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Estimation Principles

  • A song for use in helping students identify examples of biased (like the range) and unbiased (like the mean) estimators.  Lyrics © 2015 by Larry Lesser, music by Dominic Dousa. 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).

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  • A song for use in helping students apply margin of error in the context of a poll question, including that variability decreases with the square root of the sample size.  Lyrics & Music © 2015 Lawrence M. Lesser. 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).

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  • A song for use in helping students to reason about the factors that affect the width of a confidence interval (sample size, confidence level, and population standard deviation).  Lyrics by Larry Lesser and music by Dominic Sousa in 2015, both 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).

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  • A song that can be used in discussing the standard deviation of p-hat and how to estimate it in making confidence intervals. 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 1972 hit “I Can See Clearly Now,” by Johnny Nash. Also, an accompanying video may be found at https://www.youtube.com/watch?v=1a2e2O0o0lg

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  • A song that may be used in discussing the meaning and interpretation of the confidence level for a confidence interval. 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 Beatles 1965 hit song Can’t Buy Me Love, written by Paul McCartney. Also, an accompanying video may be found at
    https://www.youtube.com/watch?v=vc6gJAm3cMY

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  • A short story that might be used as an out-of-class assignment to facilitate understanding the interpretation of a 95% confidence interval as a random interval that is expected to cover the true parameter in 95% of all samples. The story was written in 2011 by Canadian mathematician Robert Dawson from Saint Mary's University in Halifax Nova Scotia. The story was published as a two part series at www.Lablit.com
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  • A quote that might be used in a discussion of why uncertainty is greatest when the probability of success is close to 50% (and also amenable to more study). The quote is by American author and Professor of Psychiatry Judith M Bardwick (1933 - ) from her book Danger in the Comfort Zone (1995). The quote may also be found at www.quotationsbywomen.com
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  • A song about the different assumptions needed for parametric statistical methods and the importance of checking how well they hold and what effect they may have on the results and conclusions. The lyrics were written in 2017 by Dennis K. Pearl from Penn State University and may be sung to the tune of "Every Breath You Take" written by Sting and made popular by The Police on their 1983 album "Synchronicity."
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  • This is a youtube video by Jeremy Balka that was published in May 2013. The video presents a discussion of the assumptions when using the t distribution in constructing a confidence interval for the population mean. By considering various population distributions, the effect of different violations of the normality assumption is investigated through simulation.
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  • This is an e-book tutorial for R. It is organized according to the topics usually taught in an Introductory Statistics course. Topics include: Qualitative Data; Quantitative Data; Numerical Measures; Probability Distributions; Interval Estimation; Hypothesis Testing; Type II Error; Inference about Two Populations; Goodness of Fit; Analysis of Variance; Non-parametric methods; Linear Regression; and Logistic Regression.
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