Pooling Error Terms
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Massachusetts, Amherst, MA 01003 (email: bogartz@psych.umass.edu) On Pooling Error Terms in Repeated Measures Designs Abstract Pooling error terms in repeated measures designs can result in extreme inflation of the Type I error rate or extreme loss
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of power. Using Bartlett's test as a preliminary procedure to protect against the error pooled variance t test terms being too different does not result in protection from such biases. It is shown here that in a repeated measures design pooled standard deviation excel with two repeated measures factors, B and C, even when Bartlett's test is nonsignificant at the .20 level, pooling can still produce an inflated Type I error rate. The results settle the case for avoiding pooling with
Cohen's D
repeated measures and using correct error terms. On Pooling Error Terms in Repeated Measures Designs The purpose of the present paper is to show that pooling error terms in repeated measures designs entails the risk of too many or too few Type I errors and that the suggestions in the literature for testing the homogeneity of these error terms do not adequately cope with the problem. In research on infant cognition
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and perception, infants may be hard to obtain and a high percentage of the infants may be unusable due to fussiness, short attention span, or change of state. Limited availability of research participants occurs in the study of some kinds of impairment, e.g. deafness or Williams syndrome. Investigators shift to repeated measures designs to cope with scarcity of participants, but even then they often have designs with a small number of degrees of freedom for error. Consider a design with two repeated measures variables, B and C. There are three error terms: one for B; one for C; and one for the BC interaction. With low numbers of degrees of freedom, these tests will lack power. This problem has tempted some investigators to pool within participant error terms. In other cases, computer programs have resorted to pooling error terms when data points are missing (e.g. Baillargeon (1987), using SAS with missing data, reports a pooled error term with 126 df when the correct, unpooled error term would have only 22). Pooling is done by adding the sums of squares for two or more error terms and dividing by the sum of their respective degrees of freedom. Such pooling is extremely dangerous. Simulation 1 Table 1 shows the expected mean squares for a design with two repeat
from GoogleSign inHidden fieldsBooksbooks.google.com - This essential textbook is designed for students or researchers in biology who need to design experiments, sampling programs, or t test formula analyze resulting data. The text begins with a revision
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of estimation and hypothesis testing methods, before advancing to the analysis of linear and standard error generalized linear models....https://books.google.com/books/about/Experimental_Design_and_Data_Analysis_fo.html?id=VtU3-y7LaLYC&utm_source=gb-gplus-shareExperimental Design and Data Analysis for BiologistsMy libraryHelpAdvanced Book SearchGet print bookNo eBook availableCambridge University PressAmazon.comBarnes&Noble.com - $55.76 and upBooks-A-Million http://people.umass.edu/~bogartz/on_pooling_error_terms..html - $110.00IndieBoundFind in a libraryAll sellers»Get Textbooks on Google PlayRent and save from the world's largest eBookstore. Read, highlight, and take notes, across web, tablet, and phone.Go to Google Play Now »Experimental Design and Data Analysis for BiologistsGerry P. Quinn, Michael J. KeoughCambridge University https://books.google.com/books?id=VtU3-y7LaLYC&pg=PA260&lpg=PA260&dq=pooling+error+terms&source=bl&ots=czvp5tikiE&sig=Qv1SaG-tDPikLT8q5Ep3-kJfajs&hl=en&sa=X&ved=0ahUKEwjuudPD3-fPAhVElxoKHf6IBooQ6AEIVzAL Press, Mar 21, 2002 - Mathematics - 537 pages 8 Reviewshttps://books.google.com/books/about/Experimental_Design_and_Data_Analysis_fo.html?id=VtU3-y7LaLYCThis essential textbook is designed for students or researchers in biology who need to design experiments, sampling programs, or analyze resulting data. The text begins with a revision of estimation and hypothesis testing methods, before advancing to the analysis of linear and generalized linear models. The chapters include such topics as linear and logistic regression, simple and complex ANOVA models, log-linear models, and multivariate techniques. The main analyses are illustrated with many examples from published papers and an extensive reference list to both the statistical and biological literature is also included. The book is supported by a web-site that provides all data sets, questions for each chapter and links to software. Preview this book » What people are saying-Write a reviewUser
