5 ms·

I always sucked at stats, so can someone clarify the income / hapiness case. From what I understand, we have : * a straight line on a log scale - which is misl

I always sucked at stats, so can someone clarify the income / hapiness case. From what I understand, we have : * a straight line on a log scale - which is misleading, since the man on the street is used to straight lines on linear scales - telling that money buys happiness * a "log-like" graph on a linear scale, which tells you that "money buys happiness a lot at the start, and then it doesn't change things a lot" - and the graph uses a linear scale on both axis, so there is less deformation. What am I missing ?

Dylan16807 12y ago
People are making the claim that money buys happiness up to a certain number and then stops. But there is no inflection point. 10% more money always buys you the same amount of happiness. Nothing makes $75k the point where you have 'enough' money as opposed to $5k. 75 million is just as far ahead of 5 million (at least if it continues to be logarithmic).
- phtrivier 12y ago
  That's where I'm lost. 10% more money is much more money when you're rich than when you're poor (Captain obvious to the rescue.) So if you want to make me 10% more happy, that's going to cost you a lot more actual dollars / euros / yuan / whatever ; and the last 10$ are going to make me less "happier" (in absolute) than the first 10$. Considering people don't buy stuff in percentage of their salaries, but in absolute dollars (if i'm not mistaken), isn't that a case where the absolute / relative difference is relevant ? I'm pretty sure I'm having a stats 101-level argument, and there is something obvious that I'm missing, so please forgive and educate ;)
  - msandford 12y ago
    So the point is that 10% more money always makes you a certain amount happier. People trot this out and say "look, once you have a certain amount of money you don't get happier by having more!" Why should dollars buy happiness the same way they buy gumballs? It doesn't make any sense. The first gallon of water you have every day is pretty freaking valuable. The 1000th gallon of water you have every day is just about worthless unless you're a farmer. In engineering we use log-log charts to look at how systems respond to a HUGE range of inputs from the very, very slow to the very, very fast. Like filters. You want to know how it looks from 1Hz to 1GHz in a useful way. This is generally done with a Bode plot which is log on both x and y. http://en.wikipedia.org/wiki/Bode_plot http://en.wikipedia.org/wiki/Bode_plot If your plot covers several orders of magnitude (and income is many orders of magnitude) then the most informative way to understand it is by compressing it via logarithm. Here's a good example only on the Y since the company is growing X% per year. http://blogs-images.forbes.com/naomirobbins/files/2012/01/linear_log.jpg http://blogs-images.forbes.com/naomirobbins/files/2012/01/li...
    - phtrivier 12y ago
      > Why should dollars buy happiness the same way they buy gumballs? It doesn't make any sense. Which is precisely the point of the old "money does not buy happiness" adage, isn't it ? Science that says "This 1000ths gallon of water is gonna be as good as worthless" seems to favor the point rather than oppose it. I don't know if "happinness == gumballs" would make "sense" to anyone (I personnaly doubt it), but that's the subtext of a lot of messages in a consumer society (and we're leaving the realm of maths from the realm of politics. Stats 101 vs PolSci 101, all over again, I know, sorry.) As for your graphs, what I was saying is precisely that, unless you've been trained to read graphs (and most people are not), you're going to be "fooled" more easily by the second one, won't you ?
      - msandford 12y ago
        > Which is precisely the point of the old "money does not buy happiness" adage, isn't it ? Not the way I read it, really. If money doesn't buy happiness, then the graph should be completely flat right? Or at the very least a uniformly distributed scatter plot? But it doesn't really seem to look that way. While I suspect that there's some truth to the adage, it's definitely not absolute. > Science that says "This 1000ths gallon of water is gonna be as good as worthless" seems to favor the point rather than oppose it. That's not the point. The point is that as you have more of a thing, it takes more to move the needle. EVERYTHING has decreasing marginal utility, and money does too. But I don't think the marginal utility of money ever becomes zero, or goes negative. Do you think that? If so, please start sending me your money so that you can be happier! Here's a great example for you. Raises are nearly always percentages right? Why not just give everyone a $100 a year raise? I mean, that $100 is supposed to be the same to everyone, isn't it? 10% more money increases your happiness approximately the same, no matter what number that 10% increase is applied to. > As for your graphs, what I was saying is precisely that, unless you've been trained to read graphs (and most people are not), you're going to be "fooled" more easily by the second one, won't you ? I think that if you want to understand the way a system works across many orders of magnitude the only way to do so without fooling yourself is to look at a log/log plot. If you don't, only the most extreme change on the plot shows up and all the rest gets compressed into a "straight" line by the vagaries of turning an infinitely variable thing into a finite set of pixels.
