5 ms·

No ones mentioned this, but it's unlikely skittles are "randomly distributed". Instead it's likely in the Skittles factory there's some system that attempts to

No ones mentioned this, but it's unlikely skittles are "randomly distributed". Instead it's likely in the Skittles factory there's some system that attempts to reasonably distribute colours so no one bag is too skewed. So the whole premise is faulty.

jdreaver 8y ago
No one has mentioned it? Did you read the article? The article discusses exactly what you just said.
- Chinjut 8y ago
  Where? I don't see it anywhere. There's some discussion of total volume perhaps being non-independent from box to box, so an underfilled box is followed by an overfilled one, but this isn't the point the grandparent is making. The grandparent is making the point that there are probably systems in place to prevent a box from being 80% red, say, so that the assumption each individual skittle in a box is independently uniformly drawn from each possible color does not likely accurately model the dynamics.
  - possiblywrong 8y ago
    Author of the article here; you have a point that there is no explicit discussion of validating this assumption, beyond the variability shown in the colored curves in the "count per pack" plot. Having said that, this small sample is indeed reasonably consistent (or at least not inconsistent) with that iid assumption for the color of each individual Skittle. We would not expect to see any 80+% red packs even assuming that color was perfectly uniformly iid, because the probability of observing such a pack is so small (less than 10^(-19)). However, still assuming this model, we should expect to see packs with very small proportion of reds... and we do, with one pack having just 3 red Skittles, for example. The entire distribution of proportion of red follows the assumed binomial distribution very closely.
- deleted 8y ago
  [deleted]
learnstats2 8y ago
I would bet the Skittles factory has no such system - the data appears to be highly consistent with what you would expect from mixing the skittles well and making entirely random bags.

jdreaver 8y ago

No one has mentioned it? Did you read the article? The article discusses exactly what you just said.

Chinjut 8y ago
Where? I don't see it anywhere. There's some discussion of total volume perhaps being non-independent from box to box, so an underfilled box is followed by an overfilled one, but this isn't the point the grandparent is making. The grandparent is making the point that there are probably systems in place to prevent a box from being 80% red, say, so that the assumption each individual skittle in a box is independently uniformly drawn from each possible color does not likely accurately model the dynamics.
- possiblywrong 8y ago
  Author of the article here; you have a point that there is no explicit discussion of validating this assumption, beyond the variability shown in the colored curves in the "count per pack" plot. Having said that, this small sample is indeed reasonably consistent (or at least not inconsistent) with that iid assumption for the color of each individual Skittle. We would not expect to see any 80+% red packs even assuming that color was perfectly uniformly iid, because the probability of observing such a pack is so small (less than 10^(-19)). However, still assuming this model, we should expect to see packs with very small proportion of reds... and we do, with one pack having just 3 red Skittles, for example. The entire distribution of proportion of red follows the assumed binomial distribution very closely.
deleted 8y ago
[deleted]

learnstats2 8y ago

I would bet the Skittles factory has no such system - the data appears to be highly consistent with what you would expect from mixing the skittles well and making entirely random bags.