Continuous data sample size

The role of quality in reliability would seem obvious, and yet at times has been rather elusive. While it seems intuitively correct, it is difficult to measure. Since much of the equipment discussed in this book is built as a custom engineered product, the classic statistical methods do not readily apply. Even for the smaller, more standardized rotary units discussed in Chapter 4, the production runs are not high, keeping the sample size too small for a classical statistical analysis. Run adjustments are difficult if the run is complete before the data can be analyzed. However, modified methods have been developed that do provide useful statistical information. These data can be used to determine a machine tool s capability, which must be known for proper machine selection to match the required precision of a part. The information can also be used to test for continuous improvement in the work process. 

Second, while we applaud the fact that more Hispanics are being included in clinical studies, the sample sizes continue to be small, limiting the interpretations that can be made from the data. In some cases, multiple studies have been pooled together to increase the Hispanic sample size. This is methodologically less rigorous as there may be variability in the methods employed between studies, for example inter-rater differences. 

It is generally true that sample size calculations are undertaken based on simple test procedures, such as the unpaired t-test or the test. In dealing with both continuous and binary data it is likely that the primary analysis will ultimately be based on adjusting for important baseline prognostic factors. Usually such analyses will give higher power than the simple alternatives. These more... 

For continuous data, the sample size is inversely proportional to the square of the clinically relevant difference. So if the crd is reduced by a factor of two then the sample size is increased by a factor of four, if the crd is increased by a factor of two then the sample size is reduced by a factor of four. In our earlier example the sample size requirement to detect a difference of 8 mmHg was 33... 

The sample size calculation should be detailed in the trial publication, indicating the estimated outcomes in each of the treatment groups (and this will define, in particular, the clinically relevant difference to be detected), the type I error, the type II error or power and, for a continuous primary outcome variable in a parallel group trial, the within-group standard deviation of that measure. For time-to-event data details on clinically relevant difference would usually be specified in terms of the either the median event times or the proportions event-free at a certain time point. 

A meta-analysis for continuous data cannot be calculated unless the pertinent standard deviations are known. Unfortunately, clinical reports often give the sample size and mean ratings for the various groups but do not report the standard deviations (or standard error of the mean), which are necessary for effect size calculations. Thus, investigators should always report the indices of variability (e.g., confidence intervals, SDs) for the critical variables related to their primary hypothesis. 

Since investigators continuously strive to extract increasing amounts of data from shrinking sample sizes, much commercial and academic research on NMR hardware focuses on optimizing RF probe sensitivity to allow the analysis of trace materials. Significant advances have been achieved through several distinct modifications of instrumentation. This present chapter provides a review of the characterization of nanoliter volumes via static NMR spectroscopy and emphasizes some of the more relevant developments in probe technology that have enabled such measurements. 

Clonazepam is widely used for the treatment of sleep disturbances related to post-traumatic stress disorder, despite very limited published data supporting its use for this indication. In a randomized, single-blind, placebo-controlled, crossover trial of clonazepam 1 mg at bedtime for 1 week followed by 2 mg at bedtime for 1 week in six patients with combat-related post-traumatic stress disorder there were no statistically significant differences between clonazepam and placebo (4). Adverse effects of clonazepam were generally mild and essentially indiscernible from those attributed to placebo. Only one patient elected to continue taking clonazepam at the end of the trial. The small sample size was a significant limitation of the study. 

Basically, the flow control and sampling unit allows three alternative methods of operation. Firstly the eluent from the column can flow directly from the UV detector to the NMR sample tube and the spectra can be continuously monitored during the development of the separation. The success of this procedure will depend on the volume of the cell, the sample size, the column flow rate, the resolution of the NMR spectrometer and the rate of data acquisition by the computer. In general, unless the new micro-cell facilities mentioned above are exploited, this procedure will rarely be successful, particularly if microbore columns are used and multi-component mixtures are being examined. 

An alternative (or addition) to repeating the fixed-sample size trial is to use a sequential design in which the trial is run until a useful result is reached. These adaptive designs, in which decisions are taken on the basis of results to date, can assess results on a continuous basis as data for each subject that becomes available or, more commonly, on groups of subjects... 

Cross-validation is used to estimate the generalization error of a model or to compare the performance of different models. K-fold cross-validation divides a data set into k different subsets of equal size n. The validation procedure includes k runs and applies a round-robin approach. During each run one of the k subsets is left out and used as the test set while the remaining subsets are used for training the model. Leave-one-out cross-validation is present if k equals the sample size (i.e., each subset includes only one case). The selection between leave-one-out cross-validation and k-fold cross-vahdation depends on the situation. The former is preferred for continuous error functions, whereas the latter is preferred for determining the number of misclassified cases. A frequent value for k-fold cross-validation is k = 10. 

In Chapter 10 we saw that there are various methods for the analysis of categorical (and mostly binary) efficacy data. The same is true here. There are different methods that are appropriate for continuous data in certain circumstances, and not every method that we discuss is appropriate for every situation. A careful assessment of the data type, the shape of the distribution (which can be examined through a relative frequency histogram or a stem-and-leaf plot), and the sample size can help justify the most appropriate analysis approach. For example, if the shape of the distribution of the random variable is symmetric or the sample size is large (> 30) the sample mean would be considered a "reasonable" estimate of the population mean. Parametric analysis approaches such as the two-sample t test or an analysis of variance (ANOVA) would then be appropriate. However, when the distribution is severely asymmetric, or skewed, the sample mean is a poor estimate of the population mean. In such cases a nonparametric approach would be more appropriate. 

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