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Topic: ANOVA

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F distribution

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MANOVA

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	PA 765: Univariate GLM, ANOVA, and ANCOVA
		The key statistic in ANOVA is the F-test of difference of group means, testing if the means of the groups formed by values of the independent variable (or combinations of values for multiple independent variables) are different enough not to have occurred by chance.
		Thus some key ANOVA assumptions are that the groups formed by the independent variable(s) are relatively equal in size and have similar variances on the dependent variable ("homogeneity of variances").
		That is, the ANOVA F-test is a function of the variance of the set of group means, the overall mean of all observations, and the variances of the observations in each group weighted for group sample size.
	www2.chass.ncsu.edu /garson/pa765/anova.htm (15037 words)

	anova()
		When you omit Model (anova() or anova(,...)), the model used by the most recent GLM command such as anova(), regress() or poisson() is used.
		For example, the A main effect sum of squares in a two way unbalanced ANOVA is the sum of squares for 'a' from anova("y=b+a") and the B main effect sum of squares is the sum of squares for 'b' from anova("y=a+b").
		For example, even when a, b, and c are factors, the commands Cmd> regress("y=a+b+c",weights:w); anova() print a summary of the weighted multiple regression, followed by an weighted regression ANOVA table with 1 degree of freedom for each of a, b and c.
	www.stat.umn.edu /macanova/htmlhelp/node14.htm (613 words)

	Analysis of Variance (ANOVA)
		ANOVA allows you to break up the group according to the grade and then see if performance is different across these grades.
		ANOVA is available for both parametric (score data) and non-parametric (ranking/ordering) data.
		ANOVA calculates the mean for each of the final grading groups (HD, D, Cr, P, N) on the tutorial exercise figure - the Group Means.
	www.csse.monash.edu.au /~smarkham/resources/anova.htm (665 words)

	EPA Statistical Primer - Anova
		Description: You provide Anova with a categorical variable to group cases and a dependent variable that is (typically) continuous.
		Anova tells you whether pebble is significantly different for different ecoregions.
		Anova was used to estimate the components of variance for the diatom index and its component metrics.
	www.epa.gov /bioiweb1/statprimer/anova.html (528 words)

	The Prism Guide to Interpreting Statistical Results
		ANOVA is not an appropriate test for assessing the effects of a continuous variable, such as blood pressure or hormone level (use a regression technique instead).
		Two-way ANOVA of such data would reject the null hypothesis of no interaction, because the difference between Y values in the middle of the curves is very different than the difference at the ends.
		ANOVA also assumes that all sets of replicates have the same SD overall, and that any differences between SDs are due to random sampling.
	www.graphpad.com /articles/interpret/ANOVA/two_way.htm (3450 words)

	One-way ANOVA
		The significant one-way ANOVA result by itself, however, was not enough to prove the experimental hypothesis, and the research team performed additional statistical testing to understand the results.
		The reason one-way ANOVA was not sufficient is that it returns a significant result when it finds a difference between any of the independent variable group means and the aggregate mean.
		So, for example, one-way ANOVA could return a statistically significant result if the mean amount of time to perform the task using a printed manual was different than the aggregate mean performance time, and this result would not have proven the experimental hypothesis.
	www-users.cs.umn.edu /~ludford/Stat_Guide/One_way_ANOVA.htm (707 words)

	Nested anova
		In a two-level nested anova, one null hypothesis would be that the subgroups within each group have the same means; the second null hypothesis would be that the groups have the same means.
		This would be a pure Model II anova, because you would want to know what proportion of the total variation in ammonia content was due to variation among roosters, as a way of estimating heritability; you wouldn't be interested in which rooster had offspring with the lowest or highest ammonia content in their feces.
		The difference is that in a two-way anova, the values of each attribute variable are found in all combinations with the other attribute variable; in a nested anova, each value of one attribute variable (the subgroups) is found in combination with only one value of the other attribute variable (the groups).
	udel.edu /~mcdonald/statnested.html (1722 words)

	Statistics Solutions: Analysis of Variance (ANOVA)
		ANCOVA uses built-in regression using the covariates to predict the dependent, then does an ANOVA on the residuals (the predicted minus the actual dependent variables) to see if the factors are still significantly related to the dependent variable after the variation due to the covariates has been removed.
		For instance, performance test might be the interval dependent variable, noise distraction might be the within-subjects repeated factor (measure) administered to all subjects in a counterbalanced sequence, and the between-subjects factor might be mode of testing (ex., having a pen-and-paper test group and a computer-tested group).
		Toothaker (1993: 69) notes that in two-way ANOVA most researchers set the alpha significance level (ex.,.05) at the same level for the two main effects and the interaction effect, but that "when you make this choice, you should realize that the error rate for the whole experiment is approximately three times " alpha.
	www.statisticssolutions.com /ANOVA.htm (10002 words)

