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Topic: Hypothesis tests

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	Hypothesis Tests
		By contrast, hypothesis testing consists of identifying some special model or models within the class (the "null hypothesis") and assessing the degree to which the experimental outcome constitutes evidence against the special model, relative to all other models we are considering.
		One view is that a test assigns a number, the "confidence," to the data and that the confidence is the probability that a particular state of nature (the "hypothesis") is true.
		The situation is a "composite" hypothesis test, meaning that the decision is distinguishing an entire class of states of nature N((-1,0), sigma) (sigma could be any positive value) from another large class of states N((1,0), sigma).
	www.quantdec.com /envstats/notes/class_13/tests.htm (2578 words)

	Hypothesis Testing (Site not responding. Last check: 2007-10-09)
		Hypothesis testing is one of the most important tools of application of statistics to real life problems.
		Hence the test statistic is tested for occurrence within either of the two critical regions on the two extremes of the distribution.
		The tests used in the testing of hypothesis, viz., t-tests and ANOVA have some fundamental assumptions that need to be met, for the test to work properly and yield good results.
	ewr.cee.vt.edu /environmental/teach/smprimer/hypotest/ht.html (2437 words)

	1.3.5. Quantitative Techniques
		To reject a hypothesis is to conclude that it is false.
		Thus hypothesis tests are usually stated in terms of both a condition that is doubted (null hypothesis) and a condition that is believed (alternative hypothesis).
		Based on the distribution of the test statistic and the significance level, a cut-off value for the test statistic is computed.
	www.itl.nist.gov /div898/handbook/eda/section3/eda35.htm (882 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.
		The choice between a one-sided and a two-sided test is determined by the purpose of the investigation or prior reasons for using a one-sided test.
		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.cas.lancs.ac.uk /glossary_v1.1/hyptest.html (2167 words)

	Significance Tests / Hypothesis Testing
		If t were -3.7 or 2.6, we would reject the hypothesis that the population mean difference is 0 because we've observed a value of t that is unusual if the hypothesis were true.
		The null hypothesis is usually stated as the absence of a difference or an effect.
		To illustrate this, suppose we are testing the hypothesis that two population means are equal at the 0.05 level of significance by selecting equal sample sizes from the two populations.
	www.tufts.edu /~gdallal/sigtest.htm (1474 words)

	The Blood of St. Januarius (Site not responding. Last check: 2007-10-09)
		This hypothesis was first recorded as early as 1826 [10] and was quickly supported by numerous recipes, mostly based upon waxes, fats or gelatines (plus suitable dyes).
		This test is always referred to as the "scientific proof" of the presence of blood in the vial.
		Further tests to investigate the real nature of the holy "blood" without opening the ampoule come readily to mind: for example, molecular absorptions and fluorescence spectroscopy, and Raman scattering measurements, made with modern electronic instruments by qualified spectroscopists.
	www.cicap.org /en_artic/at101014.htm (2510 words)

	Understanding Hypothesis Tests (Site not responding. Last check: 2007-10-09)
		The probability of obtaining the test statistic calculated from our data is 0.04, assuming we are taking simple random samples of the same size and the null hypothesis is true.
		The p-value is the probability of observing a value of the test statistic at least as extreme as the one we actually obtained.
		The p-value is the probability of observing a value of the test statistic at least as extreme as the one we actually obtained, if indeed the null hypothesis is true, assuming that we are only taking simple random samples of the same size from the same population.
	www.ma.utexas.edu /~mks/384G04/hyptests.html (392 words)

	Bill Thompson's References on Hypothesis Testing (Site not responding. Last check: 2007-10-09)
		Ironically, modern statistical hypothesis testing is actually a hybridization of R. Fisher's "significance testing" and J. Neyman's and E. Pearson's "null hypothesis testing," which were two fundamentally different philosophical approaches to the same problem.
		The general lack of awareness of problems with statistical hypothesis testing is especially acute in my own field (ecology/environmental science/fish and wildlife biology), where scant few papers have addressed this issue (essentially Quinn and Dunham 1983, Jones 1984, Parkhurst 1985, Jones and Matloff 1986, Perry 1986, Yoccuz 1991, McBride et al.
		Hammond, G. The objections to null hypothesis testing as a means of analysing psychological data.
	www.cnr.colostate.edu /~anderson/thompson1.html (3392 words)

	Hypothesis Testing
		The test statistic for the one-tailed test is computed in the same way as for a two-tailed test.
		The tests involved in the hypothesis are enclosed between a header that is a blank
		Typically, an assumption in hypothesis testing is that the residuals are normally distributed.
	shazam.econ.ubc.ca /intro/olstest.htm (938 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.
		The alternate hypothesis is that the process change or treatment has an effect, or something is wrong with the process.
	www.ganesha.org /spc/hyptest.html (1243 words)

