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• Power Analysis in [R] for Two-Way Anova

  - by Thomas

  I am trying to calculate the necessary sample size for a 2x2 factorial design. I have two questions. 1) I am using the package pwr and the one way anova function to calculate the necessary sample size using the following code pwr.anova.test(k = , n = , f = , sig.level = , power = ) However, I would like to look at two way anova, since this is more efficient at estimating group means than one way anova. There is no two-way anova function that I could find. Is there a package or routine in [R] to do this? 2) Moreover, am I safe in assuming that since I am using a one-way anova power calculations, that the sample size will be more conservative (i.e. larger)?

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• Homoscedascity test for Two-Way ANOVA

  - by aL3xa

  I've been using var.test and bartlett.test to check basic ANOVA assumptions, among others, homoscedascity (homogeniety, equality of variances). Procedure is quite simple for One-Way ANOVA: bartlett.test(x ~ g) # where x is numeric, and g is a factor var.test(x ~ g) But, for 2x2 tables, i.e. Two-Way ANOVA's, I want to do something like this: bartlett.test(x ~ c(g1, g2)) # or with list; see latter: var.test(x ~ list(g1, g2)) Of course, ANOVA assumptions can be checked with graphical procedures, but what about "an arithmetic option"? Is that manageable? How do you test homoscedascity in Two-Way ANOVA?

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• ANOVA with 3 fixed factors in R

  - by TKBell

  Im trying to run a model with a response variable p and 3 fixed factors to get ANOVA. this is how my code looks like : #run it as 3 fixed factor model p1=c(37,38,37,41,41,40,41,42,41) p2=c(42,41,43,42,42,42,43,42,43) p3=c(30,31,31,31,31,31,29,30,28) p4=c(42,43,42,43,43,43,42,42,42) p5=c(28,30,29,29,30,29,31,29,29) p6=c(42,42,43,45,45,45,44,46,45) p7=c(25,26,27,28,28,30,29,27,27) p8=c(40,40,40,43,42,42,43,43,41) p9=c(37,38,37,41,41,40,41,42,41) p10=c(35,34,34,35,35,34,35,34,35) p = cbind(p1,p2,p3,p4,p5,p6,p7,p8,p9,p10) partnumber=c(rep(1,9),rep(2,9),rep(3,9),rep(4,9),rep(5,9),rep(6,9),rep(7,9),rep(8,9),rep(9,9),rep(10,9)) test=c(rep(c(rep(1:3,3)),10)) inspector = rep(c(rep(1,3),rep(2,3),rep(3,3)),10) fpartnumber = factor(partnumber) ftest = factor(test) finspector = factor(inspector) model=lm(p~fpartnumber*ftest*finspector) summary(model) anova(model) but when I run it I get this error : it says my variable length for fpartnumber is different , but when I checked the length of each variable and is 90. What is going on ? model=lm(y~fpartnumber*ftest*finspector) Error in model.frame.default(formula = yang ~ fpartnumber * ftest * finspector, : variable lengths differ (found for 'fpartnumber')

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• 2-way anova on unbalanced dataset

  - by mortalitysequence

  Is aov appropriate for unbalanced datasets. According to help ...provides a wrapper to lm for fitting linear models to balanced or unbalanced experimental designs. But later on it says aov is designed for balanced designs, and the results can be hard to interpret without balance. How should I perform a 2-way anova on an unbalanced dataset in R? I would like to reproduce the different results for type I and type III sum of squares of SAS output (when using proc glm). I remember we were using type III sum of squares for unbalanced datasets. Thank you in advance.

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• Homoscedascity test for Two-Way ANOVA

  - by aL3xa

  I've been using var.test and bartlett.test to check basic ANOVA assumptions, among others, homoscedascity (homogeniety, equality of variances). Procedure is quite simple for One-Way ANOVA: bartlett.test(x ~ g) # where x is numeric, and g is a factor var.test(x ~ g) But, for 2x2 tables, i.e. Two-Way ANOVA's, I want to do something like this: bartlett.test(x ~ c(g1, g2)) # or with list; see latter: var.test(x ~ list(g1, g2)) Of course, ANOVA assumptions can be checked with graphical procedures, but what about "an arithmetic option"? Is that, at all, manageable? How do you test homoscedascity in Two-Way ANOVA?

