U.S. Employees Are the Happiest | Hacker News Reader

U.S. Employees Are the Happiest

statista.com

There is no link to the original study. There are two links within the text, but neither of them link to the study. In fact, one of those two links is misleadingly presented as the link to the study, but is not actually the link to the study.

Challenge question for stats and math nerds: if 93% of a sample of 1000 Americans claim they enjoy their job, and if 91% of a sample of ~650 Netherlanders claim that they love their job, then what are the odds that this is a statistical fluke and that a greater portion of Netherlanders enjoy their jobs than Americans?

If the methodology is good, the chance of a fluke is pretty low, given the 2% difference and large sample size.

It is much more likely that the result would be thrown off by a sampling error.

You're looking to test the difference in proportions. I entered 0.93 / 1000 / 0.91 / 650 into this online calculator [1] and got a p-value of 0.14 which means that the difference is not statistically significant. Technically you would want to do some correction for multiple comparisons since your actual question is "are Americans more happy than workers in every other country?" not "are Americans more happy than Netherlanders specifically?" but it's a moot point since the difference already isn't significant.

A more important question is probably how the sampling was conducted. How did they guarantee a representative sample in each country? How did they account for the gig economy, small businesses, part-time employees, and employees paid under the table? So many ways a survey like this could be wrong.

[1] https://www.socscistatistics.com/tests/ztest/default2.aspx

I'm replying to myself. Warning: serious math ahead.

This is part of a class of statistical problems that I really want to figure out how to solve, because I feel like understanding problems like this will give me a much, much stronger foundational understanding of statistics. For example, can anyone here explain how sampling a normally-distributed population with unknown mean and unknown variance brings forth the Student-T distribution? No explanation that I have read makes any sense on a pre-computation, intuitive level of understanding.

So let me at least set up the foundation for the math needed to answer the question: "What are the odds that Netherlanders are actually happier than Americans regarding their jobs, given that a sample of 1000 random Americans produced 93% whom are happy with their jobs, and a sample of 650 Netherlanders produced 91% whom are happy with their jobs".

The setup: let's imagine a multiverse. Inside this multiverse are an infinite number of universes, and inside each universe, x% of Americans are happy with their jobs. The value of "x" varies between each universe; for each universe, there is a single, unique value of "x", and for each value of "x", there is a single, unique universe.

Let's imagine that when we see the results of a survey of 1000 Americans, we do not know which universe it came from. It's possible that exactly 930 out of 350,000,000 Americans are happy with their job (essentially 0%), but that random selection of 1000 Americans just so happened to pick those 930. It's possible that 99% of Americans are happy with their jobs, but the sample just so happened to randomly pick up too many unhappy workers.

If we have a universe where 50% of the American population is happy, then there is a 1000-Choose-930 * 0.50^930 * 0.50^70 chance that a random sample of 1000 will have 93% of the sample will be happy with their jobs (binomial distribution; the odds that 10 coin flips will land on 5 heads depends partially on the number of ways 10 coins can be deliberately arranged so that 5 specific coins will be heads up). 1000-Choose-930 * 0.50^930 * 0.50^70 = 6.5710^-193. If we have a universe where 93% of the American population is happy with their jobs, then there is a 1000-Choose-930 0.93^930 * 0.07^70 chance that a random sample of 1000 will have 93% of that sample be happy with their jobs. 1000-Choose-930 * 0.93^930 * 0.07^70 = 0.0494. In general, when we have a universe with x% of the population happy with their jobs, the odds that a random sample will show 93% happiness is 1000-Choose-930 * x^930 * (1-x)^70.

We now need to step back into our multiverse and realize that we're sampling 1000 people from each universe with equal probability, and then collecting the number of "samples of 1000 people show 93% happiness" instances into a single pot. We need to ask ourselves, "given that we have a sample of 1000 people showing 93% happiness, what are the odds that we are in a universe where x% of the American population is happy?". The answer to that is: "The number of times a universe with x% happiness produces a sample of 1000 with 93% happiness, divided by the number of times all the universes in the multiverse produces a sample of 1000 with 93% happiness.

The percentage of "93% of sample of 1000 are happy with their jobs" samples in a universe with x% happiness, compared to all the other equally-likely-to-be-chosen universes, in a situation where each universe has been sampled 10^99999 times, is approximately: (1000-Choose-930 * x^930 * (1-x)^70 * 10^99999) / sum(i=0;i<100;i+=1 { 1000-Choose-930 * i^930 * (1-i)^70 * 10^99999 } ), assuming that there are only 100 universes in a multiverse where "x" takes on only integer values. For a bit more rigor, we have to allow x to take on all real values, and recognize that the probability of picking a single value of "x" out of a continuum of real values from 0 to 100 is effectively 0%; what we ultimately have to do is calculate the probability that the universe we inhabit rests within a range of values of x.

So, bringing a bit of calculus into the fold: The percentage of "93% of sample of 1000 are happy with their jobs" samples in a universe with x% happiness (where x is between numbers x1 and x2), compared to all the other infinite equally-likely-to-be-chosen universes between x=0 and x=100, is: integral(x1 through x2: 1000-Choose-930 * x^930 * (1-x)^70) / integral(0 through 100: 1000-Choose-930 * i^930 * (1-i)^70)

Likewise, if we create another multiverse of universes where y% of Netherlanders (with varying values of y) are happy about their jobs, then the odds that a random sample of 650 Netherlanders will have 91% of that sample confess happiness with their job is: 650-Choose-592 * y^592 * (1-y)^58. So if we consider all universes equally likely, and we are given a sample of 650 people, 91% of whom are happy with their jobs, then the odds that we are living in a universe where the real, actual percentage of Netherlanders are happy with their jobs lies in between values y1 and y2 can be calculated. That calculation is: integral(y1 through y2: 650-Choose-592 * y^592 * (1-y)^58) / integral(0 through 100: 650-Choose-592 * y^592 * (1-y)^58).

My original question was this: what are the odds that the original survey was a statistical fluke, and that Netherlanders are happier than Americans with their jobs? Well, if 0% of Americans are happy with their jobs, then we need to know the odds of 0%-100% of Netherlanders are happy with their jobs. If 1% of Americans are happy with their jobs, then we needs to know the odds of 1%-100% of Netherlanders are happy with their jobs. If there is a 50% chance that 0% of Americans are happy with their jobs, and also a 50% chance that 1% of Americans are happy with their jobs, then the odds that Netherlanders are happier with their jobs than Americans is 50% times the odds of 1%-100% Netherlander satisfaction, plus 50% times the odds of 2%-100% satisfaction. Generalizing this pattern, we get this equation: The odds of Netherlanders being happier = The odds of x% of Americans being happy with their jobs * the odds of x%-100% of Netherlanders being happy with their jobs.

The odds that x% of Americans are happy with their jobs is: integral(x through x+epsilon: 1000-Choose-930 * x^930 * (1-x)^70) / integral(0 through 100: 1000-Choose-930 * i^930 * (1-i)^70). The odds of x%-100% of Netherlanders are happy with their jobs is: integral(x through 100: 650-Choose-592 * y^592 * (1-y)^58) / integral(0 through 100: 650-Choose-592 * y^592 * (1-y)^58). Now we need to multiply those values together and take the limit as epsilon goes to zero:

lim (as epsilon -> 0): integral(0 through 100: {integral(x through x+epsilon: 1000-Choose-930 * x^930 * (1-x)^70) / integral(0 through 100: 1000-Choose-930 * i^930 * (1-i)^70)} * {integral(x through 100: 650-Choose-592 * y^592 * (1-y)^58) / integral(0 through 100: 650-Choose-592 * y^592 * (1-y)^58)}.

