Normal probability plots

Figure 10. Normal-probability plots of zinc concentrations in 20 um sediments. A - all Willamette River Basin samples B -uncontaminated area samples. B curve is an enlargement of the lower portion of A curve. Discontinuity is interpreted as concentration limit of uncontaminated sediments.

Determined from log-normal probability plots of individual rate... 

FIGURE 6 (a) Normal probability plot and (b) half-normal probability or Birnbaun plot, for I I... 

This visual approach based on inspecting the normal probability plot may seem fairly crude. However, most of the test procedures, such as the unpaired t-test, are what we call robust against departures from normality. In other words, the... 

For the subplot analysis it appears that the effects due to A, and the interaction between B and Humidity are real, with some evidence of an interaction between B and Temperature. It is possible to split the two degrees of freedom for Temperature and Humidity into linear and quadratic contrasts and to construct a normal probability plot for the whole plot contrasts. This would reveal important effects due to the linear components of both Temperature and Humidity. 

Normal probability plots or half normal probability plots (Bimbaun plots) [24,29] are graphical methods that help to decide which factors are significant. Effects that are normally distributed around zero are effects... 

Figure 3.2a Example of a Normal probability plot (taken from ref [29]).

Figure 3.2 b Example of a Birnbaun plot (half normal probability plot) (Reprinted from International Laboratory, volume 16, page 43, 1986. Copyright 1986 by International Scientific Communications Inc. [24])... 

The normal probability plots also lead to identical conclusions as the statistical analysis with the /-tests. 

Figure 3.3 Normal probability plot of the normalized effects for the resolution between epianhydrotetracycline and tetracycline obtainedfrom the fractional factorial design...

Fig. 9.4.3 Normal-probability plot (a) and lognormal probability plot (b) for In particles shown in Figure 9.4.2. The ordinate stands for the cumulative percent of particles, with diameters smaller than d on the abscissa. This follows an error function and should give a straight line if the plot obeys the correspondent distribution, as seen in case (b). (From Ref. 4.)...

Normal Probability Plot The normal probability plot is a graphical technique for assessing whether or not a data set is approximately normally distributed. The data are plotted against a theoretical normal distribution in such a way that the points form an approximate straight line. Departures from this straight line indicate departures from normality. The normal probability plot is important for quality process improvement since many other tools require the normality assumption. A normal... 

FIGURE 5 Normal probability plot of drug shelf life with 95% confidence interval. 

The variance ratio (F value) is not readily calculated because replicated data are not available to allow the residual error term to be evaluated. However, it is usual practice to use the interaction data in such instances if the normal probability plot has shown them to be on the linear portion of the graph. By grouping the interaction terms from Table 7 as an estimate of the residual error,... 

The real power of the use of half-normal probability plots, however, comes with data that are likely to have embedded outliers. These data profoundly distort the half-normal plots, as illustrated with the data for methyl isobutyl ketone shown in Figure 9. The plot shows neither normal random error nor significant effects cleanly. Thus, this... 

Figure 7. Half-normal probability plot for methylene chloride.

Compound recovery data for duplicate runs differed by 2-15, depending on the compound. Half-normal probability plot analysis of the new data for the anomalous compounds indicated none of the distortion encountered earlier. Results for acetone and tetrachloroethylene now indicated only random variation with no significant outliers. Results for 2,4-dichlorophenol and 2,5-dichlorophenol indicated a significant pH effect. A significant interaction effect (AB) was detected between variables pH and primary column type for the dichlorophenols and also for methyl isobutyl ketone. This interaction effect indicates that at approximately low pH (pH 2), compound recoveries for dichlorophenols will be greater when a C18 phase is used as the primary column. The half-normal plot for 2,5-dichlorophenol is shown in Figure 10. In examining data for all the compounds from the 23 replicate factorials, this interaction consistently appears for phenolic compounds. 

Small departures of normality do not significantly influence the use of the calibration model in residue analysis. However, major departures of normality are mostly related to analytical or instrumental problems. The use of an inappropriate calibration model can give rise to nonnormality of the residuals. In this case also, one or more of the other four basic assumptions have been violated. Normality can be evaluated by means of several statistical tests (i.e., Kolgomorov-Smirnov, Shapiro-Wilk W) or by constructing normal probability plots [8]. 

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