	List of selected publications of Tom Snijders
		A test is a statistical procedure to obtain a statement on the truth or falsity of a proposition, on the basis of empirical evidence.
		Hypotheses are formulated and tested on data from a study on the diffusion of petty crime in pupils' networks in high schools.
		The test is conditional on the entire digraph at time I, the numbers of new arcs to and from each actor, and the numbers of disappeared arcs to and from each actor.
	stat.gamma.rug.nl /snijders/publ.htm (11082 words)

	Westgard QC © 1999, Z-Stats 7: Hypothesis testing, Tests of Significance, and Confidence Intervals
		Hypothesis testing makes use of the unit normal distribution that was discussed in the previous lesson, which emphasized the use of z-scores to draw some conclusions.
		A test of significance is a statistical test that attempts to determine whether or not an observed difference indicates that a given characteristics of two groups are the same or different.
		This area of rejection for the null hypothesis (demonstrating that the means of both groups are not the same) is the 2.5% on the right side of the curve and in the 2.5% on the left side of the curve.
	www.westgard.com /lesson37.htm (2507 words)

	Practice Exam Hypothesis Tests
		For a two-tailed hypothesis, the critical value of the test statistic is 1.96 when alpha = 0.10.
		If the 90% confidence interval is 5.2 to 7.5 and the two-tailed hypothesis is Ho: MU = 8.3 at alpha = 0.10 level of significance, then one must ________ the Ho.
		One assumes that the null hypothesis is correct unless strong evidence is presented against it.
	jan.ucc.nau.edu /quizserver/pinto/BA201Hypothesis.html (358 words)

	The Student Room - Hypothesis tests (Site not responding. Last check: 2007-10-09)
		Test at the 5% level whether the mean has increased.
		under 5%), the null hypothesis is rejected and the alternative hypothesis is accepted.
		Since 0.0099<0.05, this is treated as significant and the nulll hypothesis is rejected.
	www.thestudentroom.co.uk /printthread.php?t=88796 (151 words)

	Stats Audio Lectures--Hypothesis Tests
		Because.0013 is very small, there is a very low probability that you would get a sample mean of 77.5 with 1600 people if the true mean were 77.8, so we reject the hypothesis that the true mean is 77.8 in favor of the alternative that the true mean is lower than that.
		The null hypothesis is that the mean longevity of people born in May is 77.8 years.
		The alternative hypothesis is the the mean longevity is lower than that.
	www.arnoldkling.com /apstats/audio/hypothesis.html (509 words)

	Hypothesis Tests (Site not responding. Last check: 2007-10-09)
		An hypothesis test is set up as a null hypothesis against an alternative.
		In this example, the null hypothesis will be rejected 17 percent of the time if the mean is two rather than the hypothesized value of one.
		The test’s power to distinguish between true and false hypotheses depends crucially on the variance of the sample mean, which in turn depends on the variance of X and the sample size.
	jhunix.hcf.jhu.edu /~mlettau/hypoth.htm (398 words)

	Hypothesis Testing: Statistics as Pseudoscience (Site not responding. Last check: 2007-10-09)
		Statistical hypothesis testing should be distinguished from scientific hypothesis testing, in which truly viable alternative hypotheses are evaluated in a real attempt to falsify them.
		The foundations of modern hypothesis testing were laid by Fisher (1925), although the modifications propounded by Neyman and Pearson (1933) are the generally accepted norm.
		Tests for the identity of population distributions, for equality of treatment means, for presence of interactions, for the nullity of a correlation coefficient, and so on, have been responsible for much bad science, much lazy science, and much silly science.
	www.npwrc.usgs.gov /perm/hypotest/hypotest.htm (9924 words)

	Stats Audio Lectures--Hypothesis Tests II (Site not responding. Last check: 2007-10-09)
		Pretend that the null hypothesis is true, and find the cutoff point, in natural units, where you would just fail to reject the null hypothesis.
		Example: Suppose that we want to test the hypothesis that the mean weight of NFL linebackers today is the same as it was ten years ago against the specific alternative hypothesis that the mean weight is 5 pounds higher.
		The null hypothesis that m = 238, and the alternative is that m is greater than 238.
	www.arnoldkling.com /apstats/audio/hyp2.html (392 words)

	Deltoid: A new flavour of Global Warming denial
		The hypothesis tests that the IPCC refers to achieved levels of confidence greater than 95%.
		As a final note on the power of a test, note that for a given level of significance of the test, α, as the sample size increases (to infinity) the power of the test increases (to one) for every β ≠ 1.
		The intuition for this is based in the fact that the test is constructed around a consistent estimator.
	scienceblogs.com /deltoid/2007/04/a_new_flavour_of_global_warmin.php (8439 words)

	Alzforum: Tests
		The test for the most common of these, presenilin-1, is commercially available from Elan Pharmaceuticals and may be recommended for individuals with a clear family pattern of Alzheimer's with an unusually early onset.
		These tests can be expensive, invasive (for example requiring injection of a chemical into the blood) and restricted to hospital that own the costly equipment.
		Tests for various proteins that have been associated with Alzheimer pathology, including tau, amyloid beta peptide and AD7C-NTP are being developed by companies.
	www.alzforum.org /dis/dia/tes (1115 words)

