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Comparison of different statistical analyses in visual stimulus fMRI.

The present study evaluated four different clinically relevant statistical approaches with respect to a response to a visual stimulus paradigm. Healthy volunteers were subjected to a visual stimulus consisting of a checkerboard black-and-white box car pattern with on-off blocks of 10s. Simultaneously, sensitivity encoding (SENSE) dynamic MR imaging was acquired using a 1.5 T MR system. Statistical analyses were conducted with z-cluster analysis, Student's t-test, Spearman's correlation, and time-series normalized cross-correlation. A figure-of-merit for neural activity was measured from calculated maps using pixel counting. The results demonstrated that the index of activity estimated from the number of "activated" pixels did not differ markedly among the four different statistical methods, except when comparing the cross-correlation statistics with z-clustering in the whole brain, implying that all methods lead to similar statistical information when using fMRI to map the activity of the visual cortex in response to a visual stimulus.

Adult↗

Multiple fragment statistical analysis of post-spike effects in spike-triggered averages of rectified EMG.

Spike-triggered averaging of EMG is a useful experimental technique for revealing functional connectivity from central neurons to motoneurons. Because EMG waveforms constitute time series, statistical analysis of spike-triggered averages is complicated. Empirical methods generally have been employed to detect the presence of post-spike effects (PSEs), since, as we argue in this report, it is not feasible to develop a rigorous yet sensitive statistical test that detects PSEs in a single grand average of rectified EMG. We have developed a method of multiple fragment statistical analysis (MFSA) of PSEs, based on dividing an experimental record into a large numbers of non-overlapping fragments. The calculations necessary to obtain accurate P-values using the multiple fragment method are simple and efficient, and therefore preliminary results can be obtained while recording. In this report, we present the rationale for MFSA, and give examples of its application. We found MFSA to have considerable utility in accurately testing the significance of small PSEs, and in detecting PSEs in shorter recordings. Statistical corrections that should be used when recording multiple channels simultaneously are discussed. MFSA could be implemented for statistical analysis of other waveforms averaged, such as evoked potentials, movement-related cortical potentials, or event-related desychronizations.

Algorithms↗

First-order statistics of human stabilogram.

We investigated the statistical properties of the centre of pressure (COP) vector during quiet standing, as measured on a force platform. To derive a statistical model for the data, the COP vector, locally averaged COP, and deviations from the average COP were analysed. Whereas indefinite multimodal distributions for the components of the COP were observed, the density functions of deviation from the averaged COP had reproducible properties. The anterior-posterior and mediolateral components of the deviations had in common that they were correlated variables with a non-circular statistic. The main axes of the equiprobability density curves were rotated with respect to the natural anterior-posterior and mediolateral directions. By means of more detailed statistical analysis of the data, two distinct populations of subjects were identified. In some cases we have found Gaussian distributions of the components of deviation from the average COP. In most cases the statistics was non-Gaussian. The average contrast, a new dimensionless characteristic quantity, independent of platform calibration, was introduced as a useful indicator of non-Gaussian effects in the postural control system.

Humans↗

Reproducibility and responsiveness of health status measures. Statistics and strategies for evaluation.

Before being introduced to wide use, health status instruments should be evaluated for reliability and validity. Increasingly, they are also tested for responsiveness to important clinical changes. Although standards exist for assessing these properties, confusion and inconsistency arise because multiple statistics are used for the same property; controversy exists over how to measure responsiveness; many statistics are unavailable on common software programs; strategies for measuring these properties vary; and it is often unclear how to define a clinically important change in patient status. Using data from a clinical trial of therapy for back pain, we demonstrate the calculation of several statistics for measuring reproducibility and responsiveness, and demonstrate relationships among them. Simple computational guides for several statistics are provided. We conclude that reproducibility should generally be quantified with the intraclass correlation coefficient rather than the more common Pearson r. Assessing reproducibility by retest at one-to-two week intervals (rather than a shorter interval) may result in more realistic estimates of the variability to be observed among control subjects in a longitudinal study. Instrument responsiveness should be quantified using indicators of effect size, a modified effect size statistic proposed by Guyatt, or the use of receiver operating characteristic (ROC) curves to describe how well various score changes can distinguish improved from unimproved patients.