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• R: including model specifications in xtable(anova(...))

  - by HamiltonUlmer

  Hello R comrades: I have a bunch of loglinear models, which, for our purposes will just be glm() objects called mx, my, mz. I want to get a nicely-formatted xtable of the analysis of deviance, so naturally I would want to perform xtable(anova(mx, my, mz, test = "Chisq")). The vanilla output of xtable, however, doesn't include the model specifications. I'd like to include those for all the ANOVA tests I'm running, so if there is not a param I'm missing that does this I'll probably just have to hack up my own solution. But looking over the help page, there doesn't seem to be an easy way to include the model specifications. Any thoughts? Alternatives? If it helps this was done in 2.9.1 with xtable 1.5-5.

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• Anova test in the loop and outputing the p-value in separate column

  - by Juanhijuan

  Once again I'm trying to get an answer. I am already stuck for like 5h with that so that's why I keep trying to get an answer. That's my data: id Sequence variable value 75 AAAAGAAAVANQGKK BiotinControl1_2 3893050.50 192 AAAAGAAAVANQGKK BiotinControl1_2 900604.61 3770 AAFTKLDQVWGSE BiotinControl1_2 90008.14 The code which I am trying to use to calculate the p-value: My Code: tbl_anv <- tbl_all_onlyK[,c("id", "BiotinControl1_2", "BiotinControl2", "BiotinControl3", "BiotinTreatment1_2", "BiotinTreatment2", "BiotinTreatment3", "Sequence")] tbl_reo <- melt(tbl_anv, measure.vars=2:7) set.seed(1) vars <- c("id", "BiotinControl1_2", "BiotinControl2", "BiotinControl3", "BiotinTreatment1_2", "BiotinTreatment2", "BiotinTreatment3", "Sequence") tbl_reo <- as.data.frame(tbl_reo) by(tbl_reo,tbl_reo$Sequence,function(x){ anova(lm(value ~ variable, data = x))$"Pr(>F)"[1] }) An error ocurs: There were 50 or more warnings (use warnings() to see the first 50) Anyway, how can I do that and export the p-value in the separate column. That's what I tried to do on my own: aov_test <- by(tbl_reo,tbl_reo$Sequence,function(x){ anova(lm(value ~ variable, data = x))$"Pr(>F)"[1] }) tbl_reo[,5] <- aov.test[[1]]$'Pr(>F)'[1]

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• Exponential regression : p-value and F significance

  - by Saravanan K

  I am new to statistics. I have a set of independent data and dependent data (X,Y), where I would like to do an exponential regression to obtain its p-value and significant F (already obtained R2 and also the coefficients through mathematical calculation). What is the natural evolution from the (X,Y) data to mathematically calculate those variables. Spent a week on the internet to study this but unable to find the right answer. Often an exponential data, y=be^(mx) will be converted first to a linear data, ln y = mx + ln b . Then a linear regression will done on the converted data, obtaining its p-value etc. Assume we use a statistical tool such as Excel's Analysis ToolPak: Data Analysis : Regression, it will produce a result such as below, I believe the p-value and Significant F value is representing the converted linear data and not the original exponential data. Questions: What is the approach/steps used by Excel to get the p-value and Significant F value for the converted linear data as shown in the statistic output in the image above? It is not clear in their help page or website. Can the p-value and Significant F could be mathematically calculated for exponential regression without using a statistical tool? Can you assist to point me to the right link if this has been answered before.

