> I personally don't like sandals. I'd happily give you lots of reasonable-sounding explanations for why I don't [...] Nobody [considers] my personal choice is relevant to the futures of the footware (sic) industry.
Of course it is relevant. In your case, the footwear industry would like to know whether the general public likes sandals or not, in order to decide whether to make more or less of them, and what types of advertising should be purchased. We can go with the initial assumption that there is nothing special about you, as a sample, and work on the principle that you are representative of the footwear buying public as a whole. So, we now know that not everyone likes sandals, and since we know other people that also hold the same view, we can be confident that you are not absolutely unique. Of course we want to seek out more opinions, and determine more accurately how widespread this dislike of sandals is, but I would be foolish to completely ignore this data point.
Similarly for teens and Internet services, the single data point here is interesting and thought-provoking because we know it isn't a freak outlier, and is instead somewhat representative of teens as a group. Since the actual quantitive information (that is, user retention and engagement at Facebook, Snapchat et al) tells us only what is happening, we must seek out qualitative opinion pieces like this to determine why. Everyone here is capable of understanding the limitations of small sample sizes and self-selection effects, and should be able to control for that. And of course, it's also just interesting to know what ones fellow human beings feel about a subject, and even important when there are business models predicated on these same humans doing things because their friends are. Network effects like that are obviously one of the main drivers for social network adoption, and thus increasing the value of a product.
> We can go with the initial assumption that there is nothing special about you, as a sample, and work on the principle that you are representative of the footwear buying public as a whole.
That's an absolutely terrible assumption. A sample of one is never ever representative.
Of course it is relevant. In your case, the footwear industry would like to know whether the general public likes sandals or not, in order to decide whether to make more or less of them, and what types of advertising should be purchased. We can go with the initial assumption that there is nothing special about you, as a sample, and work on the principle that you are representative of the footwear buying public as a whole. So, we now know that not everyone likes sandals, and since we know other people that also hold the same view, we can be confident that you are not absolutely unique. Of course we want to seek out more opinions, and determine more accurately how widespread this dislike of sandals is, but I would be foolish to completely ignore this data point.
Similarly for teens and Internet services, the single data point here is interesting and thought-provoking because we know it isn't a freak outlier, and is instead somewhat representative of teens as a group. Since the actual quantitive information (that is, user retention and engagement at Facebook, Snapchat et al) tells us only what is happening, we must seek out qualitative opinion pieces like this to determine why. Everyone here is capable of understanding the limitations of small sample sizes and self-selection effects, and should be able to control for that. And of course, it's also just interesting to know what ones fellow human beings feel about a subject, and even important when there are business models predicated on these same humans doing things because their friends are. Network effects like that are obviously one of the main drivers for social network adoption, and thus increasing the value of a product.