On Toast

Toast represents a colossal feat of human ingenuity and tenacity. Rather than accepting that our bread was past its prime, we instead redoubled our efforts. From the ashes of the ovens we stoked a new flame and screamed to the cosmos “We will cook it again!” So it was that our ancestors simultaneously set the course for invention, discovery, and brunch!

Absolutely. I encourage you to try the following experiment at your next brunch.

Now that you have comfortably settled into the world of toast, we will go on to using probability at brunch.

Your friend Bob always talks about the AMAZING butter he had in Ireland. “I can always tell the difference between Irish butter and American butter” he says disdainfully. As you can see, this attitude is clearly ruining everyone’s appetite. Besides, both butters are amazing and here at Fancy Data Toaster we do not discriminate. So let’s test his claim.

We all think Bob is trying to inflate his importance, so we design an experiment that he can’t easily b.s. (butter scrape), his way through. So how many does he need to get right to show us he can really taste a difference? Generally speaking in statistics when we in doubt we default to 95%. So for this case, we want Bob to get at least 95% of the butters correct for us to be satisfied. So let’s build some models using R code to illustrate.

Looking at the graph, we see that right around 6 pieces we see a potential testing point. So we quickly verify using pbinom at 5 and 6 and find that pbinom(5,8,.05) = 0.855, and pbinom(6,8,0.5) = 0.965.

So we see that Bob needs to get at least 6 out of the 8 correct to demonstrate he can taste the difference. Please note that this method may also result in Bob deciding to brunch elsewhere due to the volume of toast consumed.

There you have it folks! Non-Newtonian cats, probability, and pretentious toast disposal. Welcome to my happy, strange little world!

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