 # StatNotes: Topics in Multivariate Analysis, from North Carolina Wiki: Statistical Methods Basic statistics help: Correspondence Analysis Factor Analysis Some nice explanations: KMO and Bartlett's Test of Sphericity (Factor Analysis) The Kaiser-Meyer-Olkin measure of sampling adequacy tests whether the partial correlations among variables are small. Bartlett's test of sphericity tests whether the correlation matrix is an identity matrix, which would indicate that the factor model is inappropriate. -- from the SPSS on-line help. Path Analysis Structural Equation Modeling Software, including AMOS (which looks good, but kind of expensive): have been seeing several papers (both as a reviewer and as a reader of published work) that use AMOS for CFA, path analysis, or SEM models. Hi Matthew, Thanks very much for sending me the messages on the CRTNET listserv related to Amos. If any CRTNET members want to follow up, please ask them to get in touch with me at ggwebm@amosdevelopment.com.

Elementary Concepts in Statistics In this introduction, we will briefly discuss those elementary statistical concepts that provide the necessary foundations for more specialized expertise in any area of statistical data analysis. The selected topics illustrate the basic assumptions of most statistical methods and/or have been demonstrated in research to be necessary components of our general understanding of the "quantitative nature" of reality (Nisbett, et al., 1987). We will focus mostly on the functional aspects of the concepts discussed and the presentation will be very short. What are Variables? Variables are things that we measure, control, or manipulate in research. Correlational vs. Most empirical research belongs clearly to one of these two general categories. Dependent vs. Independent variables are those that are manipulated whereas dependent variables are only measured or registered. Measurement Scales Nominal variables allow for only qualitative classification. Relations between Variables .005 or p

Treatment of Missing Sata David C. Howell Missing data are a part of almost all research, and we all have to decide how to deal with it from time to time. I am in the process of revisng this page by breaking it into at least two pages. If your interest is in missing data in a repeated measures ANOVA , you will find useful material at Models for Repeated Measures.pdf . 1.1 The nature of missing data Missing completely at random There are several reasons why data may be missing. Notice that it is the value of the observation, and not its "missingness," that is important. This nice feature of data that are MCAR is that the analysis remains unbiased. Missing at random Often data are not missing completely at random, but they may be classifiable as missing at random (MAR). The phraseology is a bit awkward here because we tend to think of randomness as not producing bias, and thus might well think that Missing at Random is not a problem. An Example

Cluster Analysis R has an amazing variety of functions for cluster analysis. In this section, I will describe three of the many approaches: hierarchical agglomerative, partitioning, and model based. While there are no best solutions for the problem of determining the number of clusters to extract, several approaches are given below. Data Preparation Prior to clustering data, you may want to remove or estimate missing data and rescale variables for comparability. # Prepare Data mydata <- na.omit(mydata) # listwise deletion of missing mydata <- scale(mydata) # standardize variables Partitioning K-means clustering is the most popular partitioning method. # Determine number of clusters wss <- (nrow(mydata)-1)*sum(apply(mydata,2,var)) for (i in 2:15) wss[i] <- sum(kmeans(mydata, centers=i)\$withinss) plot(1:15, wss, type="b", xlab="Number of Clusters", ylab="Within groups sum of squares") A robust version of K-means based on mediods can be invoked by using pam( ) instead of kmeans( ). Hierarchical Agglomerative

Reliability Analysis: Statnotes, from North Carolina State Unive This content is now available from Statistical Associates Publishers. Click here. Below is the overview and table of contents in unformatted form. Overview Researchers must demonstrate instruments are reliable since without reliability, research results using the instrument are not replicable, and replicability is fundamental to the scientific method. Метод на най-малките квадрати » Физичен практикум Експерименталните данни често се придружават от някакъв шум. Дори да успеем да постигнем точни и постоянни стойности на контролните величини, измерените резултантни величини винаги варират. Необходим е процес, известен като регресия или пасване на крива, за получаване количествена оценка на тенденцията на измерените експериментални величини. В процеса на пасване на крива се избира такава крива, която да дава добро приближение с експерименталните данни. Изобщо казано, през даден набор от експериментални точки може да се прекарат повече от една крива. Ние ще търсим такава крива, която има минимално отклонение (девиация) за всички точки. Идеята на метода е проста. където са стойностите на контролната величина, са съответните измерени стойности на резултатната величина, а е избраната функционална зависимост, която трябва да бъде пасната. Тук ще се спрем на случая на линейна зависимост между една независима контролна величина и една резултатна величина, т.е. тя има вида: от вида: . , където

Partial Least Squares Regression (PLSR) Welcome to the Partial Least Squares Regression (PLSR) start the program mirror connection PLSR statistical analysis module performs model construction and prediction of activity/property using the Partial Least Squares (PLS) regression technique [1-3]. It is well known that Partial Least Squares (PLS) regression is quite sensitive to the noise created by the excessive irrelevant descriptors. The same code base is successfully employed in software implementing the Molecular Field Topology Analysis (MFTA) technique proposed by us  for QSAR studies of organic compounds. This software was developed by E.V. References Martens H., Naes T. Partial Least Squares (PLS) This topic describes the use of partial least squares regression analysis. If you are unfamiliar with the basic methods of regression in linear models, it may be useful to first review this information in Elementary Concepts. The different designs discussed in this topic are also described in General Linear Models, Generalized Linear Models, and General Stepwise Regression. Basic Ideas Partial least squares regression is an extension of the multiple linear regression model (see, e.g., Multiple Regression or General Stepwise Regression). Y = b0 + b1X1 + b2X2 + ... + bpXp In this equation b0 is the regression coefficient for the intercept and the bi values are the regression coefficients (for variables 1 through p) computed from the data. So for example, you could estimate (i.e., predict) a person's weight as a function of the person's height and gender. The multiple linear regression model has been extended in a number of ways to address more sophisticated data analysis problems. Overview.

PLS User Guide 1. Introduction. 2 2. 3. 4. 5. 5.1. 5.2. 5.3. 5.4. 5.5. 5.6. 5.7. 5.8. 6. 7. 7.1. 7.1.1. 7.1.2. 7.1.3. 7.1.4. 7.1.5. 7.1.6. 7.1.7. 7.1.8. 7.1.9. 7.1.10. 7.2. 7.3. 7.4. 7.4.1. 7.4.2. 7.4.3. 7.4.4. 7.4.5. 7.5. 7.5.1. 7.5.2. 7.5.3. 7.5.4. 7.5.5. 8. 8.1. 9. 9.1. 9.2. 9.3. 9.4. 9.5. 9.6. 9.7. 9.8. 9.9. 9.10. 9.11. 10. 10.1. 10.1.1. 10.1.2. fMRI Experiment 72 10.2. 10.3. 11. 12. Partial Least Squares (PLS), which was first introduced to the neuroimaging community in 1996 (McIntosh et al., 1996), has proven to be a robust method for describing the relationship between signal changes in brain and a set of exogenous variables (i.e. task demands, performance, or activity in other brain regions). PLS Applications include a Graphic User Interface - GUI application and a Command-Line computation application. If you would like to use GUI interface, path to plsgui folder must be manually added in MATLAB command window. Here are the links to some useful web pages for PLS Applications: Figure 1 5.1. 5.2.

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