p-value thinking” is central to all the work we do in this class. We think like statisticians (use “p-value thinking”) anytime we are confronted with something surprising and check how likely we were to see such a result “accidentally”, if “nothing was really going on”. For instance, recently I was changing the battery for one smoke detector in my ceiling when another smoke detector in the next room started squealing that it too was out of batteries. This seemed strange! I wondered how likely two smoke detectors were to drain their batteries within an hour of each other, assuming nothing was wrong with my house’s electrical system. This is “p-value thinking” Describe (or invent if you prefer) example from your own life when you used “p-value thinking”. Remember the essential elements:
(1) some surprising event happens,
(2) you check how likely an event like this is to happen by random coincidence,
(3) you decide whether that coincidence is too extreme to ignore.
“P-value thinking” is a fundamental concept in statistical analysis that involves assessing the likelihood of observing a surprising event by random chance alone. By considering the probability of such coincidences occurring, we can make informed judgments about the significance of unusual occurrences. In this essay, I will share an example from my own life where I applied “p-value thinking” to evaluate an unexpected event, emphasizing the essential elements of this analytical approach.
A few months ago, I was engrossed in an intense study session, preparing for an important exam the following day. In an effort to stay focused, I decided to eliminate potential distractions by turning off my phone and placing it in a drawer. Several hours went by, and I finally concluded my study session, feeling confident in my preparation. I eagerly retrieved my phone, anticipating a momentary reprieve from my studies. However, to my surprise, upon turning it on, I discovered that I had missed exactly five calls, all from different friends whom I hadn’t heard from in quite some time.
This unexpected event caught my attention, prompting me to engage in “p-value thinking.” I contemplated the likelihood of receiving precisely five calls from different individuals during the short period when my phone was powered off. Considering that I had been studying for several hours and received no calls before shutting off my phone, the timing of these calls seemed highly coincidental. The essential elements of “p-value thinking” guided my evaluation of this situation.
Firstly, the surprising event was the receipt of five missed calls from different friends simultaneously, after several hours of having my phone turned off. This event raised questions about the probability of such a coincidence occurring randomly.
Secondly, I proceeded to assess the likelihood of this occurrence happening by chance. Given that I had not been in regular contact with these friends and that they all called within the span of a few hours, I considered the probability of each friend independently deciding to reach out during this particular timeframe.
Finally, I had to decide whether this level of coincidence was too extreme to ignore. Considering the rarity of receiving multiple calls from distinct individuals in a short period while my phone was off, it seemed implausible to attribute the event solely to chance. The cumulative probability of such an event occurring by random coincidence alone appeared exceedingly low.
By applying “p-value thinking” to the surprising event of receiving multiple missed calls from different friends during a study session, I evaluated the probability of this occurrence happening by random chance. The analysis suggested that the observed coincidence was highly unlikely, indicating that there might have been an underlying cause or a common reason behind the calls. This example underscores the value of statistical thinking in everyday life, enabling us to critically assess and interpret unexpected events based on the principles of probability and significance. Whether in academic research, problem-solving, or decision-making, embracing “p-value thinking” empowers us to make more informed judgments and draw meaningful conclusions.
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