All Questions
Tagged with confidence-interval variance
110
questions
2
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1
answer
145
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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 ...
- 33
5
votes
1
answer
45
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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 ...
- 151
1
vote
1
answer
72
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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:
$$...
- 1,162
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votes
0
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56
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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 ...
- 21
3
votes
3
answers
157
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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 ...
- 35
1
vote
0
answers
23
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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 ...
- 11
0
votes
0
answers
54
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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
4
votes
2
answers
310
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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\% $ ...
- 810
10
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3
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715
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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$ ...
- 483
1
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1
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134
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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 ...
- 130
0
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0
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34
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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 ...
1
vote
0
answers
26
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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?&...
- 11
2
votes
2
answers
1k
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Confidence Intervals for Odd's Ratio? [duplicate]
I am an MBA Student and I am trying to understand how to calculate the Confidence Interval for an Odd's Ratio. Our professor gave us this link (https://www.ncbi.nlm.nih.gov/books/NBK431098/) which ...
0
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0
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25
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Variance in a confidence interval for a percentage in a survey sample
I'm teaching an undergrad class on survey sampling (not in the stats department) for the first time. This seems like a very basic question that I should know the answer to, but I can't find it ...
- 61
2
votes
1
answer
95
views
I'm stuck in a part of an exercise where I'm asked to find a variance so that its confidence interval is within some bounds
I'm trying to complete an exercise from my book, asking me to find
the variance to allow a sample of 49 items (that follows a normal law)
to stay in bounds of one confidence interval, at 95% of ...
- 243
2
votes
0
answers
74
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How to Calculate the Variance of the Aggregate of a Bernoulli Process Given Known False Positive and False Negative Rates
I have $n$ sensors which output either $0$ or $1$. These sensors have known measurement error reflected by a false positive rate, $fpr$ and false negative rate, $fnr$. In my case, $fnr > fpr$.
...
2
votes
1
answer
2k
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What is the impact of duplicate data on the variance of regression coefficient? [duplicate]
What is the impact of duplicate data on the variance of the regression coefficient?.
Does increasing the size of data always certainly decrease the variance of the model coefficients?
Suppose I have ...
- 223
0
votes
1
answer
106
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Are there possibilities to determine 95% confidence interval for right skewed data?
The dataset that I'm using for my thesis is right skewed. It is about lead times (days) I tried log10 transforming it in SPSS but it still does not meet the requirement p>0,05 (Shapiro-wilk). So ...
- 1
1
vote
0
answers
100
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What is the confidence interval of consecutive subsampling
I have a situation where I do consecutive subsampling from an original population and I'm trying to figure out what the final confidence interval would be. I know that Var(A,B) = Var(A) + Var(B) if A ...
- 121
0
votes
1
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53
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Evaluating randomized algorithms on randomized problem instances
Suppose we want to compare the performances of two algorithms — call them A and B — on a problem X. In particular, suppose that we want to evaluate the algorithms on random instances of X drawn from ...
0
votes
1
answer
80
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Calculating variance / standard errors for a Weighted Repeat Sales model
I'm writing an implementation of the Case-Shiller Real Estate Index, which is based on a variation of the weighted least squares, except for the introduction of a dummy matrix Z. I've calculated the ...
- 101
2
votes
2
answers
58
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How can I confidently state the error of a specific test is within a range with a 95% confidence interval
I have a test that provides values with known amounts of error. For instance the error on the test
(Value - TrueValue) = -7.62, -9.33, -8.36, -9.79,-10.45, -9.51, -10.83, -10.64, -9.96, -10.30
I want ...
1
vote
0
answers
128
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Confidence interval for exponentially distributed estimator
We have an estimator $\hat{\theta}\geq 0$ for $\theta$, with distribution function $P\{\hat{\theta}\leq t \}=1-e^{-t/\theta}$, which we can recognize as the cdf of the exponential distribution. Our ...
- 85
1
vote
1
answer
180
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Deriving a confidence interval for the variance $\sigma^2$ of a non-normal distribution
If $X_1, \cdots, X_n$ are normally distributed, the Student's Theorem asserts that the pivot variable $$\frac{(n-1)S^2}{\sigma^2}$$ is distributed $\chi^2(n-1)$. Then suppose I can find constants $a$ ...
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
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votes
0
answers
28
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Where does (co)variance come from in a linear (OLS) regression?
Given that linear models can be solved exactly via calculus, how is it possible to define a variance for the parameters ($\mathbf{a}$) which minimize some error function? say $Err=(o_i-f(x_i; \mathbf{...
- 143
1
vote
0
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45
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Practical use for heritability value at sub-population level?
For me as a layperson, heritability is something that much smarter people than me calculate, and there are several questions already on the forum about how to do that (eg, this and this). I ...
- 111
1
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1
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160
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How to calculate errors of best value of parameters that obtained from MCMC method and observational data
I had a model and some observational data. I used MCMC method to obtain the best value of free parameters and used some coding to plot contours of 1 to 3 sigma confidence levels (as you see in the ...
0
votes
2
answers
231
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Estimate confidence interval for the variance of whatever population distribution
Given a sample of the variable $X$ = ($X_1$, .., $X_n$).
If the $X$ follows a normal distribution, I know that we can estimate the confidence interval of the variance of $X$ by using the $\chi^{square}...
1
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0
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66
views
What are the implications of a low coverage in multiple imputation?
When testing multiple imputation algorithms in simulations, the bias of the examined estimates and the 95% coverage rate are often used as a quality metric. I understand that it is generally ...
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