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1% 5% 10% 25% 50% 75% 90% 95% 99% 0 0 0 0 0 0 0 0 0 Outlier Test Dixon's extreme value test was performed to test whether the lowest value is a statistical outlier. The test was conducted at the 5% significance level. Data should not be excluded from analysis solely on the basis of the results of this or any other statistical test. If any values are flagged as possible outliers, further investigation is recommended to determine whether there is a plausible explanation that justifies removing or replacing them. DIXON'S OUTLIER TEST for TPH Dixon Test Statistic 0 Dixon 5% Critical Value 0 The calculated test statistic does not exceed the critical value, so the test cannot reject the null hypothesis that there are no outliers in the data, and concludes that the minimum value 0 is not an outlier at the 5% significance level. Because Dixon's test can be used only when the data without the suspected outlier are approximately normally distributed, a Shapiro-Wilk test for normality was performed at a 5% significance level. NORMAL DISTRIBUTION TEST(excluding outliers) Shapiro-Wilk Test Statistic 2.624e-308 Shapiro-Wilk 5% Critical Value 1.376e-313 The calculated Shapiro-Wilk test statistic exceeds the 5% Shapiro-Wilk critical value, so the test cannot reject the hypothesis that the data are normal and concludes that the data, excluding the minimum value 0, do appear to follow a normal distribution at the 5% level of significance. Data Plots for TPH Graphical displays of the data are shown below. The Histogram is a plot of the fraction of the n observed data that fall within specified data"bins." A histogram is generated by dividing the x axis (range of the observed data values) into"bins"and displaying the number of data in each bin as the height of a bar for the bin. The area of the bar is the fraction of the n data values that lie within the bin. The sum of the fractions for all bins equals one. A histogram is used to assess how the n data are distributed (spread) over their range of values. If the histogram is more or less symmetric and bell shaped, then the data may be normally distributed. The Box and Whiskers plot is composed of a central box divided by a line, and with two lines extending out from the box, called the"whiskers". The line through the box is drawn at the median of the n data observed. The two ends of the box represent the 25th and 75th percentiles of the n data values, which are also called the lower and upper quartiles, respectively, of the data set. The sample mean (mean of the n data) is shown as a 'Y' sign. The upper whisker extends to the largest data value that is less than the upper quartile plus 1.5 times the interquartile range(upper quartile minus the lower quartile). The lower whisker extends to the smallest data value that is greater than the lower quartile minus 1.5 times the interquartile range. Extreme data values (greater or smaller than the ends of the whiskers) are plotted individually as blue Xs. A Box and Whiskers plot is used to assess the symmetry of the distribution of the data set. If the distribution is symmetrical, the box is divided into two equal halves by the median,the whiskers will be the same length, and the number of extreme data points will be distributed equally on either end of the plot. The Q-Q plot graphs the quantiles of a set of n data against the quantiles of a specific distribution. We show here only the Q-Q plot for an assumed normal distribution. The pm quantile of a distribution of data is the data value, x,,, for which a fraction p of the distribution is less than x,,. If the data plotted on the normal distribution Q-Q plot closely follow a straight line, even at the ends of the line, then the data may be assumed to be normally distributed. If the data points deviate substantially from a linear line, then the data are not normally distributed.