Analysis of Variance↗

Common statistical errors in morphometry.

Morphometry is the quantitative measurement of morphological features. Data is usually obtained by probabilistic sampling techniques and is often markedly variable due to intrinsic variations in sampled specimens. Statistical analyses are required both to allow for and to control such variability. Care is needed in the analysis of morphometric data if false conclusions are to be avoided. Examination of any reasonably sized sample of publications in morphometry usually results in the detection of at least several common errors of statistical practice. Commonest errors involve statistics being carried out on untransformed percentage data, statistics on ratios, repeated multiple applications of tests designed for single comparisons, misuse of correlation and violations of statistical assumptions.

Analysis of Variance↗

A new statistical method for testing hypotheses of neuropsychological/MRI relationships in schizophrenia: partial least squares analysis.

We applied partial least squares (PLS) as a novel multivariate statistical technique to examine neuropsychological correlates of magnetic resonance imaging (MRI) measures of brain volumes in a well studied sample of 15 male patients with chronic schizophrenia. In the current study, because the total number of measures far surpassed the total number of subjects, extant multivariate techniques such as canonical correlation could not be used to examine relationships among simultaneous measures of MRI and neuropsychology. Moreover, because MRI measures were expected to be highly inter-correlated, as would be neuropsychological test scores, extant multivariate statistical techniques would be substantially limited because they typically assume statistical independence among sets of measures. PLS, on the other hand, proved to be especially well suited to examining the relationships among function and anatomy measures in this sample, where statistically significant relationships were demonstrated that were entirely consistent with prior studies using univariate correlation techniques. In particular, statistically significant relationships emerged among sets of MRI temporal lobe measures and neuropsychological tests of verbal memory and categorization as well as among MRI frontal measures and neuropsychological tests of working memory.

Adult↗

Research publications in vascular and interventional radiology: research topics, study designs, and statistical methods.

PURPOSE: Statistical analysis is the universal language of medical research and is a vital tool for communicating the results of vascular and interventional radiology (VIR) procedures. Major articles in two radiology journals were surveyed to characterize the research topics, study designs, and statistical methods seen in recent VIR research publications. MATERIALS AND METHODS: The authors retrospectively reviewed 130 major clinical VIR articles published from July 2000 to June 2001: 72 articles (55%) from JVIR and 58 articles (45%) from RADIOLOGY: Articles were categorized by research topic and study design. Data were collected on the statistical methodology of each article. RESULTS: Research topics included vascular intervention in 65 of 130 articles (50%), nonvascular intervention in 26 (20%), vascular imaging in 23 (18%), biopsy in nine (7%), and other topics in seven (5%). Study design was descriptive in 87 studies (67%), comparative in 39 studies (30%), and involved secondary data analysis in four studies (3%). Of 126 primary clinical studies, outcome was cross-sectional (assessed at a single time point) in 40 studies (32%) and longitudinal (measured over time) in 86 studies (68%). Median sample size was 61. Basic tests of association (t-test, chi(2) test, etc.) were used in 71 articles (56%) and advanced tests of association (regression analysis) were presented in 25 (20%). Survival analysis was applied in 34 articles (27%). Decision statistics such as sensitivity/specificity were not used commonly (12%). Confidence intervals and power calculations were reported infrequently (15% and 7%, respectively). CONCLUSIONS: VIR publications focus on time-dependent outcomes after therapeutic interventions. Readers should understand basic tests of association and survival analysis--these include only 20 named statistical tests.

Periodicals as Topic↗

A review of key research design and statistical analysis issues.

This article highlights some basic principles of the design and use of statistical tests, using a minimum of mathematics or statistical jargon. It is not the intent to summarize all the possible details involved with performing these tests, but instead to offer insight into evaluating the statistical methods found in published articles. Historically, the number of scientific articles published in which inappropriate statistical analyses were performed is alarming. Only when the reader understands the problem and demands change will this situation improve. The consequence of inaction is to be mired with an array of poorly designed articles that, at the very least, do not advance the field of study and, at worse, may influence practitioners not well versed in statistics to expose patients to useless, unnecessary, or even harmful procedures.

