Significance Testing Principles

  • This site explains small sample hypothesis testing for a normal population and hypothesis testing for a population proportion. Includes examples and exercises.
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  • This site focuses on using the LRT to compare two competing models.
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  • Using the Fisher r-to-z transformation, this page will calculate a value of z that can be applied to assess the significance of the difference between two correlation coefficients, r_a and r_b, found in two independent samples. If r_a is greater than r_b, the resulting value of z will have a positive sign; if r_a is smaller than r_b, the sign of z will be negative.

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  • 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.

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  • This page will compute the t-test for either correlated or independent samples. One may copy and paste data in or type the data in individually.

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  • 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.
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  • 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".
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  • This page discusses the understanding of and interpretation of p-values for those who read articles with statistical information.
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  • This site defines power and explains what factors may affect it, such as significance level, sample size and variance.

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  • This resource defines what a p-value is, why .05 is significant, and when to use it. It also covers related topics such as one-tailed/two-tailed tests and hypothesis testing.
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