	One-Way ANOVA
		Given "scores" from samples from several population groups, ANOVA is used to decide whether the differences in the samples' average scores are large enough to conclude that the groups' average scores are unequal.
		It is a significance test: it begins with the null hypothesis that all the groups have equal averages and that any differences in the sample averages are due to chance in, for example, the way the samples were taken.
		Then on the basis of this hypothesis, ANOVA computes the value of a variable F; the larger the value of F, the more unlikely it is to have occurred by chance, and hence the more likely that at least one of the populations has an average different from the others.
	math.colgate.edu /math102/dlantz/examples/ANOVA/anova.html (1392 words)

	One-Way ANOVA
		While ANOVA models can accommodate any type of independent variable (including nominal/categorical variables), regression models assume that the independent variable is also (like the dependent variable) an interval/ratio level variable.
		With the ANOVA model, we estimate/predict the mean values on the outcome variable for each category defined by the independent variable; with the linear regression model, we impose the additional restriction/assumption that the predicted means of the outcome variable all lie on a straight line.
		For instance, we would use he ANOVA model to estimate the mean diastolic blood pressures for various patient groups like male and female diabetics or male and female stroke patients.
	www.msu.edu /~nurse/classes/summer2001/813/anovaregress2.htm (1917 words)

	7.4.3. Are the means equal?
		ANOVA is a general technique that can be used to test the hypothesis that the means among two or more groups are equal, under the assumption that the sampled populations are normally distributed.
		In each of these ANOVA's we test a variety of hypotheses of equality of means (or average responses when the factors are varied).
		The alternative hypothesis for case 3 is: there is an interaction between A and B. For the 3-way ANOVA: The main effects are factors A, B and C. The 2-factor interactions are: AB, AC, and BC.
	www.itl.nist.gov /div898/handbook/prc/section4/prc43.htm (591 words)

	SixSigma First - Article \| ANOVA
		But while ANOVA seeks to define the scope of the variables that will be included in an experiment, the regression analysis determines the coefficients for each variable.
		ANOVA is a basic step in the Design Of Experiment (DOE), which is a powerful statistical tool aimed at statistically quantifying interactions between independent variables through their methodical modifications to determine their impact on the predicted variables.
		So the computation of the ANOVA is done through the Sums of squares of the treatments, the error and their total.
	www.sixsigmafirst.com /anova.htm (2058 words)

	anova - multi-factor analysis of variance
		The input to anova consists of each datum on a separate line, preceded by a list of index labels, one for each factor, that specifies the level of each factor at which that datum was obtained.
		With this information, anova determines the number of factors, the number and names of levels of each factor, and whether a factor is between groups or within groups so that error terms for F- ratios can be chosen.
		anova uses a temporary file to store its input and will complain if it is unable to create it.
	www.acm.org /~perlman/stat/doc/anova.htm (1204 words)

	One-way Anova and Pairwise Comparisons (Site not responding. Last check: 2007-10-13)
		If given a research scenario, be able to use the one-way anova and Tukey’s HSD to test the null hypothesis by hand.
		Determine the significance of the anova by comparing the significance level to the alpha level.
		If given a research scenario, be able to use the one-way anova and Welch t tests with Bonferroni adjusted alpha levels to test the null hypothesis based on the SPSS output.
	www.mtsu.edu /~dkfuller/psy302/studyguide/sganova1.htm (390 words)

	ANOVA (Site not responding. Last check: 2007-10-13)
		ANOVA is used to compare two independent groups.
		It is the numerator for the ANOVA statistic.
		It is the denominator of the ANOVA statistic.
	carbon.cudenver.edu /~lsherry/rem/anova.html (528 words)

	Repeated Measures Anova
		Using a standard ANOVA in this case is not appropriate because it fails to model the correlation between the repeated measures: the data violate the ANOVA assumption of independence.
		ANOVA comparisons between the two groups for this final measure would be most efficient using a repeated measures ANOVA.
		Repeated measures ANOVA carries the standard set of assumptions associated with an ordinary analysis of variance, extended to the matrix case: multivariate normality, homogeneity of covariance matrices, and independence.
	www.ats.ucla.edu /stat/sas/library/repeated_ut.htm (4781 words)

	Factorial ANOVA (including two-way ANOVA)
		For example, one-way ANOVA measures the effect of one independent variable on a dependent variable, and two-way ANOVA measures the effect of two independent variables on the dependent variable.
		In practice, ANOVA with greater than three independent variables is rarely used because of the complexity of interpreting the results.
		The ANOVA results are significant, but there is not a linear trend from left to right with respect to the ‘survey format’ condition.
	www-users.cs.umn.edu /~ludford/Stat_Guide/Factorial_ANOVA.htm (635 words)

	anova
		ANOVA will only indicate a difference between groups, not which group(s) are different.
		ANOVA is incomplete on its own if you have more than two samples.
		The values are used in exactly the same way as the 1-way ANOVA but "Sample" relates to the first factor (hormone), "Columns" relates to the second factor (sex) and "Interaction" relates to the interaction between the two factors.
	www.le.ac.uk /bl/gat/virtualfc/Stats/anova.html (785 words)

	Analysis of Variance (ANOVA)
		Hypothesis testing in ANOVA is about whether the means of the samples differ more than you would expect if the null hypothesis were true.
		In ANOVA, an estimate of variability between groups is compared with variability within groups.
		Also, as with the t test, you assume in ANOVA that all populations have the same variance.
	www.rci.rutgers.edu /~keer/anova1.htm (810 words)

