Let's say we do this same experiment again and again...would we get the same results? Yes. It was a very controlled experiment. It's not like flipping a coin and I find it hard to believe that you would even use that to compare.
First, we may or may not get the same results; we don't know. This is precisely what we are trying to estimate. We are modeling a random process with a single binary outcome (in this case "are the beers different or not ") where the only influencing factor is the pitch rate, which we can effectively model as binary as well ("low" or "high"). I make the comparison to a coin being flipped to illustrate the fact that, no matter what the higher-level process is, if we are modeling some stochastic process with binary outcomes, the uncertainty in the final estimate is rather high with only one observation. While it is a minor simplification to the true model, I think the coin flipping example illustrates the point that any estimate derived from a small sample size lacks information in the statistical sense.
As a short description, and using the coin example for now, assume we have a coin with unknown bias, which we call p. In a fair coin, the value of p is one half, or .5. We are trying to estimate the posterior over the variable p given data, X, where X is a set that contains one or more observed results. If we use the traditional conjugate prior (the Beta distribution) for the Bernoulli distribution parameterized by p, we can easily (in closed form) compute a posterior estimate for p dependent on the observations we've seen. Further, the volume of uncertainty in the value of p will reduce more and more with more observations in the set X. This can be seen from the formula for the entropy of the Beta distribution. This means that if the set X is small (we only have on observation of an outcome, or 1 experiment in this case) then the uncertainty in the estimate of p is actually pretty high. I used the limiting case in my first post, where I said if you saw only a single flip of the coin (or 1 experimental result) would you trust the frequentist analysis that says "the coin is biased completely" or p = 1. No, of course you wouldn't. Unfortunately, with little or no a priori information about p (low values for the hyperparameters of the Beta distribution), only more data helps in estimating p; what I was saying is that I cannot with any confidence estimate whether or not pitch rate does or doesn't matter from a single experimental outcome.
My hypothesis is that pitch rate is not the only thing that matters; I think gravity, yeast, fermentation temperature, etc. all matter. That's why I said that selecting basically any lager over 1.050 that is pitched and fermented around 50 F will most likely show the opposite. Maibock is another great example. And I think that this particular beer is not as informative because it's an ale with a lot of hops and a fairly clean yeast. I think if you changed that, and made it a high gravity beer requiring a fairly clean profile, and fermented at low temps, you'll likely see a very different result. What I think that this experiment "proves" is that one CAN make a good hoppy, amber beer with OG of ~1.065 with WLP090 when pitching a starter or not, which I think someone else has already noted.
Also, I am definitely not trying to be a jerk. I just proofread this and thought it may come off that way, and if it does, I apologize. I'm just trying to explain what I meant, and why I made the comparison.
![Craft A Brew - Safale S-04 Dry Yeast - Fermentis - English Ale Dry Yeast - For English and American Ales and Hard Apple Ciders - Ingredients for Home Brewing - Beer Making Supplies - [1 Pack]](https://m.media-amazon.com/images/I/41fVGNh6JfL._SL500_.jpg)
