV's expected daily power demand profiles obtained under the uniform, Gaussian with positive support and Rician distributions for charging time are identical when the first and second order statistics of these distributions are the same. This gives us useful insights into the long-term planning for upgrading power systems' infrastructure to accommodate PHEVs. In addition, the results from this modelling can be incorporated into designing demand response (DR) algorithms and evaluating the available DR techniques more accurately.

Recently Kim (2016) published a meta-analysis on the effects of enrichment programs for gifted students. She found that these programs produced substantial effects for academic achievement (g = 0.96) and socioemotional outcomes (g = 0.55). However, given current theory and empirical research these estimates of the benefits of enrichment programs are unrealistically high. In this manuscript I make the argument that Kim's results--and those from a previous meta-analysis on the same topic (Vaughn, Feldhusen, & Asher, 1991)--are likely distorted by publication bias. Using statistical power analysis, Schimmack's (2012) incredibility index, and an examination of the correlation between sample size and effect size, I present circumstantial evidence that publication bias is distorting the enrichment literature. As a result, gifted education scholars and practitioners do not really know the effectiveness of enrichment programs. I conclude the manuscript by discussing how to reduce publication bias in the gifted education literature.

Recently Kim (2016) published a meta-analysis on the effects of enrichment programs for gifted students. She found that these programs produced substantial effects for academic achievement (g = 0.96) and socioemotional outcomes (g = 0.55). However, given current theory and empirical research these estimates of the benefits of enrichment programs are unrealistically high. In this manuscript I make the argument that Kim's results--and those from a previous meta-analysis on the same topic (Vaughn, Feldhusen, & Asher, 1991)--are likely distorted by publication bias. Using statistical power analysis, Schimmack's (2012) incredibility index, and an examination of the correlation between sample size and effect size, I present circumstantial evidence that publication bias is distorting the enrichment literature. As a result, gifted education scholars and practitioners do not really know the effectiveness of enrichment programs. I conclude the manuscript by discussing how to reduce publication bias in the gifted education literature.

Structural equation modeling (SEM) has been deemed as a proper method when variables contain measurement errors. In contrast, path analysis with composite-scores is preferred for prediction and diagnosis of individuals. While path analysis with composite-scores has been criticized for yielding biased parameter estimates, recent literature pointed out that the population values of parameters in a latent-variable model depend on artificially assigned scales. Consequently, bias in parameter estimates is not a well-grounded concept for models involving latent constructs. This article compares path analysis with composite-scores against SEM with respect to effect size and statistical power in testing the significance of the path coefficients, via the z- or t-statistics. The data come from many sources with various models that are substantively determined. Results show that SEM is not as powerful as path analysis even with equally-weighted-composites. But path analysis with Bartlett-factor- scores and the partial-least-squares approach to SEM perform the best with respect to effect size and power. [This paper will be published in "Behavior Research Methods." Discrepancy between the title of the article and authored paper.]

Structural equation modeling (SEM) has been deemed as a proper method when variables contain measurement errors. In contrast, path analysis with composite-scores is preferred for prediction and diagnosis of individuals. While path analysis with composite-scores has been criticized for yielding biased parameter estimates, recent literature pointed out that the population values of parameters in a latent-variable model depend on artificially assigned scales. Consequently, bias in parameter estimates is not a well-grounded concept for models involving latent constructs. This article compares path analysis with composite-scores against SEM with respect to effect size and statistical power in testing the significance of the path coefficients, via the z- or t-statistics. The data come from many sources with various models that are substantively determined. Results show that SEM is not as powerful as path analysis even with equally-weighted-composites. But path analysis with Bartlett-factor- scores and the partial-least-squares approach to SEM perform the best with respect to effect size and power. [This paper will be published in "Behavior Research Methods." Discrepancy between the title of the article and authored paper.]

