Statistics
From RationalWiki
| “ | 70% of all statistics are made-up on the spot[1] | ” |
Contents |
[edit] Introduction
Statistics is the use of mathematics to interpret data taken from representative samples of a particular population of events or opinions to give a reasonable estimate of the whole population's outcome or opinion. Statistics is a form of inductive reasoning, but because it uses almost exclusively mathematics to make its arguments and because most statistical tests are now run automatically by modern computer software it has some how gained the status of deductive reasoning to many. When someone feeds their data into a stats program and it comes out significant it is treated almost like a proof (in the mathematical sense) that the alternative hypothesis is correct.
[edit] The misuse of statistics
This problem has been exaggerated greatly in modern times because of the availability of statistical software packages that do all the math for researchers. This leads to the phenomenon where data goes into the black box and statistical significance comes out magically. Researchers can run a wide range of statistical test without having a clue what they are doing or what the underlying math is doing. Statistical tests are very sensitive to the structure of data and many assumptions must be met or the results are meaningless.
It is important to always keep in mind that statistics are simply an argument and just like any other argument it does not exist in a vacuum. The reliability of its assumptions, the accuracy of its propositions and the relationship of all of these to the conclusions being drawn are all subject to as many problems as any argument made by words. Because of the overwhelming focus on "significance" being the goal a series of major endemic biases are built into most published literature (see statistical significance for this discussion) and as such single results in single experiments are worthless for creating an accepted body of knowledge. Results must be reliable and repeatable, many cranks and quacks will take advantage of the exalted status of statistics and the likelihood of finding a few "significant" results by chance alone to sell their pseudoscience and woo nonsense.
Along the same lines, it is important to remember that a statistic is simply a number. Without knowing the background information, such as sample size, alpha level, etc., it is difficult (if not impossible) to draw any real conclusions. Moreover, a statistic merely describes a relationship...it does not comment on "cause and effect" (see Causalation).
Those wishing to see example of exactly how not to use statistics should see our article Conservapedia:Schlafly Statistics.
[edit] Topics in Statistics
[edit] Standard deviation
See the main article about this subject, Standard deviation.
In statistics, a common method of measuring how likely a value is to turn up in a given set of data is standard deviation.
[edit] Sample size
What is the proper Sample size and how should it change opinion based samples (opinion polls) vs., static samples (number of black beans in a jar of mixed beans).
[edit] Footnotes
- ↑ An unreferenced statistic, when someone uses statistics during an argument, always ask from which reliable source that statistic came from. Unreferenced statistics have no scientific value and posting them during an online discussion may be considered disruptive behavior.
[edit] See also
| Mathematics Articles on RationalWiki
| ||
|---|---|---|
| - 40gon (Fun) - Complex numbers - Conservapedian mathematics - Delta function - Fermat's last theorem - Fibonacci sequence - Golden Ratio - Groups - Gödel's incompleteness theorems - Information - Irrational number - Mathematics - Metric system - ln - Pentagon - Phli (fun) - Probability (Conservapedia) - Pyramid - Quadratic equation - Recursion - Rene Descartes - TeX - Zero - | ||
