4.1 Signal and Noise

Learning Goals

[Link to PlayPosit]

[Link to instructional video]

More details

After this lesson, students should

1. Know what scientists mean by “signal,” “noise,” and “signal-to-noise ratio.”
2. Be able to identify examples of “signal” and “noise,” recognizing that these examples are context-dependent.
3. Roughly compare measurement techniques in terms of their resultant signal-to-noise ratios.

Describe examples of techniques and tools to suppress noise and/or amplify signal.

Definitions

• Signal

  Aspects of observations or stimuli that provide useful information about the target of interest, as opposed to noise.

• Noise

  The aspects of observations that get confused with signal but do not provide the same useful information about the target of interest. Noise is frequently, but not always, the result of random measurement fluctuations.

• Signal-to-noise ratio

  The relative strength of signal compared to the relative strength of noise in a given context. Obtaining meaningful information from the world requires distinguishing signal from noise. Therefore, human cognition (both scientific and otherwise) relies on techniques and tools to suppress noise and/or amplify signal (i.e., increase signal-to-noise ratio). It is possible to design filters to increase the signal-to-noise ratio, if you know where the noise is going to appear.

Context

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 ethical considerations in deciding how strong a signal must be to be counted as a “positive” (4.2 False Positives and Negatives).

Before

2.2 Systematic and Statistical Uncertainty

Both systematic and statistical uncertainties introduce noise to every measurement.

3.1 Causation and Correlation

The detection of a “statistically significant” correlation in an RCT is the identification of a signal. The random variations that exist between experimental subjects are a source of noise.

After

4.1 Finding Patterns in Random Noise

In addition to the signal-to-noise ratio, there are other statistical tools (e.g. p-value) to quantify the strength of the signal amidst all the noise.

4.2 False Positives and Negatives

“Positive” and “negative” refer to whether we identify what we detect as a signal or not. The decision of any “threshold” of strength for a signal to be counted as positive inevitably involves human values judgment in a trade-off between the rates of false positives and false negatives.

6.1 Probabilistic Thinking

The presence of noise, which sometimes disguises as a signal, is inevitable in any measurement. The identification of a signal always comes with a quantifiable level of confidence.

Recommended Outline

Before Class

• [Any essential logistical things that need to be done for this class]
• Prepare a seating chart.
• Review PlayPosit and discussion questions and ask faculty, Gabriel, or Emlen any questions you have.
• (Optional) Prepare a presentation.

During Class

• (5 min) Come up with some fun way to assign the roles of spokesperson and notetaker (e.g. earliest birthday in the year, lives furthest from campus). Remind them of the responsibilities of these roles.
• ([#] min) [Description of some module from #Lesson Content]
• (5 min) Collect questions for plenary.

Lesson Content

Clicker Question

1. Question
   1. Option 1
   2. Options 2

Activity 1: Name

[Brief description of and motivation for the activity]

Discussion Questions

1. Question 1
   1. Subquestion a

1. 1. Subquestion b

Collect Questions for Plenary

(5 min) Collect remaining questions from the students for faculty in plenary (can be questions for clarification, extension, discussion, etc.), and add [ here].