The coefficient of variation In some cases, it may be most relevant to describe the relative variation within a sample or population. Put another way, knowing the sample SD is really not very informative unless we also know the sample mean. To indicate the level of variation relative to the mean, we can report the coefficient of variation CV. In the case of sample meansthis can be calculated as follows:
Early use[ edit ] While hypothesis testing was popularized early in the 20th century, early forms were used in the s. Modern origins and early controversy[ Triola statistics test ] Modern significance testing is largely the product of Karl Pearson p-valuePearson's chi-squared testWilliam Sealy Gosset Triola statistics test t-distributionand Ronald Fisher " null hypothesis ", analysis of variance" significance test "while hypothesis testing was developed by Jerzy Neyman and Egon Pearson son of Karl.
Ronald Fisher began his life in statistics as a Bayesian Zabellbut Fisher soon grew disenchanted with the subjectivity involved namely use of the principle of indifference when determining prior probabilitiesand sought to provide a more "objective" approach to inductive inference.
Neyman who teamed with the younger Pearson emphasized mathematical rigor and methods to obtain more results from many samples and a wider range of distributions. Fisher popularized the "significance test". He required a null-hypothesis corresponding to a population frequency distribution and a sample.
His now familiar calculations determined whether to reject the null-hypothesis or not. Significance testing did not utilize an alternative hypothesis so there was no concept of a Type II error. The p-value was devised as an informal, but objective, index meant to help a researcher determine based on other knowledge whether to modify future experiments or strengthen one's faith in the null hypothesis.
They initially considered two simple hypotheses both with frequency distributions. They calculated two probabilities and typically selected the hypothesis associated with the higher probability the hypothesis more likely to have generated the sample.
Their method always selected a hypothesis. It also allowed the calculation of both types of error probabilities. The defining paper  was abstract.
Mathematicians have generalized and refined the theory for decades. Neyman accepted a position in the western hemisphere, breaking his partnership with Pearson and separating disputants who had occupied the same building by much of the planetary diameter. World War II provided an intermission in the debate.
The dispute between Fisher and Neyman terminated unresolved after 27 years with Fisher's death in Neyman wrote a well-regarded eulogy. Great conceptual differences and many caveats in addition to those mentioned above were ignored. Neyman and Pearson provided the stronger terminology, the more rigorous mathematics and the more consistent philosophy, but the subject taught today in introductory statistics has more similarities with Fisher's method than theirs.
Sometime around in an apparent effort to provide researchers with a "non-controversial"  way to have their cake and eat it toothe authors of statistical text books began anonymously combining these two strategies by using the p-value in place of the test statistic or data to test against the Neyman—Pearson "significance level".
It then became customary for the null hypothesis, which was originally some realistic research hypothesis, to be used almost solely as a strawman "nil" hypothesis one where a treatment has no effect, regardless of the context. Set up a statistical null hypothesis. The null need not be a nil hypothesis i.
These define a rejection region for each hypothesis. Report the exact level of significance e. If the result is "not significant", draw no conclusions and make no decisions, but suspend judgement until further data is available.
If the data falls into the rejection region of H1, accept H2; otherwise accept H1. Note that accepting a hypothesis does not mean that you believe in it, but only that you act as if it were true. Use this procedure only if little is known about the problem at hand, and only to draw provisional conclusions in the context of an attempt to understand the experimental situation.
The usefulness of the procedure is limited among others to situations where you have a disjunction of hypotheses e. Early choices of null hypothesis[ edit ] Paul Meehl has argued that the epistemological importance of the choice of null hypothesis has gone largely unacknowledged. When the null hypothesis is predicted by theory, a more precise experiment will be a more severe test of the underlying theory.
When the null hypothesis defaults to "no difference" or "no effect", a more precise experiment is a less severe test of the theory that motivated performing the experiment. Pierre Laplace compares the birthrates of boys and girls in multiple European cities.
Thus Laplace's null hypothesis that the birthrates of boys and girls should be equal given "conventional wisdom".
Karl Pearson develops the chi squared test to determine "whether a given form of frequency curve will effectively describe the samples drawn from a given population. He uses as an example the numbers of five and sixes in the Weldon dice throw data.
Karl Pearson develops the concept of " contingency " in order to determine whether outcomes are independent of a given categorical factor. Here the null hypothesis is by default that two things are unrelated e.
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: The test could be required for safety, with actions required in each case.Elementary Statistics, Tenth Edition Elementary Statistics Using Excel, Third Edition Essentials of Statistics, Third Edition Elementary Statistics Using the TI/84 Plus Calculator, Second Edition Mario F.
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