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Experimental data, however, can never prove that the hypotheses (h) is true, but relies on an inductive inference by measuring the probability of the hypotheses relative to the empirical data. The proof is in the rational demonstration of using the logic of inference, math, testing, and deductive reasoning of significance. [1] [2] [6]
In carefully designed scientific experiments, null results can be interpreted as evidence of absence. [7] Whether the scientific community will accept a null result as evidence of absence depends on many factors, including the detection power of the applied methods, the confidence of the inference, as well as confirmation bias within the community.
The origin of the phrase "Lies, damned lies, and statistics" is unclear, but Mark Twain attributed it to Benjamin Disraeli [1] "Lies, damned lies, and statistics" is a phrase describing the persuasive power of statistics to bolster weak arguments, "one of the best, and best-known" critiques of applied statistics. [2]
Most people do not look for bias or errors, so they are not noticed. Thus, people may often believe that something is true even if it is not well represented. [75] To make data gathered from statistics believable and accurate, the sample taken must be representative of the whole. [76]
Simpson's paradox has been used to illustrate the kind of misleading results that the misuse of statistics can generate. [ 7 ] [ 8 ] Edward H. Simpson first described this phenomenon in a technical paper in 1951, [ 9 ] but the statisticians Karl Pearson (in 1899 [ 10 ] ) and Udny Yule (in 1903 [ 11 ] ) had mentioned similar effects earlier.
Statistics, when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator.
Popper's theory presents an asymmetry in that evidence can prove a theory wrong, by establishing facts that are inconsistent with the theory. In contrast, evidence cannot prove a theory correct because other evidence, yet to be discovered, may exist that is inconsistent with the theory. [9]
It has become one of the best-selling statistics books in history, with over one and a half million copies sold in the English-language edition. [1] It has also been widely translated. Themes of the book include "Correlation does not imply causation" and "Using random sampling." It also shows how statistical graphs can be used to distort reality.