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• specifying multiple Error in aov

  - by essopapas

  Greetings to all This is my model: aov.fit<-aov(Y~A+B+C+D+E+A:C+A:E, data=dat) In summary(aov.fit) all F values are comptuted by eg MS(A)/MS(Residuals). This is not correct (or what I want), except for F(B) and F(A:E). I suppose P values are not correct either. Can I specify how the F computations will be done? I 'd like them to be like this: F(A)=MS(A)/MS(E), F(C)=MS(C)/MS(E), F(D)=MS(D)/MS(E), F(E)=MS(E)/MS(A:E), F(A:C)=MS(A:C)/MS(A:E) thanks

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• aov define F values computation

  - by essopapas

  Greetings to all This is my model: aov.fit<-aov(Y~A+B+C+D+E+A:C+A:E, data=dat) In summary(aov.fit) all F values are comptuted by eg MS(A)/MS(Residuals). This is not correct (or what I want), except for F(B) and F(A:E). I suppose P values are not correct either. Can I specify how the F computations will be done? I 'd like them to be like this: F(A)=MS(A)/MS(E), F(C)=MS(C)/MS(E), F(D)=MS(D)/MS(E), F(E)=MS(E)/MS(A:E), F(A:C)=MS(A:C)/MS(A:E) thanks

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• SPSS - sum of squares change radically with slight model changes in ANOVA??

  - by Pat

  I have noticed that the sum of squares in my models can change fairly radically with even the slightest adjustment to my models???? Is this normal???? I'm using SPSS 16, and both models presented below used the same data and variables with only one small change - categorizing one of the variables as either a 2 level or 3 level variable. Details - using a 2 x 2 x 6 mixed model ANOVA with the 6 being the repeated measure i get the following in the between group analysis ------------------------------------------------------------ Source | Type III SS | df | MS | F | Sig ------------------------------------------------------------ intercept | 4086.46 | 1 | 4086.46 | 104.93 | .000 X | 224.61 | 1 | 224.61 | 5.77 | .019 Y | 2.60 | 1 | 2.60 | .07 | .80 X by Y | 19.25 | 1 | 19.25 | .49 | .49 Error | 2570.40 | 66 | 38.95 | Then, when I use the exact same data but a slightly different model in which variable Y has 3 levels instead of 2 levels I get the following ------------------------------------------------------------ Source | Type III SS | df | MS | F | Sig ------------------------------------------------------------ intercept | 3603.88 | 1 | 3603.88 | 90.89 | .000 X | 171.89 | 1 | 171.89 | 4.34 | .041 Y | 19.23 | 2 | 9.62 | .24 | .79 X by Y | 17.90 | 2 | 17.90 | .80 | .80 Error | 2537.76 | 64 | 39.65 | I don't understand why variable X would have a different sum of squares simply because variable Y gets devided up into 3 levels instead of 2. This is also the case in the within groups analysis too. Please help me understand :D Thank you in advance Pat

