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Testing a hypothesis suggested by the data can very easily result in false positives (type I errors). If one looks long enough and in enough different places, eventually data can be found to support any hypothesis. Yet, these positive data do not by themselves constitute evidence that the hypothesis is correct. The negative test data that were ...
The typical steps involved in performing a frequentist hypothesis test in practice are: Define a hypothesis (claim which is testable using data). Select a relevant statistical test with associated test statistic T. Derive the distribution of the test statistic under the null hypothesis from the assumptions.
The process discourages the analyst from choosing one "likely" hypothesis and using evidence to prove its accuracy. Cognitive bias is minimized when all possible hypotheses are considered. [1] Evidence – The analyst then lists evidence and arguments (including assumptions and logical deductions) for and against each hypothesis. [1]
Hypothesis testing is used when a particular hypothesis about the true state of affairs is made by the analyst and data is gathered to determine whether that state of affairs is true or false. [ 68 ] [ 69 ] For example, the hypothesis might be that "Unemployment has no effect on inflation", which relates to an economics concept called the ...
While looking for patterns in data is legitimate, applying a statistical test of significance or hypothesis test to the same data until a pattern emerges is prone to abuse. One way to construct hypotheses while avoiding data dredging is to conduct randomized out-of-sample tests. The researcher collects a data set, then randomly partitions it ...
Note that data dredging is a valid way of finding a possible hypothesis but that hypothesis must then be tested with data not used in the original dredging. The misuse comes in when that hypothesis is stated as fact without further validation. "You cannot legitimately test a hypothesis on the same data that first suggested that hypothesis.
Phrased otherwise, unbiasedness is not a requirement for consistency, so biased estimators and tests may be used in practice with the expectation that the outcomes are reliable, especially when the sample size is large (recall the definition of consistency). In contrast, an estimator or test which is not consistent may be difficult to justify ...
Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logically possible. The practical feasibility of observing a reproducible series of such counterexamples if they do exist. In short, a hypothesis is testable if there is a possibility of deciding whether it is true or false based on experimentation by anyone.