# Joint

• ### Chebychev's Estimate

For n = 50 to 400, in steps of size 5, this program computes and displays (1) the exact probability P(|A_n - p| >= epsilon), where A_n is the average outcome of n Bernoulli trials with probability p of success, and (2) the Chebyshev estimate p(1-p)/(n(epsilon^2)) for this probability. You can specify p and epsilon.
• ### Statistical Methods in Biomedical Imaging

These lecture notes are composed of nearly 180 PowerPoint slides that have been coverted to a pdf file (6 per page) on Biomedical Imaging. The following topics are outlined: Vocabulary, Displaying Data, Central Tendency and Variability, Normal Z-scores, Standardized Distribution, Probability, Samples & Sampling Error, Type I and Type II Errors, Power of a Test, Hypothesis Testing, One Sample Tests, Two Independent Sample Tests, Two Dependent Sample Tests & Estimation, Correlation and Regression Techniques, Non-Parametric Statistical Tests, Applications of Central Limit Theorem, Law of Large Numbers, Design of Studies and Experiments, Fisher's F-Test, Analysis Of Variance(ANOVA), Principle Component Analysis (PCA), Chi-Square Goodness-of-fit test, Multiple Linear Regression, General Linear Model, Bootstrapping and Resampling.
• ### Analysis Tool: Basic Linear Correlation and Regression (Direct-Entry Version)

The following pages calculate r, r-squared, regression constants, Y residuals, and standard error of estimate for a set of N bivariate values of X and Y, and perform a t-test for the significance of the obtained value of r. Values of X and Y are entered directly into individual data cells. This page will also work with samples of any size, though it will be rather unwieldy with samples larger than about N=50. As the page opens, you will be prompted to enter the value of N.

• ### Analysis Tool: Friedman Test for k = 3

Nonparametric test for the significance of the difference among the distributions of k correlated samples (A, B, etc., each of size n) involving repeated measures or matched sets. As the page opens, you will be prompted to enter the value of n. The necessary rank- ordering of your raw data will be performed automatically.

• ### Analysis Tool: Friedman Test for k = 4

Nonparametric test for the significance of the difference among the distributions of k correlated samples (A, B, etc., each of size n) involving repeated measures or matched sets. As the page opens, you will be prompted to enter the value of n. The necessary rank- ordering of your raw data will be performed automatically.

• ### Analysis Tool: Kruskal-Wallis Test for K = 3

As the page opens, you will be prompted to enter the sizes of your several samples. If you are starting out with raw (unranked) data, the necessary rank- ordering will be performed automatically.

• ### Analysis Tool: Kruskal-Wallis Test for K = 4

As the page opens, you will be prompted to enter the sizes of your several samples. If you are starting out with raw (unranked) data, the necessary rank- ordering will be performed automatically.

• ### Analysis Tool: 4x4 Orthogonal Latin Square with Restricted Full Rank Model (One Measure per Cell)

In the Latin Square computational pages on this site, the third IV, with levels designated as A, B, C, etc., is listed as the "treatment" variable. The analysis of variance within an orthogonal Latin Square results in three F-ratios: one for the row variable, one for the column variable, and one for the third IV whose j levels are distributed orthogonally among the cells of the rows x columns matrix.

• ### Analysis Tool: 5x5 Orthogonal Latin Square for Restricted Full Rank Model (One Measure per Cell)

In the Latin Square computational pages on this site, the third IV, with levels designated as A, B, C, etc., is listed as the "treatment" variable. The analysis of variance within an orthogonal Latin Square results in three F-ratios: one for the row variable, one for the column variable, and one for the third IV whose j levels are distributed orthogonally among the cells of the rows x columns matrix.

• ### Analysis Tool: Simple Logistic Regression

This page has two calculators. One will cacluate a simple logistic regression, while the other calculates the predicted probability and odds ratio. There is also a brief tutorial covering logistic regression using an example involving infant gestational age and breast feeding. Please note, however, that the logistic regression accomplished by this page is based on a simple, plain-vanilla empirical regression.