4 ms·

Perfect example of how graphs can be subtly deceptive: 1) "Variance in number of comments" is visualized as a circle's radius. 2) ... But a circle's area incr

by palish 16y ago

Perfect example of how graphs can be subtly deceptive: 1) "Variance in number of comments" is visualized as a circle's radius. 2) ... But a circle's area increases as (pi)r^2. That's an exponential increase. A fair visualization would show a linear increase, not an exponential one. EDIT: To be more clear, the goal is "more pixels" = "more variance". Growing the visualization by a radius is inherently unfair. It's precisely these kind of subtleties that make statistics such a fallacy minefield.

eru 16y ago
> 2) ... But a circle's area increases as (pi)r^2. That's an exponential increase. Oh, it's an exponential increase in 2, but a linear increase in Pi. Anyway, just pretend that the area of the circle is proportional to the variance, and the radius to the standard deviation.
- palish 16y ago
  I assume "variance of Foo" is linear quantity. Is it true that a variance of 4.0 means "twice as much as 2.0"? If so, then the circle's area (not its radius) must grow proportional to that variance. Growing the radius is an unfair visualization. The goal is: more pixels = more variance.
  - eru 16y ago
    Standard deviation is the square root of variance. A variance of 4 is twice the variance as one of 2, but that's just by definition. What is perhaps more interesting for your intuition: Adding two independent variables, the variance of the result will be the sum of the variances. Thus the standard deviation of the sum is the squareroot of the sum of squares of the standard deviations of the components. (It's easier to read in formulas.) A look at http://en.wikipedia.org/wiki/Variance http://en.wikipedia.org/wiki/Variance might help.
    - palish 16y ago
      Thank you! I really appreciate your explanation. By those definitions, shouldn't the number of pixels (circle area) reflect the deviation, rather than what it currently does (the square deviation, aka variance)? In that case, the area should grow proportionally to the deviation, not to the variance.
      - eru 16y ago
        You're welcome. I don't know what it should do. Showing variance is fine, and my professor for probability theory actually preferred variance over standard deviation.
masterzora 15y ago
> 2) ... But a circle's area increases as (pi)r^2. That's an exponential increase. No, no, no, no, no. "exponential" != "has an exponent". Exponential means the variable is the exponent, as in 2^n. The word you're looking for is "quadratic".
- palish 15y ago
  It doesn't matter whether it's unfair by a factor of n^2 or by 2^n. If it's unfair, then it cannot be looked at whatsoever without drawing incorrect conclusions. Or are you trying to educate me out of good will? If so, thanks.
  - masterzora 15y ago
    Kind of the latter, really. While the true meaning was clear from context here, it's very easy to make the same mistake in other contexts without the true meaning being so clear. And, unlike a number of other common mistakes, this is one that can really bite you in the ass in some contexts, so it's good to set the record straight before your gluteals are masticated.

by palish 16y ago

eru 16y ago

> 2) ... But a circle's area increases as (pi)r^2. That's an exponential increase. Oh, it's an exponential increase in 2, but a linear increase in Pi. Anyway, just pretend that the area of the circle is proportional to the variance, and the radius to the standard deviation.

palish 16y ago
I assume "variance of Foo" is linear quantity. Is it true that a variance of 4.0 means "twice as much as 2.0"? If so, then the circle's area (not its radius) must grow proportional to that variance. Growing the radius is an unfair visualization. The goal is: more pixels = more variance.
- eru 16y ago
  Standard deviation is the square root of variance. A variance of 4 is twice the variance as one of 2, but that's just by definition. What is perhaps more interesting for your intuition: Adding two independent variables, the variance of the result will be the sum of the variances. Thus the standard deviation of the sum is the squareroot of the sum of squares of the standard deviations of the components. (It's easier to read in formulas.) A look at http://en.wikipedia.org/wiki/Variance http://en.wikipedia.org/wiki/Variance might help.
  - palish 16y ago
    Thank you! I really appreciate your explanation. By those definitions, shouldn't the number of pixels (circle area) reflect the deviation, rather than what it currently does (the square deviation, aka variance)? In that case, the area should grow proportionally to the deviation, not to the variance.
    - eru 16y ago
      You're welcome. I don't know what it should do. Showing variance is fine, and my professor for probability theory actually preferred variance over standard deviation.

masterzora 15y ago

> 2) ... But a circle's area increases as (pi)r^2. That's an exponential increase. No, no, no, no, no. "exponential" != "has an exponent". Exponential means the variable is the exponent, as in 2^n. The word you're looking for is "quadratic".

palish 15y ago
It doesn't matter whether it's unfair by a factor of n^2 or by 2^n. If it's unfair, then it cannot be looked at whatsoever without drawing incorrect conclusions. Or are you trying to educate me out of good will? If so, thanks.
- masterzora 15y ago
  Kind of the latter, really. While the true meaning was clear from context here, it's very easy to make the same mistake in other contexts without the true meaning being so clear. And, unlike a number of other common mistakes, this is one that can really bite you in the ass in some contexts, so it's good to set the record straight before your gluteals are masticated.