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Topic: Statistical hypothesis testing

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Null hypothesis

Statistical power

Type II error

Statistical theory

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	PlanetMath: hypothesis testing
		Hypothesis testing is a statistical inferencial procedure in which a statement based on some experimental or observational study is formulated, tested, then put through a decision process.
		The concept of statistical hypothesis testing can be found in any standard introductory statistics textbooks, as well as numerous internet websites (for example, click to find the result of a Google search).
		This is version 2 of hypothesis testing, born on 2004-10-07, modified 2005-02-28.
	planetmath.org /encyclopedia/HypothesisTesting.html (358 words)

	Statistical hypothesis testing - Wikipedia, the free encyclopedia
		From the Bayesian point of view, it is appropriate to treat hypothesis testing as a special case of normative decision theory (specifically a model selection problem) and it is possible to accumulate evidence in favor of (or against) a hypothesis using concepts such as likelihood ratios known as Bayes factors.
		The distribution of the test statistic is used to calculate the probability sets of possible values (usually an interval or union of intervals).
		The hypothesis is incorrect, therefore reject the null hypothesis.
	en.wikipedia.org /wiki/Statistical_hypothesis_testing (965 words)

	Statistical hypothesis testing Information
		From the Bayesian point of view, it is appropriate to treat hypothesis testing as a special case of normative decision theory (specifically a model selection problem) and it is possible to accumulate evidence in favor of (or against) a hypothesis using concepts such as likelihood ratios known as Bayes factors.
		A test statistic must be chosen that will summarize the information in the sample that is relevant to the hypothesis.
		The distribution of the test statistic is used to calculate the probability sets of possible values (usually an interval or union of intervals).
	www.bookrags.com /wiki/Statistical_hypothesis_testing (934 words)

	Statistical hypothesis testing (Site not responding. Last check: 2007-10-14)
		Identify that hypothesis testing results in either rejection of a null hypothesis or failure to reject a null hypothesis.
		If we fail to reject the null hypothesis, we have not proven that there is no effect of the shoe on a runner's speed, just that we were unable to determine an effect of the shoe on a runner's speed.
		Hypothesis testing should look at results in terms of this null hypothesis, which we either reject or fail to reject.
	www.bsu.edu /classes/flowers2/rlo/stathyp.htm (688 words)

	Hypothesis Testing
		Hypothesis testing is a systematic method used to evaluate data and aid the decision-making process.
		The null hypothesis is the statement that is believed to be correct throughout the analysis, and it is the null hypothesis upon which the analysis is based.
		The appropriate test statistic (the statistic to be used in statistical hypothesis testing) is based on various characteristics of the sample population of interest, including sample size and distribution.
	www.referenceforbusiness.com /management/Gr-Int/Hypothesis-Testing.html (2002 words)

	Hypothesis Encyclopedia Articles @ CreatedByGod.com (Created by God) (Site not responding. Last check: 2007-10-14)
		A hypothesis is a suggested explanation of a phenomenon or reasoned proposal suggesting a possible correlation between multiple phenomena.
		In due course, a confirmed hypothesis may become part of a theory or occasionally may grow to become a theory itself.
		A falsifiable hypothesis can greatly simplify the process of testing to determine whether the hypothesis has instances in which it is false.
	www.createdbygod.com /encyclopedia/Hypothesis (855 words)

	Glossary
		In hypothesis testing, a null hypothesis (typically, that there is no effect) is compared with an alternative hypothesis (typically, that there is an effect, or that there is an effect of a particular sign).
		Statistical hypothesis testing is formalized as making a decision between rejecting or not rejecting a null hypothesis, on the basis of a set of observations.
		In an hypothesis test using a test statistic, the rejection region is the set of values of the test statistic for which we reject the null hypothesis.
	www.stat.berkeley.edu /~stark/SticiGui/Text/gloss.htm (13846 words)

	7.1.3. What are statistical tests?
		If the test statistic is greater than the upper critical value or less than the lower critical value, the null hypothesis is rejected because there is evidence that the mean linewidth is not 500 micrometers.
		This chapter gives methods for constructing test statistics and their corresponding critical values for both one-sided and two-sided tests for the specific situations outlined under the scope.
		Further guidance on statistical hypothesis testing, significance levels and critical regions, is given in Chapter 1.
	www.itl.nist.gov /div898/handbook/prc/section1/prc13.htm (645 words)

	Daubert and the Law and Science of Expert Testimony in Business Litigation
		The testing of hypotheses that the Court’s emphasized language requires is called "hypothesis testing" in the scientific community and as the Court’s quotations indicate, hypothesis testing is the essence of the scientific method.
		Hypothesis testing: Hypothesis testing is the process of deriving some proposition (or hypothesis) about an observable group of events from accepted scientific principles, and then investigating whether, upon observation of data regarding that group of events, the hypothesis seems true.
		This hypothesis is tested scientifically by proposing the "null hypothesis" that each number is equally likely to land face up, and then rolling the die (say) 600 times and recording the number of times that each number is actually found face up.
	www.daubertexpert.com /basics_daubert-v-merrell-dow.html (2767 words)