NSMI, scientific leader T.S.C Togayev Islomjon Bekpo’lat o’gli, & Tovbaev Akram Nurmonovich. (2020). Statistical analysis of power waste on 6-10 KV air power transmission lines. International Journal on Orange Technologies, 2(10), 92-94. https://doi.org/10.31149/ijot.v2i10.735 Pdf Url : https://journals.researchparks.org/index.php/IJOT/article/view/735/707 Paper Url : https://journals.researchparks.org/index.php/IJOT/article/view/735

NSMI, scientific leader T.S.C Togayev Islomjon Bekpo’lat o’gli, & Tovbaev Akram Nurmonovich. (2020). Statistical analysis of power waste on 6-10 KV air power transmission lines. International Journal on Orange Technologies, 2(10), 92-94. https://doi.org/10.31149/ijot.v2i10.735 Pdf Url : https://journals.researchparks.org/index.php/IJOT/article/view/735/707 Paper Url : https://journals.researchparks.org/index.php/IJOT/article/view/735

NSMI, scientific leader T.S.C Togayev Islomjon Bekpo’lat o’gli, & Tovbaev Akram Nurmonovich. (2020). Statistical analysis of power waste on 6-10 KV air power transmission lines. International Journal on Orange Technologies, 2(10), 92-94. https://doi.org/10.31149/ijot.v2i10.735 Pdf Url : https://journals.researchparks.org/index.php/IJOT/article/view/735/707 Paper Url : https://journals.researchparks.org/index.php/IJOT/article/view/735

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Perma.cc archive of https://meera.snre.umich.edu/power-analysis-statistical-significance-effect-size created on 2022-02-26 01:28:16.634287+00:00.

Perma.cc archive of https://meera.snre.umich.edu/power-analysis-statistical-significance-effect-size created on 2022-02-26 01:28:16.634287+00:00.

The importance of conducting a statistical power analysis at the beginning of a study is universally accepted. Without careful planning, a study can easily fail to detect an existing effect by chance. This book teaches how to conduct power analysis for a range of models from correlation and t-test to structural equation models and multilevel models. Both a graphical Web software WebPower and an R package are introduced to practically conduct the analysis.

An analytic procedure, efficiency analysis, is proposed for improving the utility of quantitative program evaluation for decision making. The three features of the procedure are explained: (1) for statistical control, it adopts and extends the regression-discontinuity design; (2) for statistical inferences, it de-emphasizes hypothesis testing in favor of interval estimation; and (3) it uses the limits of the confidence interval to qualify the level at which a program operates, rather than making a simple statement about goal attainment. Application of this procedure is illustrated with data obtained at grades 2, 3, 7, and 8 for a remedial mathematics program. Methods are suggested for making these evaluation results accessible and practical for educational decisionmakers through graphic presentations and by linking evaluation outcomes to particular administrative objectives, specific planning procedures, and a set of corrective and/or supportive program activities. (Author/GDC)

The statistical expectation values of the temperature fluctuations of the Cosmic Microwave Background (CMB) are assumed to be preserved under rotations of the sky. We investigate the Statistical Isotropy (SI) of the CMB anisotropy maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP) using Bipolar Power Spectrum (BiPS) proposed in [Hajian & Souradeep 2003]. The method can probe specific regions in multipole space using appropriate window functions. The BiPS is estimated for full sky CMB anisotropy maps based on the first year WMAP data using a range of window functions. The BiPS spectra computed for both full sky maps for all our window functions are consistent with zero, roughly within $2 \sigma$. The null BiPS results may be interpreted as an absence of strong violation of statistical isotropy in the first-year WMAP data on angular scales larger than that corresponding to $l\sim60$. However, pending a careful direct comparison, our results do not necessarily conflict with the specific SI related anomalies reported using other statistical tests.

