# Significance Testing Principles

• ### Analysis Tool: Distribution of Cohen's d, p-values, and power curves for an independent two-tailed t-test (Shiny App)

Plot the theoretical p-value distribution and power curve for an independent t-test based on the effect size, sample size, and alpha.

• ### Analysis Tool: Vovk-Sellke Maximum p-Ratio (Shiny App)

Explore the Vovk-Sellke Maximum p-Ratio, a measure that indicates the maximum diagnosticity of a given p-value. Choose your own p-value to find out how diagnostic it is for your research!

• ### Song: A Fitting Conclusion

A song for use in helping students to apply relationships among alpha, p-value, and the decision of a hypothesis test.  Music & Lyrics © 2015 by Lawrence M. Lesser from The University of Texas at El Paso.  This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smiles for the interactive version of the song, a short reading covering the topic, and an assessment item).

• ### STatistics Education Web (STEW)

Statistics and probability concepts are included in K–12 curriculum standards—particularly the Common Core State Standards—and on state and national exams. STEW provides free peer-reviewed teaching materials in a standard format for K–12 math and science teachers who teach statistics concepts in their classrooms.

STEW lesson plans identify both the statistical concepts being developed and the age range appropriate for their use. The statistical concepts follow the recommendations of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework, Common Core State Standards for Mathematics, and NCTM Principles and Standards for School Mathematics. The lessons are organized around the statistical problemsolving process in the GAISE guidelines: formulate a statistical question, design and implement a plan to collect data, analyze the data by measures and graphs, and interpret the data in the context of the original question. Teachers can navigate the STEW lessons by grade level and statistical topic.

• ### Analysis Tool(s): JSE Archive of Interactive Computing (includes JAVA Applets)

The Journal of Statistics Education provides a collection of Java applets and excel spreadsheets (and the articles associated with them) from as early as 1998 on this webpage.

• ### Song: Type II Error

A song that can be used in discussing the meaning and interpretation of Type II error in Significance Testing. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of “Barbara Ann,” written by Fred Fassert in 1961 and popularized by the Beach Boys in 1965. Also, an accompanying video may be found at

• ### Song: Type I Error

A song that can be used in discussing the meaning and interpretation of Type I error in Significance Testing. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of “We Will Rock You,” written by Brian May and recorded by Queen in 1977. Also, an accompanying video may be found at

• ### Song: Statistically Significant

A song to aid in discussing the interpretation of statistical significance as being unlikely to happen by chances computed under the null. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of the “Star Spangled Banner.” Also, an accompanying video may be found at