	NPWRC :: Statistical Significance Testing
		This null hypothesis is generally the opposite of the research hypothesis, which is what the investigator truly believes and wants to demonstrate.
		Hence, P, the outcome of a statistical hypothesis test, depends on results that were not obtained, that is, something that did not happen, and what the intentions of the investigator were.
		In 1963, Clark (1963:466) noted that it was "no longer a sound or fruitful basis for statistical investigation." Bakan (1966:436) called it "essential mindlessness in the conduct of research." The famed quality guru W. Edwards Deming (1975) commented that the reason students have problems understanding hypothesis tests is that they may be trying to think.
	www.npwrc.usgs.gov /resource/methods/statsig/stathyp.htm (2380 words)

	Summary of Hypothesis Testing
		The concept that a test-statistic is the standardized sample statistic is true for most of statistical hypothesis testing problems, including all test statistics that are/will be covered in this course and many others that are not covered I this course.
		The reasons behind using the standardized sample statistics as test statistics is that standardized measures can be compared without worrying about the units, and probability distributions for the standardized sample statistics are either known or easier to derive.
		Procedure for testing a hypothesis on population proportion is similar to the large sample test for mean, except that we are interested in p (population proportion) not in
	www.cst.cmich.edu /users/lee1c/sta282S99/ActivChap6-HP-summary.html (554 words)

	thompson5
		Ironically, null hypothesis testing as it is currently practiced is a hybridization of R. Fisher’s significance test and J. Neyman and E. Pearson’s null hypothesis test (hence the label “null hypothesis significance test”).
		Chris Ribic, a symposium on the use/misuse of null hypothesis testing in wildlife science during the Fifth Annual Conference of The Wildlife Society in Buffalo, NY on 26 September, 1998.
		Statistical hypothesis testing in biology: a contradiction in terms.
	www.warnercnr.colostate.edu /~anderson/thompson1.html (4147 words)

	Steps in Hypothesis Testing (Site not responding. Last check: 2007-10-14)
		For a two tailed test, the null hypothesis is typically that a parameter equals zero although there are exceptions.
		For a one-tailed test, the null hypothesis is either that a parameter is greater than or equal to zero or that a parameter is less than or equal to zero.
		This is the probability of obtaining a sample statistic as different or more different from the parameter specified in the null hypothesis given that the null hypothesis is true.
	psych.rice.edu /online_stat/chapter9/steps.html (269 words)

	Statistics Glossary - hypothesis testing
		The critical value(s) for a hypothesis test is a threshold to which the value of the test statistic in a sample is compared to determine whether or not the null hypothesis is rejected.
		Presumably, we would want to test the null hypothesis against the first alternative hypothesis since it would be useful to know if there is likely to be less than 50 matches, on average, in a box (no one would complain if they get the correct number of matches in a box or more).
		The choice between a one-sided test and a two-sided test is determined by the purpose of the investigation or prior reasons for using a one-sided test.
	www.stats.gla.ac.uk /steps/glossary/hypothesis_testing.html (2225 words)

	The Prism Guide to Interpreting Statistical Results
		In most circumstances, the null hypothesis is the opposite of the experimental hypothesis that the means come from different populations.
		Statistical tables were used to determine whether the P value was less than or greater than 0.05, and it would have been very difficult to determine the P value exactly.
		Today, with most statistical tests, it is very easy to compute exact P values, and you shouldn't feel constrained to only report whether the P value is less than or greater than some threshold value.
	www.graphpad.com /articles/interpret/principles/stat_sig.htm (703 words)

	Statistical Methods: introduction to hypothesis testing (Site not responding. Last check: 2007-10-14)
		This is equivalent to the sample mean being outside a 95% confidence interval for the population mean.
		In this case the test statistic is
		if our test statistic is in the critical region, in this case defined by +/-1.96.
	www.statsontheweb.com /statmeth/hyptests.html (450 words)

	In Defence of Significance TestsIn Defence of Significance Tests (Site not responding. Last check: 2007-10-14)
		(4) The substantive and statistical hypotheses are different.
		Moreover, the experimental and statistical hypotheses are indistinguishable on the surface, in that the mean yield in the "Fertilizer F" condition is higher than that in the "Fertilizer C" condition.
		Consequently, the statistical hypothesis testing is conflated with theory corroboration.
	psycprints.ecs.soton.ac.uk /perl/local/psyc/makedoc?id=641&type=xml (1277 words)

	Statistical Hypothesis Testing
		Biological hypotheses that are to be tested statistically are always phrased as in the form of a null hypothesis (written H
		Statistical tests are attempts to reject the null hypothesis.
		We reject the null hypothesis at the 5% significance level, and we begin to suspect that the coin is loaded.
	www.mun.ca /biology/scarr/2900_Hypothesis_testing.htm (790 words)

