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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 ...
An example of Neyman–Pearson hypothesis testing (or null hypothesis statistical significance testing) can be made by a change to the radioactive suitcase example. If the "suitcase" is actually a shielded container for the transportation of radioactive material, then a test might be used to select among three hypotheses: no radioactive source ...
using experience – small samples, though sometimes unavoidable, can result in wide confidence intervals and risk of errors in statistical hypothesis testing. using a target variance for an estimate to be derived from the sample eventually obtained, i.e., if a high precision is required (narrow confidence interval) this translates to a low ...
In statistical hypothesis testing, a two-sample test is a test performed on the data of two random samples, each independently obtained from a different given population. The purpose of the test is to determine whether the difference between these two populations is statistically significant .
John W. Tukey wrote the book Exploratory Data Analysis in 1977. [6] Tukey held that too much emphasis in statistics was placed on statistical hypothesis testing (confirmatory data analysis); more emphasis needed to be placed on using data to suggest hypotheses to test.
The Brown–Forsythe test uses the median instead of the mean in computing the spread within each group (¯ vs. ~, above).Although the optimal choice depends on the underlying distribution, the definition based on the median is recommended as the choice that provides good robustness against many types of non-normal data while retaining good statistical power. [3]
This is why the hypothesis under test is often called the null hypothesis (most likely, coined by Fisher (1935, p. 19)), because it is this hypothesis that is to be either nullified or not nullified by the test. When the null hypothesis is nullified, it is possible to conclude that data support the "alternative hypothesis" (which is the ...
Data analysis is a process for obtaining raw data, and subsequently converting it into information useful for decision-making by users. [1] Data is collected and analyzed to answer questions, test hypotheses, or disprove theories. [11] Statistician John Tukey, defined data analysis in 1961, as: