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May
25
comment Standard Error of the ratio of Binomial variates
$Y$ has a positive probability of being $0$ (so too does $X$) which is going to cause issues with $\frac {X-Y}{Y}$
May
17
comment Clarify probability solution re. birthdays
Remember that (in some countries at least) births on Saturday and Sunday are less common than on other days because doctors like not working at weekends.
May
17
comment Combine several days of time series into one
Yes you can, though whether a simple linear regression would be meaningful is another matter (e.g. if you were measuring tiredness, there might be a cyclical pattern)
May
12
comment Poker and the Birthday Problem
You can make order matter in your poker hands and have $\dfrac{52!}{47!}$ possible hands, i.e. $5!$ as many. You could easily adjust the rest of your analysis to fit this. But this option to choose whether to make order matter or not does not work so well with sampling with replacement especially if you want to use counting arguments.
May
10
comment Should I use A/B testing to find evidence that click-through rate has changed over four months?
I would have thought the rate was $35/100$. You can certainly do something like what you are suggesting, but I would not all it A/B testing, which I would have thought meant showing different ads to different people in the same time period and comparing response rates
May
3
comment Stationarity after differencing
If $\beta_1$ is a non-zero constant then $E[x_t]$ is increasing with $t$, so the original process is not constant in mean.
Apr
14
comment Why small values produce undulating densities when ploting logarithm of a loguniform prior (in R)?
If I try x <- 100^runif(1000000); plot(density(log(x))) then I get something which looks sensible between $0$ and about $4.6 \approx \log_e(100)$, so what did you run to get that oscillation?
Apr
10
comment Roll a 6-sided die until the total $\geq M$. Mean amount by which $M$ is exceeded?
I suspect that $M=300$ could be read as "very large $M$" as I believe that $M=301$ or $M=999$ would give almost exactly the same result. What I would do is find the distribution of the sum minus $M$.
Apr
9
comment Is there a name for this sort of plot? Is there any reason not to use it?
Difficult to find the $5$th percentile of $9$ observations. I think I would call what you are describing as a band chart: this is one (in fact two) looking at daily high and low temperature across the year in London.
Apr
8
comment Basic stats question - How to tell if my data distribution is symmetric
$-70,-63,-56,-49,-42,-35,-28,-21,-14,-7,0,1,4,9,16,25,36,49,64,81,100$ is deliberately not symmetric (uniform in the lower half but not in the upper half) and a box plot would put the median (equal to the mean) nearer the upper quartile than the lower quartile but also nearer the minimum than the maximum.
Apr
5
comment correlation between spelling ability and frequency of use of text messaging
You could start with a scatter plot to see what the results look like (though with a large sample you should be aware of overlapping points)
Mar
28
comment Closed form solution for t-stats and p-values in multiple regression
Excel has the TTEST function
Mar
28
comment Why do we need confidence intervals?
Yes. They might be equal by chance, but probably would not be.
Mar
28
comment Why do we need confidence intervals?
The expected value of the sample mean may be the population mean, but more often than not the sample mean will not be exactly equal to the population mean, and different samples are likely to have different sample means.
Mar
28
comment Why do we need confidence intervals?
It takes effort to look at every single account to get the exact answer with certainty, so taking a sample saves effort at the cost of some possible sampling error. The bigger the sample is, the smaller the sampling error is likely to be, but requires greater effort.
Mar
20
comment The abundance of P values in absence of a hypothesis
That table is actually a good example of what happens with large sample sizes (even the small differences in average age appear to be significant, suggesting perhaps that average waistlines may widen with old age or perhaps that larger waists increase average life expectancy very slightly). But the $P$-values are not dominating the table and at best this is exploratory analysis which could provide hypotheses for future study (e.g. a longitudinal study seeing whether people's waists widen or whether they die). It also suggests some factors which might be worth controlling for in future work.
Mar
19
comment Why shouldn't the denominator of the covariance estimator be n-2 rather than n-1?
The denominator of your definition of sample variance is $n−1$ probably because this makes it an unbiased estimate of the population variance. The same is true of the sample covariance using the same denominator. But there are other definitions of sample statistics, with different denominators.
Feb
21
comment When does replication reveal fraud?
"Statistics means never having to say you're certain"
Jan
25
comment How to tell the probability of failure if there were no failures?
If there are few or no failures then $\Theta \sim U(0,0.1)$ will produce almost the same result as $\Theta \sim U(0,1)$ i.e. Beta$(1,1)$, and the latter is easier to handle
Jan
12
comment Density estimation for streams of Data
You could store your data as counts in intervals, where the intervals are substantially narrower than the bandwith you are using for smoothing your kernel. Then you just need to remember as many numbers as there are intervals.