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• NET Math Libraries

  - by JoshReuben

  NET Mathematical Libraries   .NET Builder for Matlab The MathWorks Inc. - http://www.mathworks.com/products/netbuilder/ MATLAB Builder NE generates MATLAB based .NET and COM components royalty-free deployment creates the components by encrypting MATLAB functions and generating either a .NET or COM wrapper around them. .NET/Link for Mathematica www.wolfram.com a product that 2-way integrates Mathematica and Microsoft's .NET platform call .NET from Mathematica - use arbitrary .NET types directly from the Mathematica language. use and control the Mathematica kernel from a .NET program. turns Mathematica into a scripting shell to leverage the computational services of Mathematica. write custom front ends for Mathematica or use Mathematica as a computational engine for another program comes with full source code. Leverages MathLink - a Wolfram Research's protocol for sending data and commands back and forth between Mathematica and other programs. .NET/Link abstracts the low-level details of the MathLink C API. Extreme Optimization http://www.extremeoptimization.com/ a collection of general-purpose mathematical and statistical classes built for the.NET framework. It combines a math library, a vector and matrix library, and a statistics library in one package. download the trial of version 4.0 to try it out. Multi-core ready - Full support for Task Parallel Library features including cancellation. Broad base of algorithms covering a wide range of numerical techniques, including: linear algebra (BLAS and LAPACK routines), numerical analysis (integration and differentiation), equation solvers. Mathematics leverages parallelism using .NET 4.0's Task Parallel Library. Basic math: Complex numbers, 'special functions' like Gamma and Bessel functions, numerical differentiation. Solving equations: Solve equations in one variable, or solve systems of linear or nonlinear equations. Curve fitting: Linear and nonlinear curve fitting, cubic splines, polynomials, orthogonal polynomials. Optimization: find the minimum or maximum of a function in one or more variables, linear programming and mixed integer programming. Numerical integration: Compute integrals over finite or infinite intervals, over 2D and higher dimensional regions. Integrate systems of ordinary differential equations (ODE's). Fast Fourier Transforms: 1D and 2D FFT's using managed or fast native code (32 and 64 bit) BigInteger, BigRational, and BigFloat: Perform operations with arbitrary precision. Vector and Matrix Library Real and complex vectors and matrices. Single and double precision for elements. Structured matrix types: including triangular, symmetrical and band matrices. Sparse matrices. Matrix factorizations: LU decomposition, QR decomposition, singular value decomposition, Cholesky decomposition, eigenvalue decomposition. Portability and performance: Calculations can be done in 100% managed code, or in hand-optimized processor-specific native code (32 and 64 bit). Statistics Data manipulation: Sort and filter data, process missing values, remove outliers, etc. Supports .NET data binding. Statistical Models: Simple, multiple, nonlinear, logistic, Poisson regression. Generalized Linear Models. One and two-way ANOVA. Hypothesis Tests: 12 14 hypothesis tests, including the z-test, t-test, F-test, runs test, and more advanced tests, such as the Anderson-Darling test for normality, one and two-sample Kolmogorov-Smirnov test, and Levene's test for homogeneity of variances. Multivariate Statistics: K-means cluster analysis, hierarchical cluster analysis, principal component analysis (PCA), multivariate probability distributions. Statistical Distributions: 25 29 continuous and discrete statistical distributions, including uniform, Poisson, normal, lognormal, Weibull and Gumbel (extreme value) distributions. Random numbers: Random variates from any distribution, 4 high-quality random number generators, low discrepancy sequences, shufflers. New in version 4.0 (November, 2010) Support for .NET Framework Version 4.0 and Visual Studio 2010 TPL Parallellized – multicore ready sparse linear program solver - can solve problems with more than 1 million variables. Mixed integer linear programming using a branch and bound algorithm. special functions: hypergeometric, Riemann zeta, elliptic integrals, Frensel functions, Dawson's integral. Full set of window functions for FFT's. Product  Price Update subscription Single Developer License $999  $399  Team License (3 developers) $1999  $799  Department License (8 developers) $3999  $1599  Site License (Unlimited developers in one physical location) $7999  $3199    NMath http://www.centerspace.net .NET math and statistics libraries matrix and vector classes random number generators Fast Fourier Transforms (FFTs) numerical integration linear programming linear regression curve and surface fitting optimization hypothesis tests analysis of variance (ANOVA) probability distributions principal component analysis cluster analysis built on the Intel Math Kernel Library (MKL), which contains highly-optimized, extensively-threaded versions of BLAS (Basic Linear Algebra Subroutines) and LAPACK (Linear Algebra PACKage). Product  Price Update subscription Single Developer License $1295 $388 Team License (5 developers) $5180 $1554   DotNumerics http://www.dotnumerics.com/NumericalLibraries/Default.aspx free DotNumerics is a website dedicated to numerical computing for .NET that includes a C# Numerical Library for .NET containing algorithms for Linear Algebra, Differential Equations and Optimization problems. The Linear Algebra library includes CSLapack, CSBlas and CSEispack, ports from Fortran to C# of LAPACK, BLAS and EISPACK, respectively. Linear Algebra (CSLapack, CSBlas and CSEispack). Systems of linear equations, eigenvalue problems, least-squares solutions of linear systems and singular value problems. Differential Equations. Initial-value problem for nonstiff and stiff ordinary differential equations ODEs (explicit Runge-Kutta, implicit Runge-Kutta, Gear's BDF and Adams-Moulton). Optimization. Unconstrained and bounded constrained optimization of multivariate functions (L-BFGS-B, Truncated Newton and Simplex methods).   Math.NET Numerics http://numerics.mathdotnet.com/ free an open source numerical library - includes special functions, linear algebra, probability models, random numbers, interpolation, integral transforms. A merger of dnAnalytics with Math.NET Iridium in addition to a purely managed implementation will also support native hardware optimization. constants & special functions complex type support real and complex, dense and sparse linear algebra (with LU, QR, eigenvalues, ... decompositions) non-uniform probability distributions, multivariate distributions, sample generation alternative uniform random number generators descriptive statistics, including order statistics various interpolation methods, including barycentric approaches and splines numerical function integration (quadrature) routines integral transforms, like fourier transform (FFT) with arbitrary lengths support, and hartley spectral-space aware sequence manipulation (signal processing) combinatorics, polynomials, quaternions, basic number theory. parallelized where appropriate, to leverage multi-core and multi-processor systems fully managed or (if available) using native libraries (Intel MKL, ACMS, CUDA, FFTW) provides a native facade for F# developers

