Is It Time For Action?
No change no improvement. No risk no reward. No guts no glory. No samurai-sword-fighting-on-motorcycles-over-a-cliff no blockbuster. These maxims carry some exception, but mostly, they are self-evident. The real question is “When is it time for action?” And the nugatory response is “When benefits outweigh costs.”
Discussing sound methodologies for forecasting cost-benefit is too broad of a subject for this article. I will, therefore, focus on two key concepts:
1. Opportunity Costs
For each action we take, we forgo all other possible actions.
Warren Buffett subscribes to the “Ted Williams” approach. That is, swing only at pitches you can hit hard. The goal then becomes to put yourself in position to see more pitches.
Chess champions know that trading a rook for a queen is often beneficial, but not if it costs an opportunity to mate the opponent’s king. It is important to know the possible actions and not to lose sight of the overall goal.
It doesn’t matter whether goals are found conceptually or searched for meticulously. You can be Picasso or Cézanne. The important advice is to hone skills through observation and experimentation.
2. Confidence Intervals
Let’s say that we are trying to sell typewriters. Of our thousands of typewriters in storage, we have more black typewriters than red typewriters. We can get more red typewriters — and it will be necessary if significantly more buyers want red. We find 100 buyers, 58 of whom want a red typewriter. That’s more than the 42 who want black, right?
Unless there are other pressing issues pertaining to future availability of typewriters, no action is needed — other than to find more buyers.
Now, let’s say that we are experimenting with two webpage designs. The goal is to maximize the number of visitors who buy typewriters on our site. Page-A has equal sized pictures of both typewriter types. On page-B the picture of the black typewriter is enlarged. Traffic is split 10:1 such that 392 out of 1000 visitors bought a typewriter on Page-A and 58 out of 100 did so on Page-B.
We should switch to Page-B.
Confidence intervals around proportions come from the Binomial Distribution. There is plenty of literature on the Binomial Distribution, but I couldn’t find a tool that explores and explains the numbers. So, I took action and created one: https://chip1.shinyapps.io/Binomial/
You have certainly spent serious time in the classroom if you recognize the names Bonferroni, Tukey and Scheffe. If that is not the case, just be aware that it is rather foolish to be confident about a lot of things at once.