Posts Tagged ‘ Statistical Thinking ’

Should you use principal component regression?

October 25, 2017
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This article describes the advantages and disadvantages of principal component regression (PCR). This article also presents alternative techniques to PCR. In a previous article, I showed how to compute a principal component regression in SAS. Recall that principal component regression is a technique for handling near collinearities among the regression

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How to understand weight variables in statistical analyses

October 2, 2017
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How to understand weight variables in statistical analyses

How can you specify weights for a statistical analysis? Hmmm, that's a "weighty" question! Many people on discussion forums ask "What is a weight variable?" and "How do you choose a weight for each observation?" This article gives a brief overview of weight variables in statistics and includes examples of

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Fisher’s transformation of the correlation coefficient

September 20, 2017
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Fisher’s transformation of the correlation coefficient

Pearson's correlation measures the linear association between two variables. Because the correlation is bounded between , the sampling distribution for highly correlated variables is highly skewed. Even for bivariate normal data, the skewness makes it challenging to estimate confidence intervals for the correlation, to run one-sample hypothesis tests ("Is

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Dimension reduction: Guidelines for retaining principal components

August 2, 2017
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Last week I blogged about the broken-stick problem in probability, which reminded me that the broken-stick model is one of the many techniques that have been proposed for choosing the number of principal components to retain during a principal component analysis. Recall that for a principal component analysis (PCA) of

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A quantile definition for skewness

July 19, 2017
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Skewness is a measure of the asymmetry of a univariate distribution. I have previously shown how to compute the skewness for data distributions in SAS. The previous article computes Pearson's definition of skewness, which is based on the standardized third central moment of the data. Moment-based statistics are sensitive to

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Winsorization: The good, the bad, and the ugly

February 8, 2017
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On discussion forums, I often see questions that ask how to Winsorize variables in SAS. For example, here are some typical questions from the SAS Support Community: I want an efficient way of replacing (upper) extreme values with (95th) percentile. I have a data set with around 600 variables and

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Goodness-of-fit tests: A cautionary tale for large and small samples

November 28, 2016
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In the classic textbook by Johnson and Wichern (Applied Multivariate Statistical Analysis, Third Edition, 1992, p. 164), it says: All measures of goodness-of-fit suffer the same serious drawback. When the sample size is small, only the most aberrant behaviors will be identified as lack of fit. On the other hand,

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Sampling variation in small random samples

November 23, 2016
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Somewhere in my past I encountered a panel of histograms for small random samples of normal data. I can't remember the source, but it might have been from John Tukey or William Cleveland. The point of the panel was to emphasize that (because of sampling variation) a small random sample

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