Wald statistic Definition 1: For any logistic regression coefficient b whose standard error is seb, the Wald statistic is given by the formula Wald = b/seb Since the Wald statistic is approximately normal, by Property 3 of Chi-Square Distribution, Wald2 is approximately chi-square, and, in fact, Wald2 ~ χ2(df). Here df = k – k0 where k = the … Read More
Basic Concepts In Example 1 of Multiple Regression Analysis we used 3 independent variables: Infant Mortality, White, and Crime, and found that the regression model was a significant fit for the data. We also commented that the White and Crime variables could be eliminated from the model without significantly impacting the accuracy of the model. … Read More
We now show how to test the value of the slope of the regression line. Basic Approach By Theorem 1 of One Sample Hypothesis Testing for Correlation, under certain conditions, the test statistic t has the property But by Property 1 of Method of Least Squares and by Definition 3 of Regression Analysis and Property … Read More
In Dealing with Familywise Error, we describe some approaches for handling familywise errors. We now show how to apply these techniques when multiple t-tests are performed. Example Example 1: A school district uses four different methods of teaching their students how to read and wants to find out if there is a significant difference between … Read More
Basic Concepts The Kendall-Theil-Sen estimator is a non-parametric method for fitting a line to a set of points (x1, y1), …, (xn, yn). It is a robust method in that it provides a better fitting line when the data contains outliers compared to ordinary least-squares regression. It also doesn’t require that the residuals are normally … Read More
Basic Concepts When a time series x1 , …, xn contains only binary values, 0’s and 1’s, then we can use a change point test based on the two-sample Kolmogorov-Smirnov test. Such a time series can occur, for example, when xi = 1 if the stock market went up on day i and xi = … Read More
Basic Concepts The Siegel-Tukey test (for equal variability) is a nonparametric test to determine whether two samples come from populations with equal variances. When data is clearly normally distributed, a parametric test is preferred. Assumptions: The two (random) samples are independent The data is at least ordinal The two populations have the same medians If … Read More
Basic Concepts Somers’ d statistic is a measure of (asymmetric) association. d takes values between -1 and 1. A value of 1 or -1 means that the independent variable perfectly predicts the dependent variable: +1 when the relationship is positive and -1 when the relationship is negative. A value of 0 means that there is … Read More
Basic Concepts TC is the average of Kendall’s rank-order correlation coefficient between each judge and the criterion ranking. To calculate TC, first, create a preference matrix P = [aij] as described in Kendall’s u for Paired Rankings. TC can be calculated via any of the following equivalent formulas where k = the number of judges, … Read More
Basic Concepts We can also use Kendall’s u (as described in Kendall’s u for Paired Comparisons) when the data are based on ranks, although the significance test for agreement is different. Note that the minimum value for u is -1/(k-1) when k is even and -1/k when k is odd. We often prefer an agreement … Read More