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| [[File:Topic Cover - 4.1 Signal and Noise.png|thumb]]
| | {{Cover|4.1 Signal and Noise}} |
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| The challenges of finding the information we want amidst messy data.
| | To make sense of this complex world, how do we confidently identify a meaningful pattern amongst a myriad of distractions? Scientists call the pattern "signal" and the distractions "noise." We clarify this subtle distinction and introduce techniques to make the signal stand out from the noise, such as with the use of filters. |
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| == The Lesson in Context == | | == The Lesson in Context == |
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| We introduce the concept of signal and noise in "detection problems" and teach students how to identify the signal and various sources of noise in diverse scenarios. This foreshadows the [[5.1 False Positives and Negatives|ethical considerations in deciding how strong a signal must be to be counted as a "positive"]]. | | We introduce the concept of signal and noise in "detection problems" and teach students how to identify the signal and various sources of noise in diverse scenarios. This foreshadows the [[5.1 False Positives and Negatives|ethical considerations in deciding how strong a signal must be to be counted as a "positive"]]. |
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| <!-- Expandable section relating this lesson to earlier lessons. --> | | <!-- Expandable section relating this lesson to other lessons. --> |
| {{Expand|Relation to Earlier Lessons| | | {{Expand|Relation to Other Lessons| |
| | '''Earlier Lessons''' |
| {{ContextLesson|2.2 Systematic and Statistical Uncertainty}} | | {{ContextLesson|2.2 Systematic and Statistical Uncertainty}} |
| {{ContextRelation|Both systematic and statistical uncertainties introduce noise to every measurement.}} | | {{ContextRelation|Both systematic and statistical uncertainties introduce noise to every measurement.}} |
| {{ContextLesson|3.1 Probabilistic Reasoning}} | | {{ContextLesson|3.1 Probabilistic Reasoning}} |
| {{ContextRelation|The presence of noise, which sometimes disguises as a signal, is inevitable in any measurement. The identification of a signal always comes with a roughly quantifiable level of confidence.}} | | {{ContextRelation|The presence of noise, which sometimes disguises as a signal, is inevitable in any measurement. The identification of a signal always comes with a roughly quantifiable level of confidence.}} |
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| <!-- Expandable section relating this lesson to later lessons. -->
| | '''Later Lessons''' |
| {{Expand|Relation to Later Lessons|
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| {{ContextLesson|4.2 Finding Patterns in Random Noise}} | | {{ContextLesson|4.2 Finding Patterns in Random Noise}} |
| {{ContextRelation|In addition to the signal-to-noise ratio, there are other statistical tools (e.g. <math>p</math>-value) to quantify the strength of the signal amidst all the noise.}} | | {{ContextRelation|In addition to the signal-to-noise ratio, there are other statistical tools (e.g. <math>p</math>-value) to quantify the strength of the signal amidst all the noise.}} |
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| {{ContextRelation|The detection of a "statistically significant" difference between conditions in an RCT is the identification of a signal. The random variations that exist between experimental subjects are a source of noise.}} | | {{ContextRelation|The detection of a "statistically significant" difference between conditions in an RCT is the identification of a signal. The random variations that exist between experimental subjects are a source of noise.}} |
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| == Takeaways == | | == Takeaways == |
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| </tabber> | | </tabber> |
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| {{#restricted:{{4.1 Signal and Noise}}}}{{NavCard|prev=3.2 Calibration of Credence Levels|next=4.2 Finding Patterns in Random Noise}} | | {{#restricted:{{Private:4.1 Signal and Noise}}}} |
| | {{NavCard|chapter=Lesson plans|text=All lesson plans|prev=3.2 Calibration of Credence Levels|next=4.2 Finding Patterns in Random Noise}} |
| [[Category:Lesson plans]] | | [[Category:Lesson plans]] |