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• ANCOVA in Python with Scipy/Numpy stats

  - by Shax

  I would like to know a way of performing ANCOVA(analysis of covariance) using Python with scipy. It is basically a statistical comparison of regression lines. I know Python can do ANOVA and it can also do regression line fitting with Scipy.stats. I'm not sure how to put those together to get an effective ANCOVA though, if it is possible. Regards, Shax

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• Exporting Stata results

  - by Max M.

  I'm sure this is an issue anyone who uses Stata for publications or reports has run into: how do you conveniently export your output to something that can be parsed by a scripting language or Excel? There are a few ADO files that to this for specific commands (try findit tabout or findit outreg2). But what about exporting the output of the table command? Or the results of an anova? I'd love to hear about how Stata users address this problem for either specific commands or in general.

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• Extreme Optimization Numerical Libraries for .NET – Part 1 of n

  - by JoshReuben

  While many of my colleagues are fascinated in constructing the ultimate ViewModel or ServiceBus, I feel that this kind of plumbing code is re-invented far too many times – at some point in the near future, it will be out of the box standard infra. How many times have you been to a customer site and built a different variation of the same kind of code frameworks? How many times can you abstract Prism or reliable and discoverable WCF communication? As the bar is raised for whats bundled with the framework and more tasks become declarative, automated and configurable, Information Systems will expose a higher level of abstraction, forcing software engineers to focus on more advanced computer science and algorithmic tasks. I've spent the better half of the past decade building skills in .NET and expanding my mathematical horizons by working through the Schaums guides. In this series I am going to examine how these skillsets come together in the implementation provided by ExtremeOptimization. Download the trial version here: http://www.extremeoptimization.com/downloads.aspx Overview The library implements a set of algorithms for: linear algebra, complex numbers, numerical integration and differentiation, solving equations, optimization, random numbers, regression, ANOVA, statistical distributions, hypothesis tests. EONumLib combines three libraries in one - organized in a consistent namespace hierarchy. Mathematics Library - Extreme.Mathematics namespace Vector and Matrix Library - Extreme.Mathematics.LinearAlgebra namespace Statistics Library - Extreme.Statistics namespace System Requirements -.NET framework 4.0  Mathematics Library The classes are organized into the following namespace hierarchy: Extreme.Mathematics – common data types, exception types, and delegates. Extreme.Mathematics.Calculus - numerical integration and differentiation of functions. Extreme.Mathematics.Curves - points, lines and curves, including polynomials and Chebyshev approximations. curve fitting and interpolation. Extreme.Mathematics.Generic - generic arithmetic & linear algebra. Extreme.Mathematics.EquationSolvers - root finding algorithms. Extreme.Mathematics.LinearAlgebra - vectors , matrices , matrix decompositions, solvers for simultaneous linear equations and least squares. Extreme.Mathematics.Optimization – multi-d function optimization + linear programming. Extreme.Mathematics.SignalProcessing - one and two-dimensional discrete Fourier transforms. Extreme.Mathematics.SpecialFunctions

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