  - Dylan16807 12y ago
    They are claiming there is a point where money stops being important. There is no such point. There is no reason to favor any particular income level. If you use the happiness graph to make an argument that $50k is all anyone needs, I can use the same graph to show that $400 is all anyone needs. If the 'up to a certain point' hypothesis was correct, with the graph leveling out, there would be a maximum happiness-from-money. You could say "oh well 85% of max is plenty, the ideal income is X". But the data says that's not true. --- Humans intuitively understand logarithmic scales. Arguably even better than linear scales. A lot of our senses are logarithmic, after all. It's obvious that one dollar does not buy one happiness, given that millionaires aren't in ecstatic shock. But every time I double my income I gain the same number of happiness units? Sounds like money buying happiness to me.
    - phtrivier 12y ago
      Regarding your comment about log scales, is there a "sense" (or kind of perception, etc...) beside earing that "obviously" logarithmic ? Also, as another "I don't get stats get me out of here" question, isn't it problematic to plot against a "perception" level that (unless I'm mistaken) is linear ? What do you do with someone that answers "I'm happy at a 10/10 level". Do you consider it an outlier by definition ? Assuming the "happiness" self-rating is indeed linera, is it still a fallacy to think that, behind the mathematical rightness, there is value in knowing that after $x/year, y% of the population rates itself as above, say, 8/10 ? I'm under the impression that it's a different argument than say "after $x/year, everyone is happy" ; but that it can still be practical (especially if you can corelate lower levels a happiness with stuff you want / should / need to get rid of. But again, talking politics at a math cocktail, probably bad manners.)
      - Dylan16807 12y ago
        Brightness is pretty logarithmic. Touch, smell, taste, all of those seem logarithmic to me. People rating out of 10 distorts the numbers in multiple ways, that's a separate issue to deal with. Ideally you'd remove self-reporting in some manner... >value in knowing that after $x/year, y% of the population rates itself as above, say, 8/10 If it's linear with a cap of 10 then all the reasoning from before goes in the trash. The graph won't actually be logarithmic and you can set a cutoff easily. If you can calculate a linear happiness score with no cap, then it's possible to pick a point that's "happy enough", but that point will be arbitrary. It won't be based on an inflection point on the graph, because the graph has no inflection points. You can use your judgement to say that 12 happiness points is plenty, but that's not a math question.
pc86 12y ago
I'm curious about this too. I'm familiar with the economic concept of diminishing marginal utility, and I get that the $10k you get from $120-$130k/yr is much less valuable to you than the $10 from $40-50k. But there still seemed (to my Stats 101-level interpretation) that there was a decent-enough jump between $75k and $130k and beyond that happiness/utility increased significantly as income did beyond the commonly cited figure. For those of you who earn the requisite amount, is it true that it's easier to get a significant raise at the higher income levels? I live in a fairly rural area but I've found as my income rises the degree to which I need to fight for marginal pay increases has diminished, which seems counter-intuitive since each point gets more and more expensive, obviously.
- Spellman 12y ago
  You're understanding the actual data quite well as it turns out. Moving from $40k -> $50k is a much bigger gain on the happiness scales since it is a larger % increase. Moving $120k -> $130k is much smaller relatively, even though it's still $10k. As for getting larger raises, many jobs you get raises based on a percentage of your current salary. So if you get a 5% year-over-year raise and your base salary is $120k, you're getting a similar happiness boost as the 5% year-over-year raise of someone making $40k base salary. But you're getting way more in terms of net actual dollars.

