All Questions
12
questions
1
vote
1
answer
72
views
Difference between F-test and confidence intervals on variance estimates
Given n samples from a normally-distributed variable X, we estimate variance as $s^2=\frac{1}{n-1}\sum{(x_i - \bar{x})^2}$. We can also get a confidence interval for such a variance estimate as:
$$...
- 1,162
0
votes
0
answers
54
views
Variance of powers of a standard normal random variable
To predict growth of money in a stock market I try to calculate expected return over a longer timeframe (e.g. 30 years) with a confidence interval. The simple math of taking an average stock market ...
- 139
1
vote
1
answer
556
views
Confidence interval calculation: why sometimes the SD is dividted by the sqrt of sample size, and sometimes not?
I have trouble understanding the following:
Looking how reference ranges for laboratory values are calculated, I found the following:
In our sample of 72 printers, the standard error of the mean was ...
- 95
0
votes
0
answers
133
views
Bootstrapping variance in R gives weird shaped distribution- how to obtain confidence intervals?
this is the first time I've used bootstrapping so it's quite basic!
I'm trying to obtain confidence intervals for the standardised variance- defined as the variance over the square of the mean- across ...
- 41
1
vote
0
answers
63
views
Generating a confidence interval for the difference in standard deviation between two populations
Background
I've made a device which sizes potatoes, and one component in that device comes with a known error with respect to mean and standard deviation. I want to know whether my device - which ...
- 277
1
vote
2
answers
838
views
If you know a normal distribution's population variance, does a sample variance tell you nothing about the sample's mean's confidence interval?
If I understand correctly (which I might not), if I know a normal distribution's population variance but not its population mean, and take just one sample consisting of three measurements, then no ...
- 67
1
vote
1
answer
962
views
Confidence interval for $\sigma^2$
I started with any distribution and underwent the CLT on $\sqrt{n}(\widehat{\sigma}^2 - \sigma^2)$ where
$$
\widehat{\sigma}^2 = \frac{1}{n}\sum_{i=1}^n (X_i - \mu)^2
$$
is a sample mean of $\sigma^2$...
0
votes
1
answer
1k
views
Confidence intervals and variance for ordinal scale set [0-5]
We have a known sample of data coming from a multiple choice ordinal scale survey question with scores from the set [0,1,2,3,4,5].
In one sample, the mean of this ...
- 101
9
votes
4
answers
3k
views
Would a $(1-\alpha)100\%$ confidence interval for the variance be narrower if we knew the mean a-priori?
Let's say we know the mean of a given distribution. Does this affect the interval estimate of the variance of a random variable (which is otherwise computed using the sample variance)? As in, can we ...
- 193
8
votes
1
answer
932
views
Are group effects in a mixed effects model assumed to have been picked from a normal distribution?
Say we're interested in how student exam grades are affected by the number of hours that those students study. We sample students from several different schools. We run the following mixed effects ...
- 14.5k
3
votes
2
answers
8k
views
Confidence interval of quantile / percentile of the normal distribution
What is the formula (if it exists) for the sample variance / confidence interval of a quantile / percentile of the normal distribution?
For example, the 5th percentile for a standard normal ...
- 31
28
votes
3
answers
4k
views
Confidence Interval for variance given one observation
This is a problem from the "7th Kolmogorov Student Olympiad in Probability Theory":
Given one observation $X$ from a $\operatorname{Normal}(\mu,\sigma^2)$ distribution with both parameters unknown, ...
- 4,279