The Statistics of Manels
On Randomness, Bias, and Useful Tables
Panels and Manels
“We’d like you to be on our expert panel on such and such.,” the voice on the phone said.
The topic was something I was interested in, and I was free on the date and for the place.
“Thanks!,” I said, “Who else is on the panel?”
The list of others consisted of only men.
“Sorry.,” I said. “But I prefer not to appear on male-only panels.”
“But we asked a bunch of lady-experts.,” the organizer replied. “But no one was available.”
“No Problem. I can send you a list of possible woman-experts who are as qualified (probably, more qualified) than me for your panel.”
Later that day, I copy-pasted a column of names from a spreadsheet into an email, and sent it on to the event organizer’s inbox.
Colleagues and Questions
A “manel” is a portmanteau of “man” and “panel,” and refers to a panel consisting of only men.
I mentioned the previous episode to a colleague, on how I’d refused to be on a manel.
“Why?,” said colleague asked.
“The panel consisted of only men.,” said I, a little pompously. “And our industry has a lot of highly qualified women? So why discriminate?”
“But were they actually discriminating?,” my colleague replied.
“What do you mean?,” I said.
“What if they picked the panel randomly, and, just by chance, they all happened to be men?”
An interesting question. So, I thought of testing my colleague’s theory, statistically.
Statistics and Significance
The panel I was invited to had 5 spots. Four had already been filled with male candidates, and the organizers asked if I (also male) could be the fifth.
As I said, the industry under discussion was gender neutral. A 50–50 male-female balance.
Now, suppose, as my colleague suggested, the organizers picked the 5 candidates (me included) randomly. What are the odds of picking 5 males?
The answer is ½ ✕ ½ ✕ ½ ✕ ½ ✕ ½ = 1/32 or 0.03125 or a bit over 3%.
3% is not zero, but is quite small. Usually, statisticians say that something is “quite small” when it is less than 5% to 10% (also known as “significance”).
In other words, the odds that the organizers picked the panel “fairly randomly,” as my colleague suggested, is quite small.
So, a statistician would conclude that the organizers who invited me were probably biased.
…
Suppose the panel had only 3 people. And suppose, again, the organizers picked only men. What are the odds of this happening “randomly”? ½ ✕ ½ ✕ ½ = 1/8 or 0. 125 or 12.5%.
You might argue that 12.5% is also small, but a statistician would usually argue that it’s not small enough to conclude that the picking of the panel was not random.
And the organizers would have been off the hook.
…
Let’s look at a slightly different example; one where the balance between candidate groups is not 50–50.
Some time ago, I read an article that claimed that the selection of the Sri Lankan Cricket team was biased towards Sinhalese. It went on to claim that (at the time), the entire squad of 15 were Sinhalese.
What are the odds that this happened purely by chance?
Roughly, ¾ of Sri Lankans are Sinhalese. Hence, the odds of 15 Sri Lankans picked randomly all being Sinhalese is ¾ ✕ ¾ ✕ ¾ …. (15 times) = 0.0133 or a bit over 1%.
And so, a statistician would agree with the article’s claim that there clearly was some ethnic bias.
So, who should be on the panel?
This table below lists the lowest number of people from a group that should be on a panel, so that there would be no statistical evidence (at 10% significance) of bias.
[I used the Microsoft Excel function BINOM.INV(<Panel Size>,<Group %>,0.1) to generate this table.]
Let’s look at a few examples.
- What is the minimum number of females a panel of 4 should have? Answer: 1 (reading the “50%” row and the “4” column).
- What is the minimum number of non-Sinhalese a squad of 15 cricketers should have? Answer: 2 (“25%” and “15”)
- What is the minimum number of Sinhalese a panel of 2 should have? Answer: 1 (“75%” and “2”)
- What is the minimum number of female-MPs our parliament of 225 should have? Answer: 103 (“50%” and “225”)
Many would argue that a panel of 4 should have 2 females, given that they are 52% of the population. But as I explained, these are the minimums required to conclude that there is no evidence of bias. So, minimums, not optimums.
Concluding Surprisation
After this interesting discussion, my colleague said, “You know something?”
“What?”, I said.
Then she let out an enigmatic smile.
“Actually, that panel you refused?”
“Yes?,” I said.
“The organizers asked if I could be on that panel.”
“Oh,” I said.
“I declined.”
“You were busy?”
“No,” my colleague said. “I was not busy.”
“Then?”
“I thought it a waste of time.”
I wasn’t sure how to reply.