Analysis of Variance↗

Fitting Rasch model using appropriateness measure statistics.

In this paper, the distributional properties and power rates of the Lz, Eci2z, and Eci4z statistics when they are used as item fit statistics were explored. The results were compared to t-transformation of Outfit and Infit mean square. Four sample sizes were selected: 100, 250, 500, and 1000 examinees. The abilities were uniform and normal with mean 0 and standard deviation 1, and uniform and normal with mean -1 and standard deviation 1. The pseudo-guessing parameter was fixed at .25. Two ranges of difficulty parameters were selected: +/- 1 logits and +/- 2 logits. Two test lengths were selected: 15 and 30 items. The results showed important differences between the T-infit, T-outfit, Lz, Eci2z, and Eci4z statistics. The T-oufit, T-infit, and Lz statistics showed poor standardization with estimated parameters because their distributional properties were not close to the expected values. However, the Eci2z and Eci4z statistics showed satisfactory standardization on all conditions. Further, the power rates of Eci2z and Eci4z were 5% to 10% higher than the power rates of Lz, T-outfit, and T-infit to detect items that do not fit Rasch model.

Decision Making↗

Compound-specific isotope analysis coupled with multivariate statistics to source-apportion hydrocarbon mixtures.

Compound Specific Isotope Analysis (CSIA) has been shown to be a useful tool for assessing biodegradation, volatilization, and hydrocarbon degradation. One major advantage of this technique is that it does not rely on determining absolute or relative abundances of individual components of a hydrocarbon mixture which may change considerably during weathering processes. However, attempts to use isotopic values for linking sources to spilled or otherwise unknown hydrocarbons have been hampered by the lack of a robust and rigorous statistical method for testing the hypothesis that two samples are or are not the same. Univariate tests are prone to Type I and Type II error, and current means of correcting error make hypothesis testing of CSIA source-apportionment data problematic. Multivariate statistical tests are more appropriate for use in CSIA data. However, many multivariate statistical tests require high numbers of replicate measurements. Due to the high precision of IRMS instruments and the high cost of CSIA analysis, it is impractical, and often unnecessary, to perform many replicate analyses. In this paper, a method is presented whereby triplicate CSIA information can be projected in a simplified data-space, enabling multivariate analysis of variance (MANOVA) and highly precise testing of hypotheses between unknowns and putative sources. The method relies on performing pairwise principal components analysis (PCA),then performing a MANOVA upon the principal component variables (for instance, three, using triplicate analyses) which capture most of the variability in the original data set. A probability value is obtained allowing the investigator to state whether there is a statistical difference between two individual samples. A protocol is also presented whereby results of the coupled pairwise PCA-MANOVA analysis are used to down-select putative sources for other analysis of variance methods (i.e., PCA on a subset of the original data) and hierarchical clustering to look for relationships among samples which are not significantly different. A Monte Carlo simulation of a 10 variable data set; tanks used to store, distribute, and offload fuels from Navy vessels; and a series of spilled oil samples and local tug boats from Norfolk, VA (U.S.A.) were subjected to CSIA and the statistical analyses described in this manuscript, and the results are presented. The analysis techniques described herein combined with traditional forensic analyses provide a collection of tools suitable for source-apportionment of hydrocarbons and any organic compound amenable to GC-combustion-IRMS.

Chromatography, Gas↗

A meta-analysis of studies using bias and precision statistics to compare cardiac output measurement techniques.

INTRODUCTION: Bias and precision statistics have succeeded regression analysis when measurement techniques are compared. However, when applied to cardiac output measurements, inconsistencies occur in reporting the results of this form of analysis. METHODS: A MEDLINE search was performed, dating from 1986. Studies comparing techniques of cardiac output measurement using bias and precision statistics were surveyed. An error-gram was constructed from the percentage errors in the test and reference methods and was used to determine acceptable limits of agreement between methods. RESULTS: Twenty-five articles were found. Presentation of statistical data varied greatly. Four different statistical parameters were used to describe the agreement between measurements. The overall limits of agreement in studies evaluating bioimpedance (n = 23) was +/-37% (15-82%) and in those evaluating Doppler ultrasound (n = 11) +/-65% (25-225%). Objective criteria used to assess outcome were given in only 44% of the articles. These were (i) limits of agreement approaching +/-15-20%, (ii) limits of agreement of less than 1 L/min, and (iii) more than 75% of bias measurements within +/-20% of the mean. Graphically, we showed that limits of agreement of up to +/-30% were acceptable. CONCLUSIONS: When using bias and precision statistics, cardiac output, bias, limits of agreement, and percentage error should be presented. Using current reference methods, acceptance of a new technique should rely on limits of agreement of up to +/-30%.