Dylan16807 12y ago

People are making the claim that money buys happiness up to a certain number and then stops. But there is no inflection point. 10% more money always buys you the same amount of happiness. Nothing makes $75k the point where you have 'enough' money as opposed to $5k. 75 million is just as far ahead of 5 million (at least if it continues to be logarithmic).

phtrivier 12y ago
That's where I'm lost. 10% more money is much more money when you're rich than when you're poor (Captain obvious to the rescue.) So if you want to make me 10% more happy, that's going to cost you a lot more actual dollars / euros / yuan / whatever ; and the last 10$ are going to make me less "happier" (in absolute) than the first 10$. Considering people don't buy stuff in percentage of their salaries, but in absolute dollars (if i'm not mistaken), isn't that a case where the absolute / relative difference is relevant ? I'm pretty sure I'm having a stats 101-level argument, and there is something obvious that I'm missing, so please forgive and educate ;)
- msandford 12y ago
  So the point is that 10% more money always makes you a certain amount happier. People trot this out and say "look, once you have a certain amount of money you don't get happier by having more!" Why should dollars buy happiness the same way they buy gumballs? It doesn't make any sense. The first gallon of water you have every day is pretty freaking valuable. The 1000th gallon of water you have every day is just about worthless unless you're a farmer. In engineering we use log-log charts to look at how systems respond to a HUGE range of inputs from the very, very slow to the very, very fast. Like filters. You want to know how it looks from 1Hz to 1GHz in a useful way. This is generally done with a Bode plot which is log on both x and y. http://en.wikipedia.org/wiki/Bode_plot http://en.wikipedia.org/wiki/Bode_plot If your plot covers several orders of magnitude (and income is many orders of magnitude) then the most informative way to understand it is by compressing it via logarithm. Here's a good example only on the Y since the company is growing X% per year. http://blogs-images.forbes.com/naomirobbins/files/2012/01/linear_log.jpg http://blogs-images.forbes.com/naomirobbins/files/2012/01/li...
  - phtrivier 12y ago
    > Why should dollars buy happiness the same way they buy gumballs? It doesn't make any sense. Which is precisely the point of the old "money does not buy happiness" adage, isn't it ? Science that says "This 1000ths gallon of water is gonna be as good as worthless" seems to favor the point rather than oppose it. I don't know if "happinness == gumballs" would make "sense" to anyone (I personnaly doubt it), but that's the subtext of a lot of messages in a consumer society (and we're leaving the realm of maths from the realm of politics. Stats 101 vs PolSci 101, all over again, I know, sorry.) As for your graphs, what I was saying is precisely that, unless you've been trained to read graphs (and most people are not), you're going to be "fooled" more easily by the second one, won't you ?
    - msandford 12y ago
      > Which is precisely the point of the old "money does not buy happiness" adage, isn't it ? Not the way I read it, really. If money doesn't buy happiness, then the graph should be completely flat right? Or at the very least a uniformly distributed scatter plot? But it doesn't really seem to look that way. While I suspect that there's some truth to the adage, it's definitely not absolute. > Science that says "This 1000ths gallon of water is gonna be as good as worthless" seems to favor the point rather than oppose it. That's not the point. The point is that as you have more of a thing, it takes more to move the needle. EVERYTHING has decreasing marginal utility, and money does too. But I don't think the marginal utility of money ever becomes zero, or goes negative. Do you think that? If so, please start sending me your money so that you can be happier! Here's a great example for you. Raises are nearly always percentages right? Why not just give everyone a $100 a year raise? I mean, that $100 is supposed to be the same to everyone, isn't it? 10% more money increases your happiness approximately the same, no matter what number that 10% increase is applied to. > As for your graphs, what I was saying is precisely that, unless you've been trained to read graphs (and most people are not), you're going to be "fooled" more easily by the second one, won't you ? I think that if you want to understand the way a system works across many orders of magnitude the only way to do so without fooling yourself is to look at a log/log plot. If you don't, only the most extreme change on the plot shows up and all the rest gets compressed into a "straight" line by the vagaries of turning an infinitely variable thing into a finite set of pixels.
