Unequal sample size

The results of the DTS tests are shown in Table I. The values given are in MPa with the standard deviation indicated by the number in parentheses. All statistical information was generated with the general linear model program of the Statistical Analysis System software (5). Comparisons of the data were made with Duncan s Multiple Range Test (modified for unequal sample sizes) at p<0.5 ( -5). Values prece by an asterisk indicate no significant difference from each other. 

Significant differences are indicated p = 0.05) via Tukey s test for unequal sample sizes. Culver is not included in the ANOVA... 

The calibration technique used in conventional SEC does not always give the correct MWD, however. The molecular size of a dissolved polymer depends on its molecular weight, chemical composition, molecular structure, and experimental parameters such as solvent, temperature, and pressure ( ). If the polymer sample and calibration standards differ in chemical composition, the two materials probably will feature unequal molecular size/weight relationships. Such differences also will persist between branched and linear polymers of identical chemical composition. Consequently, assumption of the same molecular weight/V relation for dissimilar calibrant and sample leads to transformation of the sample chromatogram to an apparent MWD. 

When sample sizes are small and very unequal. 

There is usually an implicit assumption in this calculation that the standard deviations are the same in each of the treatment groups. Generally speaking this assumption is a reasonable one to make as the effect of treatment will be to change the mean with no effect on the variability. We will say a little more about dealing at the analysis stage with situations where this is not the case in a later section. The sample size calculation, however, is also easily modified, if needed, to allow unequal standard deviations. 

Finally note that in our considerations we have worked with groups of equal size. It is straightforward to adapt the calculations for unequal randomisation schemes and the computer packages mentioned earlier can deal with these. Altman (1991), Section 15.3 provides a simple method for adapting the standard sample size calculation to unequal group sizes as follows. If N is the calculated sample size based in an equal randomisation and k represents the ratio of the number of patients in one group compared to the other group, then the required number of patients for a A to 1 randomisation is ... 

FIGURE 2. The joining of two tubes of unequal size allows operation up to 60 kHz and a two inch diameter sample size. 

Non-parametric comparisons of location for three or more samples include the Kruskal-Wallis //-test. Here, the two data sets can be unequal in size, but again the underlying distributions are assumed to be similar. 

When the subpopulations or strata are unequal in size and in variance, it can be shown that, if an estimate of the population mean is to be unbiased and the variance of the estimate is to be minimal, the number of samples taken from each stratum should be proportional to the size of the stratum and also to its standard deviation, or... 

This apparatus is a V-shaped trough, at the bottom of which is a series of chutes feeding two trays on either side of the trough. The sample enters the chute and is halved repeatedly until the desired sample size is achieved. The distance between the slots should be at least three times the size of the largest particle diam-eter.f This method is prone to segregation and operator bias because of the unequal splitting of the sample. It has been found that a greater number of chutes can increase the overall efficiency. 

Distribution problems may be solved by dividing the population or compartment into either equal segments where the investigator selects the interval systematically and in which segment a sample is to be taken, or into segments that are unequal in size or number (strata), and where at least one sample is taken in each segment. 

Since the sample is heated from one specific source (usually from outside), potenfially significant temperature gradients exist within the sample. It is an important task in thermal analysis to create conditions in which the temperature gradients within the sample can be minimized. The temperature gradient is the unequal distribution of temperature within the sample. The temperature gradient in the sample depends on the heating rate, the sample size, and the thermal diffusivity of the sample and the sample holder. Thermal diffusivity (m /s) is determined as the ratio of thermal conductivity A, [W/(m-K)] and the volumetric heat capacity [(J/(kg-K)]... 

Macromolecules of unequal length are usually generated by polymeriza-tion. Some idea of the relative contents of chains of various size in the studied polymer sample can be obtained by fractionationt+. The results are represented graphically as distribution curves of molecular mass (or degree... 

There are also alternative ways to demonstrate bioequivalence. It may be possible to demonstrate bioequivalence using well-validated in vitro or animal methods, and these appear at 21CFR, part 320.24(ii)—(iii). For example, two oral formulations can be compared with an intravenous dose of equal or unequal size. If the drug is concentrated in the urine but has negligible concentration in the blood (e.g. nitrofurantoin antibiotics), then urine sampling with a frequency that matches the blood samples could be employed. Multiple-dose... 

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