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  2. Correlation does not imply causation - Wikipedia

    en.wikipedia.org/wiki/Correlation_does_not_imply...

    Example 3. In other cases it may simply be unclear which is the cause and which is the effect. For example: Children that watch a lot of TV are the most violent. Clearly, TV makes children more violent. This could easily be the other way round; that is, violent children like watching more TV than less violent ones. Example 4

  3. Multiple comparisons problem - Wikipedia

    en.wikipedia.org/wiki/Multiple_comparisons_problem

    For example, if one test is performed at the 5% level and the corresponding null hypothesis is true, there is only a 5% risk of incorrectly rejecting the null hypothesis. However, if 100 tests are each conducted at the 5% level and all corresponding null hypotheses are true, the expected number of incorrect rejections (also known as false ...

  4. Hypothesis - Wikipedia

    en.wikipedia.org/wiki/Hypothesis

    The hypothesis of Andreas Cellarius, showing the planetary motions in eccentric and epicyclical orbits. A hypothesis (pl.: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or ...

  5. Conditional independence - Wikipedia

    en.wikipedia.org/wiki/Conditional_independence

    Looking at the results of one die will not tell you about the result of the second die. (That is, the two dice are independent.) If, however, the 1st die's result is a 3, and someone tells you about a third event - that the sum of the two results is even - then this extra unit of information restricts the options for the 2nd result to an odd ...

  6. Conditional dependence - Wikipedia

    en.wikipedia.org/wiki/Conditional_Dependence

    In probability theory, conditional dependence is a relationship between two or more events that are dependent when a third event occurs. [1] [2] For example, if and are two events that individually increase the probability of a third event , and do not directly affect each other, then initially (when it has not been observed whether or not the ...

  7. Granger causality - Wikipedia

    en.wikipedia.org/wiki/Granger_causality

    The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969. [1] Ordinarily, regressions reflect "mere" correlations , but Clive Granger argued that causality in economics could be tested for by measuring the ability to predict the future values of ...

  8. Causal reasoning - Wikipedia

    en.wikipedia.org/wiki/Causal_reasoning

    The study of causality extends from ancient philosophy to contemporary neuropsychology; assumptions about the nature of causality may be shown to be functions of a previous event preceding a later one. The first known protoscientific study of cause and effect occurred in Aristotle's Physics. [1] Causal inference is an example of causal reasoning.

  9. Lindley's paradox - Wikipedia

    en.wikipedia.org/wiki/Lindley's_paradox

    The hypothesis would have fit the observation much better than almost all other ratios, including For example, this choice of hypotheses and prior probabilities implies the statement "if θ {\displaystyle \theta } > 0.49 and θ {\displaystyle \theta } < 0.51, then the prior probability of θ {\displaystyle \theta } being exactly 0.5 is 0.50/0. ...