	SPSS Guide \| ANOVA (Analysis of Variance)
		The advantage of the factorial ANOVA is that it also allows you to examine interaction effects between your independent variables.
		There is no need to enter data for repeated measures ANOVA separately from the rest of your data, just be sure to enter it in a way that will help you perform the analysis correctly later on.
		Be sure to include all information for the F-ratios and the follow-up test: the type of ANOVA used, F-values, degrees of freedom (between, error), p-values, all of the means and whether or not the differences were significant.
	academic.reed.edu /psychology/RDDAwebsite/spssguide/anova.html (1851 words)

	Stata help for anova
		This option is rarely needed since the anova command automatically selects the first variable listed in the between-subjects error term as the default for this option.
		This option is rarely needed since the anova command automatically selects the combination of all variables except the first (or as specified in the bseunit() option) in the between-subjects error term as the default for grouping observations.
		The anova command typically displays the ANOVA table, and in those cases, the noanova option suppresses the display.
	www.stata.com /help.cgi?anova (783 words)

	General Linear Models (GLM)
		A common arrangement for ANOVA designs is the full-factorial design, in which every combination of levels for each of the categorical predictor variables is represented in the design.
		But for ANOVA designs with missing cells, Type III sums of squares generally do not test hypotheses about least squares means, but instead test hypotheses that are complex functions of the patterns of missing cells in higher-order containing interactions and that are ordinarily not meaningful.
		The general implication of the theory of estimability of linear functions is that hypotheses which cannot be expressed as linear combinations of the rows of X (i.e., the combinations of observed levels of the categorical predictor variables) are not estimable, and therefore cannot be tested.
	www.statsoft.com /textbook/stglm.html (13045 words)

	Anova Education & Behavior Consultation Home Page
		Anova Education and Behavior Consultation, Inc., is a nonprofit, charitable corporation providing behavioral and educational services in the San Francisco Bay Area and throughout Northern California.
		Anova specializes in providing behavior support services on your local school campus which may include functional analysis assessments, positive behavior intervention plans, and 1:1 behavior support services.
		The mission of Anova Education and Behavior Consultation is to provide practical solutions and services that help individuals to function independently, engage in meaningful relationships with others, and lead an improved quality of life.
	www.anovaeducation.org /Default.asp (158 words)

	ANOVA with Counts and Proportions (Site not responding. Last check: 2007-10-13)
		The basic ANOVA model states that every observation is comprised of a deterministic model for its mean (expectation) and one or more error components.
		The ANOVA assumes that each population has the same dispersion, that there are no dependencies of the observations within or across samples and that the errors have a zero mean.
		Finally, most ANOVA models are additive in the sense that the mean of an observation is comprised of additive main effect and interaction components, plus a zero mean error.
	home.nc.rr.com /schabenb/ANOVACounts.htm (1673 words)

	Single-classification anova: Introduction
		Analysis of variance (anova) is the most commonly used technique for comparing the means of groups of measurement data.
		In a single-classification anova (also known as a one-way anova), there is one measurement variable and one attribute variable.
		If the means are significantly heterogeneous, and you are doing a Model II anova, estimate the variance components (the proportion of variation that is among groups and the proportion that is within groups).
	udel.edu /~mcdonald/statanovaintro.html (1043 words)

	Analysis of variance - Wikipedia, the free encyclopedia
		Fisher in the 1920s and 1930s, and is sometimes known as Fisher's ANOVA or Fisher's analysis of variance, due to the use of Fisher's F-distribution as part of the test of statistical significance.
		One-way ANOVA for repeated measures is used when the subjects are subjected to repeated measures; this means that the same subjects are used for each treatment.
		Factorial ANOVA can also be multi-level such as 3×3, etc. or higher order such as 2×2×2, etc. but analyses with higher numbers of factors are rarely done because the calculations are lengthy and the results are hard to interpret.
	en.wikipedia.org /wiki/ANOVA (1162 words)

	Repeated measures ANOVA
		The degrees of freedom for condition is, as in the between subjects anova, the number of conditions minus 1.
		The obtained F is simply compared to the F crit, which is easily obtained by using the F tables at the back of the book.
		The complexity of repeated measures ANOVA stems largely from the fact that repeated measures ANOVA is quite sensitive to violations of one of the major assumptions of the test.
	courses.washington.edu /stat217/rmANOVA.html (1056 words)

	Assumptions - ANOVA \| QMSS E-Lessons
		Like the t-test, ANOVA is used to test hypotheses about differences in the average values of some outcome between two groups; however, while the t-test can be used to compare two means or one mean against a known distribution, ANOVA can be used to examine differences among the means of several different groups at once.
		More generally, ANOVA is a statistical technique for assessing how nominal independent variables influence a continuous dependent variable.
		This module describes and explains the one-way ANOVA, a statistical tool that is used to compare multiple groups of observations, all of which are independent but may have a different mean for each group.
	ccnmtl.columbia.edu /projects/qmss/anova_about.html (515 words)

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