"When distributions are compared, the goal is to understand how the distributions shift in going from one data set to the next. […] The most effective way to investigate the shifts of distributions is to compare corresponding quantiles." (William S Cleveland, "Visualizing Data", 1993)
"If the sample is not representative of the population because the sample is small or biased, not selected at random, or its constituents are not independent of one another, then the bootstrap will fail. […] For a given size sample, bootstrap estimates of percentiles in the tails will always be less accurate than estimates of more centrally located percentiles. Similarly, bootstrap interval estimates for the variance of a distribution will always be less accurate than estimates of central location such as the mean or median because the variance depends strongly upon extreme values in the population."
"A feature shared by both the range and the interquartile range is that they are each calculated on the basis of just two values - the range uses the maximum and the minimum values, while the IQR uses the two quartiles. The standard deviation, on the other hand, has the distinction of using, directly, every value in the set as part of its calculation. In terms of representativeness, this is a great strength. But the chief drawback of the standard deviation is that, conceptually, it is harder to grasp than other more intuitive measures of spread.
"A useful feature of a stem plot is that the values maintain their natural order, while at the same time they are laid out in a way that emphasises the overall distribution of where the values are concentrated (that is, where the longer branches are). This enables you easily to pick out key values such as the median and quartiles.
"Having NUMBERSENSE means: (•) Not taking published data at face value; (•) Knowing which questions to ask; (•) Having a nose for doctored statistics. [...] NUMBERSENSE is that bit of skepticism, urge to probe, and desire to verify. It’s having the truffle hog’s nose to hunt the delicacies. Developing NUMBERSENSE takes training and patience. It is essential to know a few basic statistical concepts. Understanding the nature of means, medians, and percentile ranks is important. Breaking down ratios into components facilitates clear thinking. Ratios can also be interpreted as weighted averages, with those weights arranged by rules of inclusion and exclusion. Missing data must be carefully vetted, especially when they are substituted with statistical estimates. Blatant fraud, while difficult to detect, is often exposed by inconsistency." (Kaiser Fung, "Numbersense: How To Use Big Data To Your Advantage", 2013)
"Percentile points are used to define the percentage of cases equal to and below a certain point in a distribution or set of scores." (Neil J Salkind, "Statistics for People who (think They) Hate Statistics: Excel 2007 Edition", 2010)
"Had we started with this [quantile] plot, noticed that it looks straight and not looked further, we would have missed the important features of the data. The general lesson is important. Theoretical quantile -quantile plots are not a panacea and must be used in conjunction with other displays and analyses to get a full picture of the behavior of the data." (John M Chambers et al, "Graphical Methods for Data Analysis", 2011)
"[...] when measuring performance, it’s worth using percentiles rather than averages. The main advantage of the mean is that it’s easy to calculate, but percentiles are much more meaningful."
"Many researchers have fallen into the trap of assuming percentiles are interval data and using them in Statistical procedures that require interval data. The results are somewhat distorted under these conditions since the scores are actually only ordinal data." (Martin L Abbott, "Using Statistics in the Social and Health Sciences with SPSS and Excel", 2016)
"The percentile or rank is the point in a distribution of scores below which a given percentage of scores fall. This is an indication of rank since it establishes score that is above the percentage of a set of scores. [...] Therefore, percentiles describe where a certain score is in relation to others in the distribution. [...] Statistically, it is important to remember that percentile ranks are ranks and therefore not interval data." (Martin L Abbott, "Using Statistics in the Social and Health Sciences with SPSS and Excel", 2016)
"It is not enough to give a single summary for a distribution - we need to have an idea of the spread, sometimes known as the variability. [...] The range is a natural choice, but is clearly very sensitive to extreme values [...] In contrast the inter-quartile range (IQR) is unaffected by extremes. This is the distance between the 25th and 75th percentiles of the data and so contains the ‘central half’ of the numbers [...] Finally the standard deviation is a widely used measure of spread. It is the most technically complex measure, but is only really appropriate for well-behaved symmetric data* since it is also unduly influenced by outlying values." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)
"With skewed data, quantiles will reflect the skew, while adding standard deviations assumes symmetry in the distribution and can be misleading."
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