This paper provides a guide to calculating statistical power for the complex multilevel designs that are used in most field studies in education research. For multilevel evaluation studies in the field of education, it is important to account for the impact of clustering on the standard errors of estimates of treatment effects. Using ideas from survey research, the paper explains how sample design induces random variation in the quantities observed in a randomized experiment, and how this random variation relates to statistical power. The manner in which statistical power depends upon the values of intraclass correlations, sample sizes at the various levels, the standardized average treatment effect (effect size), the multiple correlation between covariates and the outcome at different levels, and the heterogeneity of treatment effects across sampling units is illustrated. Both hierarchical and randomized block designs are considered. The paper demonstrates that statistical power in complex designs involving clustered sampling can be computed simply from standard power tables using the idea of operational effect sizes: effect sizes multiplied by a design effect that depends on features of the complex experimental design. These concepts are applied to provide methods for computing power for each of the research designs most frequently used in education research. Appendices include: (1) Design Effects in Two- or Three-Level Hierarchical Designs With and Without Covariates; (2) Design Effects in Two- or Three-Level Randomized-Block Designs With and Without Covariates; (3) Computing Power in Three-Level Randomized-Block Designs; (4) Multilevel Models Defining Tests for Treatment Effects; and (5) Glossary of Terms. (Contains 5 footnotes and 2 tables.)

We describe a fast and accurate method for estimation of the cosmic microwave background (CMB) anisotropy angular power spectrum --- Monte Carlo Apodised Spherical Transform EstimatoR. Originally devised for use in the interpretation of the Boomerang experimental data, MASTER is both a computationally efficient method suitable for use with the currently available CMB data sets (already large in size, despite covering small fractions of the sky, and affected by inhomogeneous and correlated noise), and a very promising application for the analysis of very large future CMB satellite mission products.

We describe a fast and accurate method for estimation of the cosmic microwave background (CMB) anisotropy angular power spectrum --- Monte Carlo Apodised Spherical Transform EstimatoR. Originally devised for use in the interpretation of the Boomerang experimental data, MASTER is both a computationally efficient method suitable for use with the currently available CMB data sets (already large in size, despite covering small fractions of the sky, and affected by inhomogeneous and correlated noise), and a very promising application for the analysis of very large future CMB satellite mission products.

Language policy is crucial to any society's cultural and political fabric, as it shapes how individuals and groups communicate, interact, and identify. Language policy has important implications for nation-building and the creation of national identity. Language policy can also significantly impact university students' sense of belonging. Overt and inclusive policies can provide opportunities for students to develop language skills and cultural competencies, enhancing their academic and professional opportunities. Covert and implicit policies can create barriers to interaction between different language groups, leading to social fragmentation, exclusion, and discrimination. Overt language policies are those that are openly acknowledged and implemented, while covert policies are those that are more subtle and may be hidden. Overt language policies that promote a single national language can unite diverse groups within a nation. However, these policies can also lead to the suppression of linguistic and cultural diversity within a nation, potentially undermining the cultural richness of that society. Covert language policies can also have significant impacts on identity and national unity. For example, language policies not openly acknowledged can lead to confusion or mistrust among different language groups. These policies can reinforce power imbalances between language groups, perpetuating existing inequalities. Considering these concepts, this study aimed to answer the following questions: (1) What LP has been implemented in Kyrgyzstan? (2) How has LP affected university students? Information on the language policy implemented in Kyrgyzstan was necessary to answer the first question, which involved examining laws, banknotes, newspaper titles, and dissertation catalogs. It was necessary to gather data on how the language policy has affected the students to answer the second question. In addition, in-depth interviews with LP experts helped clarify both questions. The collected information was analyzed using textual analysis and statistical methods. Data analysis showed that different models of language policy were implemented in Kyrgyzstan, including multilingualism, bilingualism, and monolingualism. Overt, covert, and vague LP were used to promote these models. These models and methods have formed segregated communities, language discrimination, and different linguistic identities within the same ethnic groups.

The design and testing of a free-space optical communication system requires assessment of the impact of random fluctuations in received power from a laser beam transmitted over an atmospheric channel. A number of methods for generating fading power vectors for in-lab emulation of an atmospheric channel have previously been reported. These techniques include spectral shaping and filtering of a signal from a normally distributed pseudo-random number generator, full wave optics simulations with random phase screens, and pre-recorded measurements from experimental free-space links. In this work, a statistical analysis of atmospheric fading is presented with the goal of producing a practical engineering model for the fading channel suitable for generating synthetic fade vectors in real-time for long-duration receiver testing with channel interleaving. Specifically, a parametric model is developed for turbulence-induced fade on space-to-ground links with large-aperture receivers, including aperture-averaging and the effects of aperture size on the instantaneous coupling efficiency for mode-limited receivers. In particular, we analyze the probability density function and temporal power spectrum for fluctuations of the coupling efficiency for few-mode fibers in a range of turbulence conditions.

