Experimental Design Repeated-measures

Cropley made general recommendations to develop kinetic models for compUcated rate expressions. His approach includes first formulating a hyperbolic non-linear model in dimensionless form by linear statistical methods. This way, essential terms are identified and others are rejected, to reduce the number of unknown parameters. Only toward the end when model is reduced to the essential parts is non-linear estimation of parameters involved. His ten steps are summarized below. Their basis is a set of rate data measured in a recycle reactor using a sixteen experiment fractional factorial experimental design at two levels in five variables, with additional three repeated centerpoints. To these are added two outlier... 

Root elongation bloassay of root exudates. Five ml aliquots of the root exudates were pipetted onto three layers of Anchor1 germination paper In a 10 by 10 by 1.5 cm plastic petri dish. Twenty five radish or tomato seeds were placed in a 5x5 array in each petri dish. Radish seeds were incubated at 20C for 96 hours tomato seeds were incubated at 20C for 168 hours, before the root length was measured. Experimental design was a completely randomized design with three replications (dishes) per treatment per bioassay seed species. The bioassay was repeated each week for 23 weeks. 

The coefficients a,- are estimated from the results of experiments carried out according to a design matrix such as Table 5.9 which shows a 23 plan matrix. The significance of the several factors are tested by comparing the coefficients with the experimental error, to be exact, by testing whether the confidence intervals Aai include 0 or not. The experimental error can be estimated by repeated measurements of each experiment or - as it is done frequently in a more effective way - by replications at the centre of the plan (so-called zero replications ), see Fig. 5.2. 

A parallel setup is generally recommended, in which a different NMR tube is used for each measurement temperature (Table D3.1.1). However, when the amount of sample is limited, it may be necessary to use a serial rather than parallel experimental design. In a serial measurement, after measuring a sample at the first (lowest) temperature, it is transferred to the next warmest tempering block, held at the measurement temperature for the appropriate incubation time, and then remeasured. The process is repeated until the entire temperature range has been covered. Note that the solid fat content of a given sample is a function of thermal history, so serial and parallel measurements may give dissimilar results. 

In an experiment designed as completely randomized blocks, the effect of Co% on steel tensile strength was researched. Three vessels for producing alloys were used in experimental procedure. Each measurement of tensile strength was repeated and outcomes are shown in thousands of PSI-a in Table 2.49. 

Statistics can effectively be used to provide a best estimate of the value of a repeatedly measured variable, establish the reliability of such an estimate (confidence interval), estimate parameter values of a model from experimental data, help to discriminate between rival models on the basis of goodness of fit, and guard against acceptance of a model whose superior fit may well be due to chance. It can also help to design experimental data gathering to be most efficient [48], On the other hand, statistics alone cannot be relied upon to identify or verify reaction pathways or mechanisms. 

We close this chapter with a brief introduction to the implications of work in dynamical systems theory for experimental design and analysis. This section is meant to portray a systems perspective that may be a fruitful worldview fi om which to approach research. The multivariate, replicated, repeated-measures, single-subject design can be used to provide data for examination within this dynamical systems perspective. 

Nesselroade, J. R., Jones, C. J. (1991). Multi-modal selection effects in the study of adult development A perspective on multivariate, replicated, single-subject, repeated measures designs. Experimental Aging Research, 17, 21-27. 

In factorial repeated measures design, the effect of time (or the repeated experimental condition) can be investigated by including it as a factor in the two-way repeated measures ANOVA. It is important to know that the ANOVA does not consider the order of the time points, only the difference between them, and if we want to evaluate a trend or relationship, it is better to use a regression approach. 

The problem of designing a statistical experiment with repeated measures has been extensively studied in the DoE literature. Repeated measures implies that experimental units or subject will be used more than once (i.e. at two or more periods of time) [2], Consequently, any potential model for the response variable in terms of the factors considered in the experiment will need to contain parameters for unit or subject effects, period or time effects and possible carryover effects. Many studies of repeated measures involve observations over time (or space) and the evolution of response is often of special importance [53]. Because the same unit is producing several successive responses, those that are closer together will tend to be more closely related in other words, a previous result is playing a role on the ensemble of the response variable realization. Therefore, in such cases, these relationships must also be included in the model. 

The study utilized a repeated measures crossover design with two experimental conditions (i) tested condition, and (ii) non-rested conditioa Participants were sent a Palm Pilot seven days before participating in their first simulator session to obtain baseline scores of PVT performance. They were required to complete a PVT at 10 00h, 13 30h and 17 30h on a rested day to obtain baseline scores of sustained alertness. 

The variability of metabolie profiles can also depend on bias and technical and methodological artifacts. It is, therefore, essential to quantify this source of variability in operating tests of repeatability (application of the same measurement conditions) and reproducibility (varying the measurement conditions). This type of analysis must be generalized to each metabolomic experiment to evaluate the reliability of the results and must appear in the scientific publications. Second, the results of these analyses must be taken into account in the experimental design to minimize the exogenous sources of variability and favor the informative sourees (for a review dedicated to these metabolomic questions, see Hendriks etal. [HEN 11]). 

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