9 <strong>Topic VIII. Finding Signal in Noise</strong>

Detecting fish jumps on a lake on a day when the wind is causing waves.

Getting the words of a radio personality through static.

Hearing your conversational partner at a party where lots of conversations are happening.

Figuring out if there's a meaningful difference between the control condition and experimental condition in an RCT.

Finding the facts on a topic where there's a lot of disinformation floating around.

Two astrophysics examples are dramatic: gravitational wave detection (LIGO) and the false detection of a exoplanet around a pulsar, when neither was really there.

“It’s really hard to see the effect since there are so many other issues going on that act as noise, but there really appears to be a remarkable correlation between a young child’s ability to defer gratification and later successes in life.”

“The problem is that nowadays we are inundated with stories about every scary crime that happens anywhere in the world, so this “noise" confuses us and we can’t see the striking “signal” that crime in our country has gone down dramatically in the past three decades.”

"Any signal can count as noise, just like any noise can be considered as signal; it depends on what you're trying to see."

"Psychologists can never learn anything from surveys, because people don't pay close enough attention."

A few students thought that noise was only noise because it’s not what one is looking for, completely leaving out the other aspects of noise i.e. it distracts from perceiving the signal.

Some students also thought that something is only a signal because it carries information, and so they identified two signals for the second part of the question which was supposed to emphasize a shift in what the signal was based on the scientists’ focus.

It might be worth also going over whether or not noise has to be random.

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

Noise: The aspects of observations or stimuli that distract from, dilute, or get confused with signal, and are not signal (i.e., do not provide useful information about the target of interest).   

Observations/stimuli subject to confusion between signal and noise include communication, measurements, descriptions, etc.   

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.  

Identify examples of “signal” and “noise,” recognizing that these examples are context-dependent.  

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 (i.e., increase signal-to-noise ratio).        

Students identify “noise” and “signal” in different situations (the same event can be “signal” or “noise”depending on context).

You are watching a movie on TV. Which of the following is “noise” to you as a movie-watcher?

Same items as above, but now: Which of the following is “noise” from the point of view of the hero?

Think of cases where each of the following would be (a.) signal and (b.) noise:

Suppose you're at a party, and hoping to make a new friend. What are some 'signals' you might be looking for to help you find a good candidate? What forms of 'noise' are likely to be mistaken for those 'signals'?

Playing a sound with Morse code signal hidden in static. Demonstrate how our ear/brain is highly developed to find the signal.  

Students write down a short phrase that they proceed, by stages, to hide in more and more noise (random substituted letters). Show the concept of “signal-to-noise ratio” as away to quantify at what point they can no longer recognize the message (the signal).  

Play the game Telephone with loud music on, and with silence. In which does the message change the least? (i.e., in which case does the "noise" make the signal harder to keep track of?).

Visual version: Handwrite a sentence in pencil. One at a time, each student copies what they think it says, then adds three lines somewhere in the text that alter the letters. By the end, it should be almost impossible to read. Do this with a random sentence, and with a famous sentence (e.g. “We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America”). The famous sentence should be easier to read because it is familiar; we can more easily recognize the pattern.  Contrast with a nonsense line with strange words, e.g. some lines by Lewis Carroll students are not likely to recognize.  Demonstrates that it’s harder to detect a pattern when it’s different from the patterns we’re most used to finding.

When using iTunes “shuffle” feature, each song is played only once. However, if you turn shuffle on and off, the order is reshuffled each time, independently of the shuffle before. Consider the following user complaint :

Is the recurrence of certain bands and the exclusion of others proof that shuffle isn’t random? Why or why not?

Originally, within any particular shuffle you were just as likely to get songs in any order as any other. So if you had 101 songs on the playlist, and the first one was from Dark Side of the Moon, a given different song from Dark Side of the Moon would have a 1/100 chance of being played next. Users complained when getting multiple songs off the same album in a row that shuffle wasn’t really creating a random order. Were they correct to complain? That is, did they have reason to think the order wasn’t random? Why or why not?

In response to user complaints, Apple changed the shuffle algorithm to make it less likely you’d hear two songs from the same album in a row. So if you had 101 songs on your playlist and the first one was from Dark Side of the Moon, a given different song from Dark Side of the Moon would have significantly less than a 1/100 chance of being played next. Suppose users complained that the new order (which is still what Apple uses) wasn’t random. Would they have been correct to complain? That is, did they have reason to think the order wasn’t random? Why or why not?

Give a new example of a signal that you might be trying to detect (that is, an example not mentioned in the reading). Give an example of noise that might interfere with your detection of this signal. Explain why this is noise. Finally, explain something you could do to minimize the effect of this noise on your signal.