A statistical power analysis of research studies in special education reported in volumes 39 and 40 of Exceptional Children (1972-73 and 1973-74) was conducted. The basic concepts of a power analysis (Type I and Type II errors, and conventional effect sizes) were reviewed, and the studies evaluated for statistical power. Using the .05 level of significance, the average power to detect small effects was .11 (5% having a better than 50-50 chance to declare significant findings), for medium effects the average power was .49 (43% having a better than 50-50 chance), and for large effects the average power was .82 (76% having a better than 50-50 chance). There are several approaches to increasing power, including increasing the number of Ss, increasing the level of alpha, altering the research design, using directional tests, and using highly reliable measures. Statistical power analysis should become a part of research training and one of the criteria for the evaluation of research reports. (Author/IM)

A statistical power analysis of research studies in special education reported in volumes 39 and 40 of Exceptional Children (1972-73 and 1973-74) was conducted. The basic concepts of a power analysis (Type I and Type II errors, and conventional effect sizes) were reviewed, and the studies evaluated for statistical power. Using the .05 level of significance, the average power to detect small effects was .11 (5% having a better than 50-50 chance to declare significant findings), for medium effects the average power was .49 (43% having a better than 50-50 chance), and for large effects the average power was .82 (76% having a better than 50-50 chance). There are several approaches to increasing power, including increasing the number of Ss, increasing the level of alpha, altering the research design, using directional tests, and using highly reliable measures. Statistical power analysis should become a part of research training and one of the criteria for the evaluation of research reports. (Author/IM)

The performance of a dual-hop MIMO relay network is studied in this paper. The relay is assumed to have access to the statistical channel state information of its preceding and following channels and it is assumed that fading at the antennas of the relay is correlated. The cumulative density function (cdf) of the received SNR at the destination is first studied and closed-form expressions are derived for the asymptotic cases of the fully-correlated and non-correlated scenarios; moreover, the statistical characteristics of the SNR are further studied and an approximate cdf of the SNR is derived for arbitrary correlation. The cdf is a multipartite function which does not easily lend itself to further mathematical calculations, e.g., rate optimization. However, we use it to propose a simple power allocation algorithm which we call "proportional power allocation". The algorithm is explained in detail for the case of two antennas and three antennas at the relay and the extension of the algorithm to a relay with an arbitrary number of the antennas is discussed. Although the proposed method is not claimed to be optimal, the result is indistinguishable from the benchmark obtained using exhaustive search. The simplicity of the algorithm combined with its precision is indeed attractive from the practical point of view.

An extension is presented of previous results relating the parameters of an idealized two-dimensional linear vehicle to stable ground roughness as described by power spectral densities. Optimal vehicle parameters are obtained relative to a ride roughness criterion for ground contours described by power spectral densities estimated from real ground survey data. It is found that the ride is not sensitive to changes in the wheel base length parameter when is over 14 feet. However, the ride is found to be sensitive to damping and speed in this wheel base length range.

We provide, and perform a risk theoretic statistical analysis of, a dataset that is 75 percent larger than the previous best dataset on nuclear incidents and accidents, comparing three measures of severity: INES (International Nuclear Event Scale), radiation released, and damage dollar losses. The annual rate of nuclear accidents, with size above 20 Million US$, per plant, decreased from the 1950s until dropping significantly after Chernobyl (April, 1986). The rate is now roughly stable at 0.002 to 0.003, i.e., around 1 event per year across the current fleet. The distribution of damage values changed after Three Mile Island (TMI; March, 1979), where moderate damages were suppressed but the tail became very heavy, being described by a Pareto distribution with tail index 0.55. Further, there is a runaway disaster regime, associated with the "dragon-king" phenomenon, amplifying the risk of extreme damage. In fact, the damage of the largest event (Fukushima; March, 2011) is equal to 60 percent of the total damage of all 174 accidents in our database since 1946. In dollar losses we compute a 50% chance that (i) a Fukushima event (or larger) occurs in the next 50 years, (ii) a Chernobyl event (or larger) occurs in the next 27 years and (iii) a TMI event (or larger) occurs in the next 10 years. Finally, we find that the INES scale is inconsistent. To be consistent with damage, the Fukushima disaster would need to have an INES level of 11, rather than the maximum of 7.