Someone please evaluate that expression. Or at least check my math/logic.

There is no study. There is a poll run by a coworking space management company.

What about our lack of vacation days and holidays?

There's pizza and cake in the breakroom, let's all stay until 6:45!

Perks don't necessarily make people happier with their jobs, even if state mandated.

Americans intentionally don't utilize a large number of paid vacation days each year. Work guilt may play a role:

"Americans left 768 million days of paid time off unused last year, according to research released by the U.S. Travel Association. The study found that 55 percent of Americans did not use all of their paid vacation time."

"More than half of U.S. workers ― 54 percent — reported feeling guilty about taking vacation time either sometimes, often or always, according to a survey of more than 2,000 full-time workers in the United States by TurnKey Vacation Rentals."

https://www.washingtonpost.com/travel/2019/08/28/what-does-a...

> Americans intentionally don't utilize a large number of paid vacation days each year. Work guilt may play a role

It may, but America has relatively weak protections for paid or even merely job-protected medical, family, or other leaves and fairly weak unemployment; accruing vacation balances as a partial substitute is a common strategy; while it may not fully substitute for any of those, it a minimum provides an amount obligated to be cashed out at termination that can buffer the impacts of not having the other protections.

> More than half of U.S. workers ― 54 percent — reported feeling guilty about taking vacation time either sometimes, often or always

But is this “work guilt” or guilt about the impact on personal/family security?

> Americans intentionally don't utilize a large number of paid vacation days each year. Work guilt may play a role

That is a plausible but pessimistic view of the situation. The more optimistic reading is that american workers derive personal pleasure and fulfillment from the work itself. If you are happier working in a fulfilling job than sitting idly on a beach, then it would make sense you wouldn't use all of your vacation days.

Work guilt probably does play a role, as does corporate policies that subtly punish vacation, but I would also bet that some percentage of workers actually enjoy what they do.

> than sitting idly on a beach

Or spending time with family, learning a new skill, going on an adventure.

"Off-time" is not an adversary to great work life, productivity and innovation. Some would even claim the opposite was true.

> "Off-time" is not an adversary to great work life, productivity and innovation. Some would even claim the opposite was true.

I don't disagree, we're not talking about absolutes here. But it's reasonable to consider that, all other things being equal, someone who loves their job may be less inclined to take as many vacation days compared to someone who hates their job.

Advocating for longer vacations, leisure time, and simply being disconnected so folks can develop their interests outside of work are important. However, most people spend most of their non-sleeping life at work. Accordingly, making work itself more fulfilling can often have a far greater impact than simply requiring less of it.

As a manager I do not accept that team members skip PTO. We're not paying for it to be nice, we expect ROI. Happy, healthy people are generally productive, highly cooperative and inventive.

> As a manager I do not accept that team members skip PTO.

Sure, but as a manager, you should probably know that giving people engaging work, with meaningful impact, and significant personal growth opportunities is often a greater motivator than providing additional days off.

You misunderstand. Off-time provides benefits that are almost impossible to achieve in even the best work environment.

* PTO is not about motivation - it's about quality of work output.

I have combined PTO, vacation and sick leave, and like keeping a healthy balance.

Throughout all of the jobs I've ever had, I've always taken less time off at jobs I liked more. It was the jobs I hated where I always ran out of vacation time, even when they had good PTO packages.

A lack of vacation can make a job shitty. But a shitty job with some vacation doesn't make it a pleasant job.

If work were all unicorns and rainbows, it wouldn’t be work. Employers are businesses so things that drive revenue/profit for them are the work that needs to get done. You can’t argue that figuring out ways to show people more ads is meaningful work, but it has to get done by somebody.

If someone had enough F.U. money saved up to FIRE, you can guarantee they won’t show up for their boss the next day. As it stands, nobody ever goes to work at their current job whenever they get a windfall; they always leave to follow their passions.

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