All Questions
Tagged with confidence-interval variance
110
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Standard error of estimated sum or product mean
Updated question: Given two sample means ($\bar X, \bar Y$) and sample standard deviations ($S_X, S_Y$) with different sample sizes ($n_X, n_Y$), I want to calculate the standard errors ($SE_\theta, ...
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Expected Value Chi Square distribution
I'm trying to simulate the distribution from the sample variance $s^2$ and compare it with the theoretical distribution.
Therefore, I perform a fairly simple simulation (upfront, I'm not a ...
- 40.5k
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In Regression Through the Origin, why do the CIs of the slope depend on datapoints with zero x value?
I'm working with a Regression Through the Origin model as described in this reference.
The model is $Y_i = \beta X_i + \epsilon$ and the least squares estimate of $\beta$ is $\hat\beta = \frac{\sum ...
- 129k
28
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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, ...
- 31.3k
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Metric for run-to-run consistency of time series data
If I run $n$ samples of a physical experiment, I expect to see roughly similar time vs. position plots but with slight variations run-to-run. What are good statistical metrics to quantify the ...
- 81.4k
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Propagation of confidence interval through subtraction of variance estimates
Consider a biochemical method which is sensitive to the concentration of reagent A.
The method produces a signal with variance var(method) when reagent A is repeatedly sampled from the same stock (no ...
- 81.4k
1
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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:
$$...
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Shouldn't we consider the difference in variance between population and a sample while calculating confidence intervals?
To comprehend the concept of confidence intervals, I came up with an example. I want to share it here for your better understanding what my question is all about.
Suppose, we want to figure out what ...
- 286k
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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
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For non-normally distributed random variables, why does $[\mu - 1.96 \sigma, \mu + 1.96 \sigma]$ contain $\approx$ 95% of the distribution?
My question is, if you take a random variable $X$ with an arbitrary distribution, which has a known and well defined mean & variance, then why does the following interval contain $\approx 95\% $ ...
- 92.6k
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How to get confidence interval for the population variance?
I have data that is reasonably assumed to be iid samples from some distribution. Our goal is to put a confidence interval on the population variance. Notationally, we have IID $X_i, i = 1, ..., n$ ...
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How to calculate the p-value of a log-odds ratio, given that the variance depends on the observed frequencies?
I am a bit confused about how people calculate p-value when calculating odds-ratios.
The log-odds ratio (LOR) for a contingency table with two entries is $L = \log \frac{p_{1}}{p_{0}}$ and has an ...
- 95.7k
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Why are published stats generally given as +/- standard deviation?
I've been wondering why most publications give stats as mean +/- standard deviation, even for things like measurement devices, where reproducibility is a major concern. (E.g., for a given sample, our ...
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Probability that both the mean and sample variance are both covered by their respective confidence intervals?
I am given the question: "What is the probability that both the mean is in its confidence interval for confidence level a and the variance is in its confidence interval for confidence level a?&...
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Intuition for estimating population standard deviation
I know how to estimate population standard deviation using a chi square distribution, but I don't know why it works. I'd like to have an intuition for the why.
I've tried googling around. I always ...
- 11.9k