Statistics negative predictive value

The percentage positive deviation statistic is the percentage of the predictions that are over predicted from perfect correlation by a technique. If a predictive technique does not have a tendency to over or under predict values, i.e. over predicts as many values as it under predicts then you would expect the percentage positive deviation to be 50%. Therefore this statistic is used as a measure of the tendency of a package to over or under estimate potency. The data reported for this statistic is the distance from 50%, i.e. if positive the technique has a tendency to over-estimate the potency, if negative the technique has a tendency to under-estimate the potency whilst the further away from zero the more exaggerated this tendency. A one sample binomial test was used to identify if the identified tendency to under or over estimate the potency was significant at the 95% confidence hmit. 

If the nuU hypothesis is assumed to be true, say, in the case of a lower-tailed test, form 3, then the distribution of the test statistic t is known under the null hypothesis that limits [L = Io- Given a random sample, one can predict how far its sample value of t might be expecied to deviate from zero by chance alone when [L = Io- If ihe sample value of t is too small, as in the case of a negative value, then this would be defined as sufficient evidence to rejeci the nuU hypothesis. 

MINITAB readily produces many useful manipulations of data such as were obtained in this experiment. Figure 2 shows histograms of the responses, indicating that, for the limited number of data points, the experimental values for each response approach a normal distribution. Thus, the statistical analysis was considered valid. Table III shows a copy of the computer printout of a correlation table with all the responses. Clearly, Property A and Property B are negatively correlated, as predicted, but Property B and Property E are not well correlated. 

MRx is the calculated molar refractivity of X-substituents and its negative coefficient suggests steric hindrance. 7 is an indicator variable, which acquired a value of 1 for amides and 0 for the esters. The negative coefficient of the indicator variable suggests an unfavorable cytotoxic effect for the amide derivatives against this cancer cell line. It is interesting to note here that there is a high mutual correlation between nx and MRx (r = 0.877). Thus, it is very hard to predict for this data set if it is a positive hydrophobic or polarizability effect of the X-substituents. We derived Eq. 17a with MRx and finally preferred Eq. 17 on the basis of their statistics, which are better than those of Eq. 17a ... 

The more positive the r (closer to 1), the stronger the statistical association. That is, the accuracy and precision of predicting a y value from a value of x increases. It also means that, as the values of x increase, so do the y values. Likewise, the more negative the r value (closer to 1), the stronger the statistical association. In this case, as the x values increase, the y values decrease. The... 

Finally, though not less important, is the fact that SAM is an empirical tool that analytical chemists developed to take account of a serious practical problem. But it will not appear in any statistical textbook. The reason is that somehow chemists create a situation where an artificial signal (jo=0) gives rise to a theoretical concentration (which even in most papers and textbooks is negative and it is converted subjectively to a more convenient positive value ). Hence, serious problems arise from a statistical point of view when attempting accurately to define the variance associated with such a prediction. There will not be exact mathematical solutions, and different approaches (all of them approximately, but not totally, correct) can be considered. This will have important consequences in the calculation of the confidence intervals, as will be shown next. 

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