# Categorical Methods

• ### Analysis Tool: 2x2 Contingency Table (Version 1)

For a table of frequency data cross-classified according to two categorical variables, X and Y, each of which has two levels or subcategories, this page will calculate the Phi coefficient of association; perform a chi-square test of association, if the sample size is not too small; and perform the Fisher exact probability test, if the sample size is not too large. For intermediate values of n, the chi-square and Fisher tests will both be performed.

• ### Analysis Tool: Normal Distribution

Generate a graphic and numerical display of the properties of the Normal Distribution. For a unit normal distribution, with M=0 and SD=Œ±1, enter 0 and 1 at the prompt. For a distribution with M=100 and SD=Œ±15, enter 100 and 15. And so forth

• ### Law of Large Numbers (Chapter 8)

Part of an online statistics textbook. Topics include: (1) Law of Large Numbers for Discrete Random Variables, (2) Chebyshev Inequality, (3) Law of Averages, (4) Law of Large Numbers for Continuous Random Variables, (5) Monte Carlo Method. There are several examples and exercises that accompany the material.
• ### Family Applet 1

This applet simulates families of three children. The probability of having a boy on any attempt can be changed in the parameter statement. The percantage of times "x" number of girls occurs is updated in the bar chart. There is a 2nd applet on the page that is the same as above, but the families stop having children after the first boy or after they have had 3 girls.
• ### M and M Applet

Students can sample numerous bags of M&Ms. A plot of the relative frequency of each color is continually updated above the sampling frame. Each sample bag of M&Ms contains 56 candies.
• ### Tests of Proportions Applet

In this applet, we simulate a series of hypothesis of tests for the value of the parameter p in a Bernoulli random variable. Each column of red and green marks represents a sample of 30 observations. "Successes'' are coded by green marks and "failures'' by red marks.

• ### HyperStat Online: Ch. 6 Sampling Distributions

This chapter of the HyperStat Online Textbook discusses in detail sampling distributions of various statistics (mean, median, proportions, correlation, etc.), differences between such statistics, the Central Limit Theorem, and standard error, giving formulas, examples, and exercises.

• ### Analysis Tool: Log-Linear Analysis for an AxBxC Contingency Table

Log-linear analysis is a version of chi-square analysis in which the relevant values are calculated by way of weighted natural logarithms. This page will calculate several values of G^2.

• ### Analysis Tool: The Power of the Chi-Square Goodness of Fit Test (Monte Carlo Simulation)

In the first simulation, random samples of size n are drawn from the population one sample at a time. With df=3, the critical value of chi-square for significance at or beyond the 0.05 level is 7.815; hence, any calculated value of chi-square equal to or greater than 7.815 is recorded as "significant," while any value smaller than that is noted as "non-significant." The second simulation does the same thing, except that it draws random samples 100 at a time. The Power of the Chi-Square "Goodness of Fit" Test pertains to the questionable common practice of accepting the null hypothesis upon failing to find a significant result in a one- dimensional chi-square test.

• ### 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.