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9.6: General summary

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    As we wrap up, it is important to remember that these tools are limited by the quality of the data collected. If you are ever involved in applying these statistical models, whether in a research or industrial setting, make sure that the research questions are discussed before data collection. And before data collection is started, make sure that the methods will provide results that can address the research questions. And, finally, make sure someone involved in the project knows how to perform the appropriate graphical and statistical analysis. One way to make sure you know how to analyze a data set and, often, clarify the research questions and data collection needs, is to make a simulated data set that resembles the one you want to collect and analyze it. This can highlight the sorts of questions the research can address and potentially expose issues before the study starts. With this sort of preparation, many issues can be avoided. Remember to think about reasons why assumptions of your proposed method might be violated.

    You are now armed and a bit dangerous with statistical methods. If you go to use them, remember the fundamentals and find the story in the data. After deciding on any research questions of interest, graph the data and make sure that the statistical methods will give you results that make some sense based on the graphical results. In the MLR results, it is possible that graphs will not be able to completely tell you the story, but all the other methods should follow the pictures you see. Even when (or especially when) you use sophisticated statistical methods, graphical presentations are critical to helping others understand the results. We have discussed examples that involve displaying categorical and quantitative variables and even some displays that bridge both types of variables. We hope you have enjoyed this material and been able to continue to develop your interests in statistics. You will see it in many future situations both in courses in your area of study and outside of academia to try to address problems that need answers. You are also prepared to take more advanced statistics courses.

    References

    Benson, Roger B. J., and Philip D. Mannion. 2012. “Multi-Variate Models Are Essential for Understanding Vertebrate Diversification in Deep Time.” Biology Letters 8: 127–30. https://doi.org/10.1098/rsbl.2011.0460.
    Gundale, Michael J., Lisbet H. Bach, and Annika Nordin. 2013. “The Impact of Simulated Chronic Nitrogen Deposition on the Biomass and N2-Fixation Activity of Two Boreal Feather Moss–Cyanobacteria Associations.” Biology Letters 9 (6). https://doi.org/10.1098/rsbl.2013.0797.
    Pinheiro, José, Douglas Bates, and R Core Team. 2022. Nlme: Linear and Nonlinear Mixed Effects Models. https://svn.r-project.org/R-packages/trunk/nlme/.
    Puhan, Milo A, Alex Suarez, Christian Lo Cascio, Alfred Zahn, Markus Heitz, and Otto Braendli. 2006. “Didgeridoo Playing as Alternative Treatment for Obstructive Sleep Apnoea Syndrome: Randomised Controlled Trial.” BMJ 332 (7536): 266–70. https://doi.org/10.1136/bmj.38705.470590.55.
    Sasaki, Takao, and Stephen C. Pratt. 2013. “Ants Learn to Rely on More Informative Attributes During Decision-Making.” Biology Letters 9 (6). https://doi.org/10.1098/rsbl.2013.0667.
    1. The researchers did not do this analysis so never directly addressed this research question although they did discuss it in general ways.↩︎
    2. Instructors often get asked what a problem with non-constant variance actually looks like – this is a perfect example of it!↩︎
    3. This was not even close to their top AIC model so they made an odd choice.↩︎
    4. I had students read this paper in a class and one decided that this was a reasonable way to report small p-values – it is WRONG. We are interested in how small a p-value might be and saying it is over a value is never useful, especially if you say it is larger than a tiny number.↩︎
    5. All too often, I read journal articles that have under-utilized, under-reported, mis-applied, or mis-interpreted statistical methods and results. One of the reasons that I wanted to write this book was to help more people move from basic statistical knowledge to correct use of intermediate statistical methods and beginning to see the potential in more advanced statistical methods. It took me many years of being a statistician (after getting a PhD) just to feel armed for battle when confronted with new applications and two stat courses are not enough to get you there, but you have to start somewhere. You are only maybe two or three hundred hours into your 10,000 hours required for mastery. This book is intended get you some solid fundamentals to build on or a few intermediate tools to use if this is your last statistics training experience.↩︎
    6. They also had an error in their AIC results that is difficult to explain here but was due to an un-careful usage of the results from the more advanced models that account for autocorrelation, which seems to provide the proper ranking of models (that they ignored) but did not provide the correct differences among models.↩︎

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