# Non-symbolic math

• ### Analysis Tool: Bayes' Theorem and "Adjustment of Subjective Confidence"

An application of Bayes Theorem that performs the same calculations for the situation where the several probabilities are constructed as indices of subjective confidence.

• ### Analysis Tool: Binomial Distribution

This page will generate a graphic and numerical display of the properties of a binomial sampling distribution, for any values of p and q, and for values of n between 1 and 40, inclusive.

• ### Analysis Tool: Chi-Square "Goodness of Fit"

This page will calculate the value of chi-square for a one- dimensional "goodness of fit" test, for up to 8 mutually exclusive categories labeled A through H. To enter an observed cell frequency, click the cursor into the appropriate cell, then type in the value. Expected values can be entered as either frequencies or proportions. Toward the bottom of the page is an option for estimating the relevant probability via Monte Carlo simulation of the multinomial sampling distribution.

• ### Analysis Tool: Pascal (Negative Binomial) Probabilities (For Sequential Sampling)

For a situation in which independent binomial events are randomly sampled in sequence, this page will calculate (a) the probability that you will end up with exactly k instances of the outcome in question, with the final (kth) instance occurring on trial N; and (b) the probability that you will have to sample at least N events before finding the kth instance of the outcome.

• ### Analysis Tool: The Confidence Interval of rho (Multiple Regression)

This page will calculate the 0.95 and 0.99 confidence intervals for rho, based on the Fisher r-to-z transformation. To perform the calculations, enter the values of r and n in the designated places, then click the "Calculate" button. Note that the confidence interval of rho is symmetrical around the observed r only with large values of n.

• ### Analysis Tool: Estimating the Population Value of rho

This page will perform the procedure for up to k=12 sample values of r, with a minimum of k=2. It will also perform a chi-square test for the homogeneity of the k values of r, with df=k-1. The several values of r can be regarded as coming from the same population only if the observed chi-square value proves the be non-significant.

• ### Confidence Intervals

This resource assists the user in reading, constructing, and understanding confidence intervals.
• ### Statistical Significance

This article may help the user understand the concept of statistical significance and the meaning of the numbers produced by The Survey System. This article is presented in two parts. The first part simplifies the concept of statistical significance as much as possible; so that non-technical readers can use the concept to help make decisions based on their data. The second part provides more technical readers with a fuller discussion of the exact meaning of statistical significance numbers.
• ### Significance Level

This resource briefly explains what a significance level is and how they are used in hypothesis testing. It also includes other links related to significance level such as "Type I error" and "significance test".
• ### Interpreting Statistical p-values

This page discusses the understanding of and interpretation of p-values for those who read articles with statistical information.