Difference between revisions of "FND-STA-Significance"

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Deriving probability distributions from simulation, interpreting in terms of significance thresholds
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Probability and p-values; significance as a threshold of p-values; deriving probability distributions from simulation and interpreting in terms of significance.
 
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== Abstract ==
 
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The probability of an event is the chance of it occurring, but how do we relate that to the question whether an observation is significant? In this context we talk about ''p''-values and the meaning of a ''p''-value is not the same as the probability of an observation. The ''p''-value of an observation is the probability that - assuming a null hypothesis is true - an event as extreme or more extreme is observed. This unit contains R code to study this concept.
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=== Objectives ===
 
=== Objectives ===
 
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...
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* Introduce the difference between ''p''-values and event probability;
 +
* Show how we interpret ''p''-values in terms of "significance";
 +
* Illustrate this with an example;
 +
* Present a permutation example, a strategy that can be used as an alternative to the integration of probability density functions.
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* Discuss a common error that is made when establishing the significance of an observation in the biomedical sciences.
  
 
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=== Outcomes ===
 
=== Outcomes ===
 
<!-- included from "../components/FND-STA-Significance.components.wtxt", section: "outcomes" -->
 
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;After working thorugh this unit you should...
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* Be able to define a "''p''-value";
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* Be able to set up a permutation test or a sampling simulation to estimate a probability density;
 +
* Be able to interpret the frequency of values in that probability density in terms of a ''p''-value;
 +
* Be able to critically assess whether an observation should be considered "significant" in that context;
 +
* Be able to identify a common error that is made in the literature when two effects are compared.
  
 
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*<b>Time management</b>: Before you begin, estimate how long it will take you to complete this unit. Then, record in your course journal: the number of hours you estimated, the number of hours you worked on the unit, and the amount of time that passed between start and completion of this unit.
 
*<b>Time management</b>: Before you begin, estimate how long it will take you to complete this unit. Then, record in your course journal: the number of hours you estimated, the number of hours you worked on the unit, and the amount of time that passed between start and completion of this unit.
 
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*<b>Journal</b>: Document your progress in your [[FND-Journal|course journal]].
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*<b>Journal</b>: Document your progress in your [[FND-Journal|Course Journal]]. Some tasks may ask you to include specific items in your journal. Don't overlook these.
 
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*<b>Insights</b>: If you find something particularly noteworthy about this unit, make a note in your [[ABC-Insights|insights! page]].
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*<b>Insights</b>: If you find something particularly noteworthy about this unit, make a note in your [[ABC-Insights|'''insights!''' page]].
  
 
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== Contents ==
 
== Contents ==
 
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=== "Significance" concepts ===
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{{R-unit|FND-STA-Significance}}
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{{Vspace}}
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=== Controversies ===
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{{task|1=
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Examine the papers below that introduce difficulties with P-values and statistical significance. Rephrase the issues in your own words to make sure that you understand what the discussion is about.
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}}
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{{#pmid: 26961635}}
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{{#pmid: 21878926}}
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== Further reading, links and resources ==
 
== Further reading, links and resources ==
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<!-- {{#pmid: 19957275}} -->
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{{DOI
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|authors= Duncan J Murdoch, Yu-Ling Tsai & James Adcock
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|year= 2008
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|title= P-Values are Random Variables
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|journal= The American Statistician
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|volume= 62:3
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|pages= 242-245
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|URL=
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|doi = 10.1198/000313008X332421
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|file= Zhang(2012)StructurePrediction.pdf
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|abstract= ''P''-values are taught in introductory statistics classes in a way that confuses many of the students, leading to common misconceptions about their meaning. In this article, we argue that ''p''-values should be taught through simulation, emphasizing that ''p''-values are random variables. By means of elementary examples we illustrate how to teach students valid interpretations of ''p''-values and give them a deeper understanding of hypothesis testing.
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Revision as of 19:50, 6 September 2017

Significance


 

Keywords:  Probability and p-values; significance as a threshold of p-values; deriving probability distributions from simulation and interpreting in terms of significance.