	5.1.3 Hypothesis Tests (Proportion) - tests concerning the binomial proportion (Site not responding. Last check: 2007-10-09)
		The result of a hypothesis test run to test a hypothesis about the population proportion.
		If the P-value is less than the alpha risk which you specify, you should reject the null hypothesis at the corresponding significance level.
		The power curve shows the probability of rejecting the null hypothesis as a function of the true population proportion.
	www.mrs.umn.edu /~sungurea/statlets/usermanual/sect5_1_3.htm (223 words)

	Standard 5-1 : NCES Statistical Standards
		When estimates are compared to one another based on exploratory research and presented in descriptive reports, observed deviations in either direction are of interest and the rejection region lies within both tails of the distribution of the test statistic.
		The conclusions stated in the text are to be supported by two-tailed tests of significance (such as t tests or z tests).
		GUIDELINE 5-1-3A: If the survey purpose or prior research indicates that only differences between estimates in a specific direction are of interest or an established trend is to be updated with a new year of data, one-sided tests (in tests such as t tests or z tests) may be used to optimize power.
	nces.ed.gov /statprog/2002/std5_1.asp (1328 words)

	Tests of Proportions (Site not responding. Last check: 2007-10-09)
		In this applet, we simulate a series of hypothesis of tests for the value of the parameter p in
		The pink region in the applet represents the region in which the null hypothesis would be rejected.
		The red dots represent the samples for which the null hypothesis would be rejected, while the fl
	www.math.csusb.edu /faculty/stanton/m262/proportions/proportions.html (100 words)

	Penn State Statistical Education Resource Kit--Hypothesis Testing Concepts
		Hypothesis testing: Part I. An introduction to the general ideas of hypothesis testing.
		A continuation of the introduction to hypothesis testing including types of errors and making a decision based on the p-value.
		The strengths and weaknesses of significance tests are assessed.
	www.stat.psu.edu /%7Eresources/Topics/htconcpt.htm (276 words)

	(10) Hypothesis tests with frequencies (Site not responding. Last check: 2007-10-09)
		He performed a CHISQUARED test for GOODNESS of FIT between the numbers we would expect from the genetic theory (3:1) and the observed numbers in the Batch sample.
		The data are presented in the report pad of the project file and it is your job to analyse the data using a goodness of fit test.
		Experiment 1 was a control with nothing, except seawater, in the arena to test whether the snails show any bias towards any of the quadrats and if so what that bias was (same type of control as a Y-maze but with 4 rather than two possibilities).
	www.sos.bangor.ac.uk /marine/mb/o1b03/Goodness.htm (1307 words)

	Confidence Intervals (Site not responding. Last check: 2007-10-09)
		Purpose: Constructing t tests and confidence intervals for the population mean and standard deviation.
		The results of a t-test and confidence interval for the mean are shown (if a one-sided test is requested, a one-sided confidence bound is used instead of a two-sided confidence interval):
		Null Hypothesis: mean = 6.0 Alternative: greater than Computed t statistic = -0.374958 P-Value = 0.64353 Do not reject the null hypothesis for alpha = 0.1.
	www.statlets.com /confidence_intervals.htm (304 words)

	Penn State Statistical Education Resource Kit--Hypothesis Testing--Means
		An introduction to hypothesis testing for a single population mean.
		An introduction to hypothesis testing for two dependent population means using the paired T-test.
		Students are asked to randomly sample from a population to create a confidence interval and perform a hypothesis test about a mean and the difference in paired means.
	www.stat.psu.edu /%7Eresources/Topics/htmeans.htm (253 words)

	One tailed hypothesis tests.
		Suppose you want to test the research question that cities in the south have experienced positive growth since 1980.
		The alternative hypothesis to the null is that the population distribution contains a mean value less than or equal to zero.
		Example: You want to test if the mean growth rate for southern cities is greater than northeast cities (or the difference of the means is greater than zero).
	www.uh.edu /~odonnell/econ2370/onetailed.html (517 words)

	On the Nature and Role of Hypothesis Tests
		Hypothesis testing is widely regarded as an essential part of statistics, but it s use in research has led to considerable controversy in a number of disciplines, especially psychology, with a number of commentators suggesting it should not be used at all.
		A root cause of this controversy was the overenthusiastic adoption of hypothesis testing, based on a greatly exaggerated view of its role in research.
		A second cause was confusion between the two forms of hypothesis testing developed by Fisher on the one hand and Neyman and Pearson on the other.
	ideas.repec.org /p/msh/ebswps/2001-4.html (315 words)

	Power of a Hypothesis Test Applet (24-Mar-1997) (Site not responding. Last check: 2007-10-09)
		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 a doubt;'' that is, to accept the null hypothesis unless there is strong evidence to support the alternative.
		If is true, however, the test statistic Z does not follow a standard normal distribution -- it follows a normal distribution with a different mean, and thus, the probability of (correctly) rejecting the null hypothesis is larger than
	www.stat.sc.edu /~ogden/javahtml/power/power.html (359 words)

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