Fixed frequency graph

Another method for checking the consistency of the data and subsequent superposition is to plot a fixed frequency graph (corresponding to one or more frequency that is represented in the experimental data set) generated from the calculated master curve and compare it with the actual experimental data. Figures 4 and 5 show E and E" (respectively) vs. temperature for a fixed frequency of 0.1 Hz. The solid line represents the actual experimental data determined by DMA at 0.1 Hz. From inspection one can see there is excellent agreement between the calculated data and the experimentally measured data. 

Figure 4. Fixed Frequency (0.1 Hz) Graph of E for PMMA Generated from Master Curve of Figure 3. Solid Line Represents Experimental 0.1 Hz Data.

A probability distribution function for a continuous random variable, denoted by fix), describes how the frequency of repeated measurements is distributed over the range of observed values for the measurement. When considering the probability distribution of a continuous random variable, we can imagine that a set of such measurements will lie within a specific interval. The area under the curve of a graph of a probability distribution for a selected interval gives the probability that a measurement will take on a value in that interval. 

Figure 5.1 shows that all three graphs used to characterize the relationship between the dose of toxic chemical and the frequency of toxic effect—i.e., the frequency histogram, the cumulative dose-effect curve, and the linear probit plot—put the logarithm of the dose on the x-axis. The reason the probit plot is linear is because of a clever invention a statistically derived scale that represents cumulative-effect frequency on the y-axis. Called probit units, or simply probits, this scale is based on a particular statistic, the standard deviation of the mean. Standard deviations correspond to fixed percentages of a population, and they can therefore be used in place of percentages to represent the fraction of a population that manifests a toxic effect. The mean dose corresponds to a standard deviation of zero because it is located in the exact middle of the bell curve. In terms of standard deviations, a disease frequency of 50% of the population is equivalent to zero standard deviations. One standard deviation below and above the mean corresponds, respectively, to manifestation... 

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