Bias↗

How meta-analysis increases statistical power.

One of the most frequently cited reasons for conducting a meta-analysis is the increase in statistical power that it affords a reviewer. This article demonstrates that fixed-effects meta-analysis increases statistical power by reducing the standard error of the weighted average effect size (T.) and, in so doing, shrinks the confidence interval around T.. Small confidence intervals make it more likely for reviewers to detect nonzero population effects, thereby increasing statistical power. Smaller confidence intervals also represent increased precision of the estimated population effect size. Computational examples are provided for 3 effect-size indices: d (standardized mean difference), Pearson's r, and odds ratios. Random-effects meta-analyses also may show increased statistical power and a smaller standard error of the weighted average effect size. However, the authors demonstrate that increasing the number of studies in a random-effects meta-analysis does not always increase statistical power.

Humans↗

Some issues in the statistical analysis of completely randomized and repeated measures designs for speech, language, and hearing research.

Contemporary investigators in the areas of speech, language, and hearing rely heavily on inferential statistical procedures to answer both basic and applied research questions. Such statistical procedures typically involve a number of assumptions that need to be fulfilled in order for the procedure to be appropriate for a specific data set. Unfortunately, a review of recent publications in the Journal of Speech, Language, and Hearing Research indicated that some pivotal issues related to those underlying assumptions, although widely discussed and emphasized in the statistical literature, often appear to be neglected in these fields of research. This tutorial therefore addresses two issues that are particularly important for an appropriate and accurate use of some of the most commonly used statistical procedures. The first issue concerns the importance of addressing the sphericity assumption in studies with a repeated measures design. The second issue concerns the definition of the experimental units in a statistical analysis and applies to both completely randomized and repeated measures designs. Theoretical aspects associated with each issue are discussed, and appropriate strategies for data entry and analysis are presented.

Hearing↗

Statistical medium optimization and production of a hyperthermostable lipase from Burkholderia cepacia in a bioreactor.

AIM: Statistical medium optimization for maximum production of a hyperthermostable lipase from Burkholderia cepacia and its validation in a bioreactor. METHODS AND RESULTS: Burkholderia cepacia was grown in shake flasks containing 1% glucose, 0.1% KH2PO4, 0.5% NH4Cl, 0.24% (NH4)2HPO4, 0.01% MgSO4.7H2O and 1% emulsified palm oil, at 45 degrees C and pH 7.0, agitated at 250 rev min(-1) with 6-h-old inoculum (2% v/v) for 20 h. A fourfold enhancement in lipase production (50 U ml(-1)) and an approximately three fold increase in specific activity (160 U mg(-1)) by B. cepacia was obtained in a 14 litre bioreactor within 15 h after statistical optimization following shake flask culture. The statistical model was obtained using face centred central composite design (FCCCD) with five variables: glucose, palm oil, incubation time, inoculum density and agitation. The model suggested no interactive effect of the five factors, although incubation period, inoculum and carbon concentration were the important variables. CONCLUSIONS: The maximum lipase production was 50 U ml(-1), with specific activity 160 U mg(-1) protein, in a 14 litre bioreactor after 15 h in a medium obtained after statistical optimization in shake flasks. Further, the model predicted reduction in time for lipase production with reduction in total carbon supply. SIGNIFICANCE AND IMPACT OF THE STUDY: Statistical optimization allows quick optimization of a large number of variables. It also provides a deep insight into the regulatory role of various parameters involved in enzyme production.

Bacterial Proteins↗

Basic statistical testing, including interim analysis.