 



 


 


Abstract

The probability of an event is the chance of it occurring, but how do we relate that to the question whether an observation is significant? In this context we talk about p-values and the meaning of a p-value is not the same as the probability of an observation. The p-value of an observation is the probability that - assuming a null hypothesis is true - an event as extreme or more extreme is observed. This unit contains R code to study this concept.


 


This unit ...

Prerequisites

You need to complete the following units before beginning this one:


 


Objectives

  • Introduce the difference between p-values and event probability;
  • Show how we interpret p-values in terms of "significance";
  • Illustrate this with an example;
  • Present a permutation example, a strategy that can be used as an alternative to the integration of probability density functions.
  • Discuss a common error that is made when establishing the significance of an observation in the biomedical sciences.


 


Outcomes

After working thorugh this unit you should...
  • Be able to define a "p-value";
  • Be able to set up a permutation test or a sampling simulation to estimate a probability density;
  • Be able to interpret the frequency of values in that probability density in terms of a p-value;
  • Be able to critically assess whether an observation should be considered "significant" in that context;
  • Be able to identify a common error that is made in the literature when two effects are compared.


 


Deliverables

  • Time management: Before you begin, estimate how long it will take you to complete this unit. Then, record in your course journal: the number of hours you estimated, the number of hours you worked on the unit, and the amount of time that passed between start and completion of this unit.
  • Journal: Document your progress in your Course Journal. Some tasks may ask you to include specific items in your journal. Don't overlook these.
  • Insights: If you find something particularly noteworthy about this unit, make a note in your insights! page.


 


Evaluation

Evaluation: NA

This unit is not evaluated for course marks.


 


Contents

"Significance" concepts

Template:R-unit


 

Controversies

Task:
Examine the papers below that introduce difficulties with P-values and statistical significance. Rephrase the issues in your own words to make sure that you understand what the discussion is about.

Baker (2016) Statisticians issue warning over misuse of P values. Nature 531:151. (pmid: 26961635)

[ PubMed ] [ DOI ]

Nieuwenhuis et al. (2011) Erroneous analyses of interactions in neuroscience: a problem of significance. Nat Neurosci 14:1105-7. (pmid: 21878926)

[ PubMed ] [ DOI ] In theory, a comparison of two experimental effects requires a statistical test on their difference. In practice, this comparison is often based on an incorrect procedure involving two separate tests in which researchers conclude that effects differ when one effect is significant (P < 0.05) but the other is not (P > 0.05). We reviewed 513 behavioral, systems and cognitive neuroscience articles in five top-ranking journals (Science, Nature, Nature Neuroscience, Neuron and The Journal of Neuroscience) and found that 78 used the correct procedure and 79 used the incorrect procedure. An additional analysis suggests that incorrect analyses of interactions are even more common in cellular and molecular neuroscience. We discuss scenarios in which the erroneous procedure is particularly beguiling.



 


Further reading, links and resources

Duncan J Murdoch, Yu-Ling Tsai & James Adcock (2008) P-Values are Random Variables. The American Statistician 62:3:242-245. (pmid: None)
[ DOI ] P-values are taught in introductory statistics classes in a way that confuses many of the students, leading to common misconceptions about their meaning. In this article, we argue that p-values should be taught through simulation, emphasizing that p-values are random variables. By means of elementary examples we illustrate how to teach students valid interpretations of p-values and give them a deeper understanding of hypothesis testing.


 


Notes


 


Self-evaluation

 



 



 

If in doubt, ask! If anything about this learning unit is not clear to you, do not proceed blindly but ask for clarification. Post your question on the course mailing list: others are likely to have similar problems. Or send an email to your instructor.


 

About ...
 
Author:

Boris Steipe <boris.steipe@utoronto.ca>

Created:

2017-08-05

Modified:

2017-09-06

Version:

1.0

Version history:

  • 1.0 First live
  • 0.1 First stub

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