	Statistical Power
		In statistical hypothesis testing, we use data to make a decision about whether to reject a statistical hypothesis (usually stated as a null hypothesis) in favor of an alternative hypothesis.
		The approach is then to calculate a test statistic from the data (e.g., a t-test) and compare its value to the statistics distribution assuming that the null hypothesis is true.
		The variance of the test statistic is a function of (1) experimental error (sometimes reducible, sometimes not), and (2) sample size.
	fisher.forestry.uga.edu /popdyn/Power.html (1151 words)

	Power of a Hypothesis Test Applet
		This applet illustrates the fundamental principles of statistical hypothesis testing through the simplest example: the test for the mean of a single normal population, variance known (the Z test).
		This hypothesis testing procedure is set up to give the null hypothesis the "benefit of the doubt;" that is, to not reject the null hypothesis unless there is strong evidence to support the alternative.
		The fl curve represents the distribution of the test statistic when the null hypothesis is true.
	www.amstat.org /publications/jse/v6n3/applets/power.html (386 words)

	STEPS IN STATISTICAL HYPOTHESIS TESTING
		Step 3: State the test statistic that will be used to conduct the hypothesis test (the appropriate test statistics for the different kinds of hypothesis tests are given in the tables of the reference page, “Statistical Inference for Values of Population Parameters”).
		If the null hypothesis were true, there would be only a probability of a of obtaining a value of the test statistic that would be at least this extreme.
		If the value of the test statistic computed from the sample data is beyond the critical value, the decision will be made to reject the null hypothesis in favor of the alternative hypothesis.
	www.unf.edu /~jgleaton/HypSteps.html (435 words)

	Brainstorms: “Design-centric ID” as statistical hypothesis testing
		The statistic used to test for the rejection of the null hypothesis is the quantity of “CSI” in the system.
		But the practice of making repeated statistical tests until the desired outcome is found is known to be fraught with potential for artifactual bias.
		While the developers of the statistical theory for detecting design have been admirably (perhaps excessively!) conservative in some assumptions, these questions, left unanswered, are enough to diminish the value of this conservatism.
	www.iscid.org /boards/ubb-get_topic-f-6-t-000187.html (1456 words)

	BBSPrints Archive: Précis of "STATISTICAL SIGNIFICANCE: RATIONALE, VALIDITY AND UTILITY"
		The null-hypothesis significance-test procedure (NHSTP) is defended in the context of the theory-corroboration experiment, as well as the following contrasts: (a) substantive hypotheses versus statistical hypotheses, (b) theory corroboration versus statistical hypothesis testing, (c) theoretical inference versus statistical decision, (d) experiments versus nonexperimental studies, and (e) theory corroboration versus treatment assessment.
		Statistical significance means only that chance influences can be excluded as an explanation of data; it does not identify the nonchance factor responsible.
		The validity of statistical power is debatable because statistical significance is determined with a single sampling distribution of the test statistic based on H0, whereas it takes two distributions to represent statistical power or effect size.
	www.bbsonline.org /documents/a/00/00/04/42/index.html (645 words)

	Statistical Hypothesis Testing
		Hypothesis testing often confuses people but it is the keystone of most statistical applications.
		In statistical testing, the significance level, Type I risk, or alpha risk is the "reasonable doubt." It is the chance of wrongly rejecting the null hypothesis when it is true.
		It is the integral of the distribution from 0 to 12.59, and 95 percent of the area under the curve is to the left of 12.59.
	www.ganesha.org /spc/hyptest.html (1256 words)

	BioMed Central \| Full text \| GeneTools- application for functional annotation and statistical hypothesis testing
		Statistically we need to distinguish between three situations, to correctly handle the possible dependencies between gene reporter lists A and B. An illustration of these situations is given in figure 5.
		Statistically this situation is very similar to the master-target situation and can be transformed into a problem where we for each GO category under consideration want to test if two independent binomial proportions are equal.
		However, the statistical test of FatiGO [37] is valid for the mutually exclusive target-target situation, and was in a simulation study found to preserve the test size when the gene reporter lists are of equal length [30].
	www.biomedcentral.com /1471-2105/7/470 (6073 words)

	Statistical hypothesis testing at opensource encyclopedia (Site not responding. Last check: 2007-10-14)
		This article describes the frequentist treatment of hypothesis testing.
		From the Bayesian point of view, it is appropriate to treat hypothesis testing as a special case of normative decision theory.
		This is not the same as evidence for the hypothesis.
	www.wiki.tatet.com /Statistical_hypothesis_testing.html (532 words)

	Hypothesis Testing
		The terminology relating to populations and samples can be introduced early in the study of statistics and used consistently throughout the unit.
		A conclusion might be, 'It is highly unlikely that the actual density of the earth is 5.3 or lower.' Students who understand this conclusion are well are their way towards understanding hypothesis testing.
		When the class started covering two-sided hypothesis tests, he had a lot of trouble remembering where to put the equal sign.
	exploringdata.cqu.edu.au /hy_test.htm (473 words)

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