We provide, and perform a risk theoretic statistical analysis of, a dataset that is 75 percent larger than the previous best dataset on nuclear incidents and accidents, comparing three measures of severity: INES (International Nuclear Event Scale), radiation released, and damage dollar losses. The annual rate of nuclear accidents, with size above 20 Million US$, per plant, decreased from the 1950s until dropping significantly after Chernobyl (April, 1986). The rate is now roughly stable at 0.002 to 0.003, i.e., around 1 event per year across the current fleet. The distribution of damage values changed after Three Mile Island (TMI; March, 1979), where moderate damages were suppressed but the tail became very heavy, being described by a Pareto distribution with tail index 0.55. Further, there is a runaway disaster regime, associated with the "dragon-king" phenomenon, amplifying the risk of extreme damage. In fact, the damage of the largest event (Fukushima; March, 2011) is equal to 60 percent of the total damage of all 174 accidents in our database since 1946. In dollar losses we compute a 50% chance that (i) a Fukushima event (or larger) occurs in the next 50 years, (ii) a Chernobyl event (or larger) occurs in the next 27 years and (iii) a TMI event (or larger) occurs in the next 10 years. Finally, we find that the INES scale is inconsistent. To be consistent with damage, the Fukushima disaster would need to have an INES level of 11, rather than the maximum of 7.

We provide, and perform a risk theoretic statistical analysis of, a dataset that is 75 percent larger than the previous best dataset on nuclear incidents and accidents, comparing three measures of severity: INES (International Nuclear Event Scale), radiation released, and damage dollar losses. The annual rate of nuclear accidents, with size above 20 Million US$, per plant, decreased from the 1950s until dropping significantly after Chernobyl (April, 1986). The rate is now roughly stable at 0.002 to 0.003, i.e., around 1 event per year across the current fleet. The distribution of damage values changed after Three Mile Island (TMI; March, 1979), where moderate damages were suppressed but the tail became very heavy, being described by a Pareto distribution with tail index 0.55. Further, there is a runaway disaster regime, associated with the "dragon-king" phenomenon, amplifying the risk of extreme damage. In fact, the damage of the largest event (Fukushima; March, 2011) is equal to 60 percent of the total damage of all 174 accidents in our database since 1946. In dollar losses we compute a 50% chance that (i) a Fukushima event (or larger) occurs in the next 50 years, (ii) a Chernobyl event (or larger) occurs in the next 27 years and (iii) a TMI event (or larger) occurs in the next 10 years. Finally, we find that the INES scale is inconsistent. To be consistent with damage, the Fukushima disaster would need to have an INES level of 11, rather than the maximum of 7.

The design and testing of a free-space optical communication system requires assessment of the impact of\nrandom fluctuations in received power from a laser beam transmitted over an atmospheric channel. A number\nof methods for generating fading power vectors for in-lab emulation of an atmospheric channel have previously\nbeen reported. These techniques include spectral shaping and filtering of a signal from a normally distributed\npseudo-random number generator, full wave optics simulations with random phase screens, and pre-recorded\nmeasurements from experimental free-space links. In this work, a statistical analysis of atmospheric fading is\npresented with the goal of producing a practical engineering model for the fading channel suitable for generating\nsynthetic fade vectors in real-time for long-duration receiver testing with channel interleaving. Specifically, a\nparametric model is developed for turbulence-induced fade on space-to-ground links with large-aperture receivers,\nincluding aperture-averaging and the effects of aperture size on the instantaneous coupling efficiency for mode-\nlimited receivers. In particular, we analyze the probability density function and temporal power spectrum for\nfluctuations of the coupling efficiency for few-mode fibers in a range of turbulence conditions.