Clinical trials, due to the randomization process, require statistical methods for testing key hypotheses that are straightforward and involve simple comparisons of group proportions or group means. Differences between group proportions are tested using a chi 2 statistic or a Fisher's exact test. Differences between group means are tested using a two-sample t statistic. When there are more than two groups, the F statistic is calculated. When ordinal data or data not normally distributed are analyzed, nonparametric testing is performed. A critical decision prior to analysis is the choice of the endpoint, which must be clearly defined and consistently applied. Monitoring a clinical trial is important, and may lead to interim analysis. This should be done by independent study monitors. Interim results play an important role in analyzing clinical trials; however, they create problems due to multiple testing. An early stoppage rule is frequently applied when independent interim results are obtained. The statistical methods for interim analysis are discussed.

Data Interpretation, Statistical↗

Statistics of Poincaré recurrences for maps with integrable and ergodic components.

Recurrence gives powerful tools to investigate the statistical properties of dynamical systems. We present in this paper some applications of the statistics of first return times to characterize the mixed behavior of dynamical systems in which chaotic and regular motion coexist. Our analysis is local: we take a neighborhood A of a point x and consider the conditional distribution of the points leaving A and for which the first return to A, suitably normalized, is bigger than t. When the measure of A shrinks to zero the distribution converges to the exponential e(-t) for almost any point x, if the system is mixing and the set A is a ball or a cylinder. We consider instead a system, a skew integrable map of the cylinder, which is not ergodic and has zero entropy. This map describes a shear flow and has a local mixing property. We rigorously prove that the statistics of first return is of polynomial type around the fixed points and we generalize around other points with numerical computations. The result could be extended to quasi-integrable area preserving maps such as the standard map for small coupling. We then analyze the distribution of return times in a region which is composed by two invariants subdomains: one with a mixing dynamics and the other with an integrable dynamics given by our shear flow. We show that the statistics of first return in this mixed region is asymptotically given by the exponential law, but this limit is attained by an intermediate regime where exponential and polynomial laws are linearly superposed and weighted by some factors which are proportional to the relative sizes of the chaotic and regular regions. The result on the statistics of first return times for mixed regions in the phase space can provide a basis to analyze such a property for area preserving maps in mixed regions even when a rigorous result is not available. To this end we present numerical investigations on the standard map which confirm the results of the model.

Algorithms↗

Statistical power and effect sizes of clinical neuropsychology research.

Cohen, in a now classic paper on statistical power, reviewed articles in the 1960 issue of one psychology journal and determined that the majority of studies had less than a 50-50 chance of detecting an effect that truly exists in the population, and thus of obtaining statistically significant results. Such low statistical power, Cohen concluded, was largely due to inadequate sample sizes. Subsequent reviews of research published in other experimental psychology journals found similar results. We provide a statistical power analysis of clinical neuropsychological research by reviewing a representative sample of 66 articles from the Journal of Clinical and Experimental Neuropsychology, the Journal of the International Neuropsychology Society, and Neuropsychology. The results show inadequate power, similar to that for experimental research, when Cohen's criterion for effect size is used. However, the results are encouraging in also showing that the field of clinical neuropsychology deals with larger effect sizes than are usually observed in experimental psychology and that the reviewed clinical neuropsychology research does have adequate power to detect these larger effect sizes. This review also reveals a prevailing failure to heed Cohen's recommendations that researchers should routinely report a priori power analyses, effect sizes and confidence intervals, and conduct fewer statistical tests.

Data Interpretation, Statistical↗

Are classification accuracy statistics underused in neuropsychological research?

The prevalence of classification accuracy statistics was calculated in five prominent neuropsychology journals and five leading neurology journals for the years 2000 and 2001. Only 29% of neuropsychological articles judged to be appropriate for classification accuracy statistics presented sufficient data to calculate a full range of such analyses. Moreover, classification accuracy statistics were significantly less prevalent in neuropsychology journal articles than in studies published in neurology journals during the same time period. Various indices of sensitivity and/or specificity were present in 31% of neuropsychology articles, whereas fewer than 3% reported predictive values or risk ratios. These findings indicate that classification accuracy statistics, most notably predictive values and risk ratios, are potentially underused in neuropsychology. Investigators and research consumers are encouraged to consider the applicability of classification accuracy statistics as a means of evaluating the clinical relevance of neuropsychological research findings.

Bibliometrics↗