However, when they drop the toast from a two-story building (27'5") and find that the dry toast side X lands up 26 out of 48 drops (54%) and the buttered side X lands up 29 out of 48 drops (60%), Jamie posits that the 6% discrepancy is because he could see that the buttered side had a concave impression, and like a leaf, the convex non-buttered side tended to fall face down. Adam concludes, "if you really want to ensure, in general, you're toast landing buttered side up or down, we can tell you, you should butter with a good vigor and that the resultant bowl will make your toast generally fall butter side up." However, though he "generally" qualified his statement, strictly speaking, it is not statistically supported and when Jamie is offering a mechanism for a perceived statistical finding, he is premature. (However, if he is offering a simple observation, that's all it is.)
In this case, the null hypothesis is that the difference between the dry 54% and the buttered 60% is just due to chance. (Or, if we were to repeat the experiment, it's probable that a similar skew would happen.) The alternate theory is that there is some causal mechanism (i.e. the bowl shaped impression) that affects the outcome. If we can show that there is a low probability of repeating the experiment and observing a similar significance of difference (6%), that implies support for the alternative hypothesis. Unfortunately, neither test alone is statistically significant. For example, the probability of getting 29 out of 48 drops buttered side up even on a fair coin is 8.5 %.
z = (observed - expected) / StandardError
z = (29 - 24) / Sqrt(48)*Sqrt(.5*.5) = 1.445
=> P = 8.5%
The random chance of getting 26 buttered side up his 27%.
The probability that the difference between getting 26 in the "dry" control case, and 29 in the buttered case also is 27% and not significant.
z = (observed - expected) / StandardErrorofDifference
z= ((60%-54%) - 0%) / Sqrt((SEdry)^2 + (SEbuttered)^2)
z=6% / Sqrt(7.19^2 + 7.07^2)% = .5950
=> P = 27%