- Dylan16807 12y ago
  They are claiming there is a point where money stops being important. There is no such point. There is no reason to favor any particular income level. If you use the happiness graph to make an argument that $50k is all anyone needs, I can use the same graph to show that $400 is all anyone needs. If the 'up to a certain point' hypothesis was correct, with the graph leveling out, there would be a maximum happiness-from-money. You could say "oh well 85% of max is plenty, the ideal income is X". But the data says that's not true. --- Humans intuitively understand logarithmic scales. Arguably even better than linear scales. A lot of our senses are logarithmic, after all. It's obvious that one dollar does not buy one happiness, given that millionaires aren't in ecstatic shock. But every time I double my income I gain the same number of happiness units? Sounds like money buying happiness to me.
  - phtrivier 12y ago
    Regarding your comment about log scales, is there a "sense" (or kind of perception, etc...) beside earing that "obviously" logarithmic ? Also, as another "I don't get stats get me out of here" question, isn't it problematic to plot against a "perception" level that (unless I'm mistaken) is linear ? What do you do with someone that answers "I'm happy at a 10/10 level". Do you consider it an outlier by definition ? Assuming the "happiness" self-rating is indeed linera, is it still a fallacy to think that, behind the mathematical rightness, there is value in knowing that after $x/year, y% of the population rates itself as above, say, 8/10 ? I'm under the impression that it's a different argument than say "after $x/year, everyone is happy" ; but that it can still be practical (especially if you can corelate lower levels a happiness with stuff you want / should / need to get rid of. But again, talking politics at a math cocktail, probably bad manners.)
    - Dylan16807 12y ago
      Brightness is pretty logarithmic. Touch, smell, taste, all of those seem logarithmic to me. People rating out of 10 distorts the numbers in multiple ways, that's a separate issue to deal with. Ideally you'd remove self-reporting in some manner... >value in knowing that after $x/year, y% of the population rates itself as above, say, 8/10 If it's linear with a cap of 10 then all the reasoning from before goes in the trash. The graph won't actually be logarithmic and you can set a cutoff easily. If you can calculate a linear happiness score with no cap, then it's possible to pick a point that's "happy enough", but that point will be arbitrary. It won't be based on an inflection point on the graph, because the graph has no inflection points. You can use your judgement to say that 12 happiness points is plenty, but that's not a math question.

pc86 12y ago

I'm curious about this too. I'm familiar with the economic concept of diminishing marginal utility, and I get that the $10k you get from $120-$130k/yr is much less valuable to you than the $10 from $40-50k. But there still seemed (to my Stats 101-level interpretation) that there was a decent-enough jump between $75k and $130k and beyond that happiness/utility increased significantly as income did beyond the commonly cited figure. For those of you who earn the requisite amount, is it true that it's easier to get a significant raise at the higher income levels? I live in a fairly rural area but I've found as my income rises the degree to which I need to fight for marginal pay increases has diminished, which seems counter-intuitive since each point gets more and more expensive, obviously.

Spellman 12y ago
You're understanding the actual data quite well as it turns out. Moving from $40k -> $50k is a much bigger gain on the happiness scales since it is a larger % increase. Moving $120k -> $130k is much smaller relatively, even though it's still $10k. As for getting larger raises, many jobs you get raises based on a percentage of your current salary. So if you get a 5% year-over-year raise and your base salary is $120k, you're getting a similar happiness boost as the 5% year-over-year raise of someone making $40k base salary. But you're getting way more in terms of net actual dollars.