different effects. Consider the analysis of a balanced two-factor study where the common cell count is n. Sum of Squares Degrees of Freedom A a-1 B b-1 AB http://www.jerrydallal.com/lhsp/pool.htm (a-1)(b-1) Residual (n-1)ab Total nab-1 For both sums of squares and degrees of freedom, Total=A+B+AB, that is the total variability in the data set is partitioned into three pieces. One piece https://books.google.com/books?id=8zPRk5xMH7AC&pg=PA6&lpg=PA6&dq=pooling+error+terms&source=bl&ots=hO9-hN4pvg&sig=Fw_LEvQwWXDtbon4Lv21ZSWOxZQ&hl=en&sa=X&ved=0ahUKEwjuudPD3-fPAhVElxoKHf6IBooQ6AEIdjAR describes how the row means differ from each other. Another describes how the column means differ from each other. The third describes the extent to which the row and column effects are t test not additive. Each piece of the variability is associated with a particular piece of the ANOVA model Yijk = + i + j + ( )ij + ij The following dicussion of pooling is an immediate consequence of a few facts. The Total Sum of Squares is unaffected by the model fitted to the data, that is, it is the same regardless of the pooled standard deviation model being used. Any variability the model fails to account for ends up in the Residual Sum of Squares. For this balanced experiment, the sum of squares for each of the treatment effects is the same regardless of whatever other effects are in the model. (This assumes the "usual constraints" are being used to constrain the parameters.) Pooling The idea behind pooling is that any effect that is not statistically significant can be eliminated from the model and the model can be refitted. In that case, the sums of squares and degrees of freedom corresponding to the eliminated terms are added into the residual sum of squares and degrees of freedom. The first question should be, "Why bother?! What does it gain?" Primarly, residual degrees of freedom. This can help if the residual degrees of freedom for the full model is small--less than 10 or 20, say. In most studies, however, this is not an issue. Pooling is a bad idea because the decision whether to pool is based on looking at the data. Any time the decision whether to do something is based on looking at the data,
from GoogleSign inHidden fieldsBooksbooks.google.com - Ergonomics touches every man, woman and child each day of their lives whether they recognise it or not. Ergonomics (or lack of it) plays a more significant role in the lives of about two-thirds of the world s population over 10 years of age who work for one-third of their lives to make a living. There...https://books.google.com/books/about/Advances_in_Occupational_Ergonomics_and.html?id=8zPRk5xMH7AC&utm_source=gb-gplus-shareAdvances in Occupational Ergonomics and SafetyMy libraryHelpAdvanced Book SearchGet print bookNo eBook availableIOS PressAmazon.comBarnes&Noble.comBooks-A-MillionIndieBoundFind in a libraryAll sellers»Get Textbooks on Google PlayRent and save from the world's largest eBookstore. Read, highlight, and take notes, across web, tablet, and phone.Go to Google Play Now »Advances in Occupational Ergonomics and Safety: Proceedings of the XIIIth Annual International Occupational Ergonomics and Safety Conference 1998S. KumarIOS Press, 1998 - Science - 847 pages 0 Reviewshttps://books.google.com/books/about/Advances_in_Occupational_Ergonomics_and.html?id=8zPRk5xMH7ACErgonomics touches every man, woman and child each day of their lives whether they recognise it or not. Ergonomics (or lack of it) plays a more significant role in the lives of about two-thirds of the world s population over 10 years of age who work for one-third of their lives to make a living. There are 120 million occupational accidents and injuries and 200,000 fatalities each year according to WHO 95. Occupational accidents, injuries and fatalities are undesired events. The occupational activities are planned and designed, and executed with a purpose under supervision but accidents are not. Hence it stands to reason that better planning, design and execution will help to reduce these undesirable outcomes. One must also recognise that under global scheme of biological evolution, the human beings were not designed to endure a life lon