Business Insider has been flogging this headline since late August, and it was still on the front page last week:

I don't have a premium subscription so I don't know what evidence they have for this. I'm imagining that someone collected data, zeroed in on the teams that are deemed successful, and computed the percentage of team members who "swear and gossip". How do they know they "swear and gossip"? I have no idea - the data may have come from one of those Big Brother surveillance technologies.

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I love this headline because it can be turned into a test of one's statistical acumen.

**Question #1: Are the following headlines identical (i.e. interchangeable)?**

What's your first instinct? Now, think about it a bit, and see if you change your mind. I'll present some hints in the second half of this post, and the answer in a future post.

**Question #2: Do the following headlines contradict or can both be true at once?**

What's your answer? Come back later in the week to check what my answers are.

For those needing some hints, keep reading.

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For Question #1, one perspective is whether the order of presentation matters. Is the relationship symmetric? Imagine throwing a dice twice, and getting 1 then 5 in that order. If the question is the sum of the values, then the order does not matter. One followed by 5 is the same as 5 following 1, both adding to 6, in the context of this question. However, if the question is the values are increasing, then order matters. One followed by 5 and 5 followed by 1 are evaluated differently.

One approach that helps with either question involves writing down the entire set of possibilities. When you have two binary variables, there are four possible states. Are the two headlines talking about the same things?

Identity requires that each statement implies the other. Check both directions. If it's not true, then find counter-examples in which one statement is true while the other one is false. Question #2 asks about non-contradiction which is less stringent than identity. Identical statements cannot contradict each other but non-identity does not imply contradiction.

Remember we are doing statistics, not pure math. Almost nothing in statistics apply universally. Think of counter-examples not as a single example but a class of examples sharing the same characteristics.

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Feel free to use the comments to discuss with other readers.

From the article:

"A new survey of more than 1,100 American office workers [https://front.com/blog/how-to-build-a-high-performing-team] provides clues. The survey, from Ignite80, a learning and development company, finds that high-performing teams are more likely to joke around, use GIFs and emojis in digital messaging, tease their teammates, and swear around coworkers than low-performing teams."

Posted by: Dagonet | 10/19/2021 at 03:37 AM