Tuesday 29 July 2008

Smelling or tasting? (ii)

So, last week end I made again the oil experiment with the help of a friend. It was very funny, sort of Coca-Cola/Pepsi contests.

The Idea: as in the previous experiment, the idea/belief to test is the following:

We cannot tell the difference between the taste of olive oil and sunflower oil just tasting them (so, closing our eyes and blocking our nose).

The material: Two cups, olive oil, sunflower oil and three coins (just two are shown in the photo).

The set-up: before starting to measure, we agreed three tries each. To avoid psychological advantage (I mean, thinking about my friend's behaviour in where she/he was going to place the cups with olive oil and sunflower oil could have provided some sort of advantage where taste was not the only thing measured), a coin decided where the olive oil was going to be placed: if the coin was a head, the cup with olive oil was to be placed on another coin that was lying on the table showing its head. Otherwise, the cup with olive oil went to the coin with the tail side up (actually we were no playing heads or tails, but heads or legs, as we used Manx pounds... ok, doesn't matter).

So, how can we accept or reject the result? If we flip a Manx pound six times, we can get:

  • three triskelions and three heads with probability ~31%, which comes from (6!/3!3!)*(1/2)^3*(1/2)^3 = 0.3125.
  • four triskelions and two heads (or four heads and two triskelions) with probability ~23%, as (6!/4!2!)*(1/2)^3*(1/2)^3 = 0.234375.
  • five triskeliions and one head (or five heads and one triskelions) with probability ~9%, result of (6!/5!1!)*(1/2)^3*(1/2)^3 = 0.09375.
  • six triskelions (or six heads) with probability 1/64 ~ 1.6%.

In short, this means that we have a chance of nearly 80% to get two, three or four triskelions. So, using a rather big significance level, we will accept as true the idea if we get this, and we will reject it otherwise (which would mean that we can actually tell the difference just tasting).

The measures: So, let's start the experiment!

Here are the two subjects:

apparently two normal individuals of Homo sapiens.

Subject A prepares before flipping the Manx pound...
I place the olive oil where the coin tells me.
Deciding after trying both oils.
After opening the eyes everything seems quite different!
After the three tries for subject A, subject B prepares to measure...
Subject B during one of the tries.
Subect B makes his decision.

The results: And after three tries each, we have got the results!

Which would be:

  1. Wrong
  2. Correct
  3. Wrong
  4. Correct
  5. Correct
  6. Wrong

Conclusion: This means we have got three wrong and three correct answers, more or less the same we would have got flipping a coin! Or, in other words, blocking our nose, we had no idea which oil we were trying, which means that, to the agreed significance level, the idea stated was correct.

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