The design and testing of a free-space optical communication system requires assessment of the impact of\nrandom fluctuations in received power from a laser beam transmitted over an atmospheric channel. A number\nof methods for generating fading power vectors for in-lab emulation of an atmospheric channel have previously\nbeen reported. These techniques include spectral shaping and filtering of a signal from a normally distributed\npseudo-random number generator, full wave optics simulations with random phase screens, and pre-recorded\nmeasurements from experimental free-space links. In this work, a statistical analysis of atmospheric fading is\npresented with the goal of producing a practical engineering model for the fading channel suitable for generating\nsynthetic fade vectors in real-time for long-duration receiver testing with channel interleaving. Specifically, a\nparametric model is developed for turbulence-induced fade on space-to-ground links with large-aperture receivers,\nincluding aperture-averaging and the effects of aperture size on the instantaneous coupling efficiency for mode-\nlimited receivers. In particular, we analyze the probability density function and temporal power spectrum for\nfluctuations of the coupling efficiency for few-mode fibers in a range of turbulence conditions.

This article is from BMC Medical Research Methodology , volume 14 . Abstract Background: Analysis of variance (ANOVA), change-score analysis (CSA) and analysis of covariance (ANCOVA) respond differently to baseline imbalance in randomized controlled trials. However, no empirical studies appear to have quantified the differential bias and precision of estimates derived from these methods of analysis, and their relative statistical power, in relation to combinations of levels of key trial characteristics. This simulation study therefore examined the relative bias, precision and statistical power of these three analyses using simulated trial data. Methods: 126 hypothetical trial scenarios were evaluated (126 000 datasets), each with continuous data simulated by using a combination of levels of: treatment effect; pretest-posttest correlation; direction and magnitude of baseline imbalance. The bias, precision and power of each method of analysis were calculated for each scenario. Results: Compared to the unbiased estimates produced by ANCOVA, both ANOVA and CSA are subject to bias, in relation to pretest-posttest correlation and the direction of baseline imbalance. Additionally, ANOVA and CSA are less precise than ANCOVA, especially when pretest-posttest correlation ≥ 0.3. When groups are balanced at baseline, ANCOVA is at least as powerful as the other analyses. Apparently greater power of ANOVA and CSA at certain imbalances is achieved in respect of a biased treatment effect. Conclusions: Across a range of correlations between pre- and post-treatment scores and at varying levels and direction of baseline imbalance, ANCOVA remains the optimum statistical method for the analysis of continuous outcomes in RCTs, in terms of bias, precision and statistical power.

This article is from BMC Medical Research Methodology , volume 14 . Abstract Background: Analysis of variance (ANOVA), change-score analysis (CSA) and analysis of covariance (ANCOVA) respond differently to baseline imbalance in randomized controlled trials. However, no empirical studies appear to have quantified the differential bias and precision of estimates derived from these methods of analysis, and their relative statistical power, in relation to combinations of levels of key trial characteristics. This simulation study therefore examined the relative bias, precision and statistical power of these three analyses using simulated trial data. Methods: 126 hypothetical trial scenarios were evaluated (126 000 datasets), each with continuous data simulated by using a combination of levels of: treatment effect; pretest-posttest correlation; direction and magnitude of baseline imbalance. The bias, precision and power of each method of analysis were calculated for each scenario. Results: Compared to the unbiased estimates produced by ANCOVA, both ANOVA and CSA are subject to bias, in relation to pretest-posttest correlation and the direction of baseline imbalance. Additionally, ANOVA and CSA are less precise than ANCOVA, especially when pretest-posttest correlation ≥ 0.3. When groups are balanced at baseline, ANCOVA is at least as powerful as the other analyses. Apparently greater power of ANOVA and CSA at certain imbalances is achieved in respect of a biased treatment effect. Conclusions: Across a range of correlations between pre- and post-treatment scores and at varying levels and direction of baseline imbalance, ANCOVA remains the optimum statistical method for the analysis of continuous outcomes in RCTs, in terms of bias, precision and statistical power.