All Questions
Tagged with confidence-interval variance
112 questions
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Find the confidence interval of ratio of variance with unknown distribution but known mean [closed]
From the previous question, I'm going to assume that for a random sample $X_1,X_2,\dots,X_n$ and $Y_1,Y_2,\dots,Y_n$, that $\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}} \xrightarrow{D} N(0,1)$ by ...
2
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57
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Learning to do the parametric bootstrap
I learned about the parametric bootstrap (Can we bootstrap regression coefficients instead of data?) and I am interested in applying this method to determine the confidence interval on the ratio of ...
- 721
3
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1
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71
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Can we bootstrap regression coefficients instead of data?
I have a question about using the bootstrap in situations (e.g. Confidence intervals for the ratio of marginal effects? (GAM Regression)) where the traditional bootstrap method might be complicated (e....
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2
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1
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205
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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 ...
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59
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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 ...
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1
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104
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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:
$$...
- 1,176
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3
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222
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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 ...
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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 ...
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62
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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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358
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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\% $ ...
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799
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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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214
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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 ...
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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 ...
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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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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 ...
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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 ...
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95
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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
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0
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76
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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
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1
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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 ...
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1
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137
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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 ...
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108
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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 ...
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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 ...
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86
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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 ...
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2
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2
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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 ...
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0
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129
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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 ...
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185
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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
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1
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763
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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 ...
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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{...
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47
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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 ...
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1
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167
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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 ...
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2
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239
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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}...
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0
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70
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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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169
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Question about confidence intervals and prediction intervals
Considering following linear multiple regression model:
\begin{equation}
y=X\beta + e,
\end{equation}
where observations $y\in\Re^n$, coefficents $\beta\in\Re^p$ and $e\sim N(0,\sigma I)$ is a white ...
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143
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Bootstrap estimation of variance and C.I. in cases with small group of outliers
I have a given quantity, say $y_a$ which parametrically depends on $a$ value. I consider $N$ values for the $a$ parameter and, for each one take multiple measures of the corresponding $y_a$ (say $N_a$ ...
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0
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56
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Confidence interval for relative risk with uncertain incidences
The usual suggestion for computing a confidence interval for a relative risk estimate is to start from the variance:
$$
\text{CI}_R = R \pm z \cdot \exp \sqrt{\sigma^2_{\log R}}
$$
where $R$ is the ...
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0
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137
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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 ...
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1
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50
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How to compute the confidence interval for the Difference of Two Means with unknown variance?
I have to determine the 90% confidence interval for the difference of Two Means of expenses in products for the cleaning of Palace A and Palace B.
I have the following data: on a sample of 21 cleaners ...
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0
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18
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Calculate confidence interval for the population variance [duplicate]
Here is the problem:
When cheching the Chi squared distribution table, the it seems like in the solution the denominators should be switched, because for .025 quantile the value is 13.844 and for ....
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2
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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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Calculating confidence intervals for the variance of the residuals in R
I have three variables:
Number of house sales
Month (in couples)
Region of a city (N-W-E-S)
and I want to calculate confidence intervals for the residual of the errors. So, given the data:
...
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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 ...
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Linear model – confidence interval for $\sigma$
I'd like to derive a $100\%(1-\alpha)$ confindence interval for $\sigma$ in a linear model $Y=X\beta+\epsilon$, $X$ - $n\times p$. I thought that I could make use of the fact that:
$\frac{RSS}{\sigma}=...
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How to estimate the confidence interval for a "predicted difference" from a quadratic model?
Assume you have past consumption levels $c_1, \dots c_n$ at times $t_1, \dots t_n$ and cumulated consumption levels $y_1=c_1, y_2 = c_1 + c_2, \dots y_n=\sum_{k=1}^{n} c_k$.
(I use the quadratic term ...
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1
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360
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Confidence intervals for averages of averages
Suppose we have an experiment involving $N$ independent samples of single variable functions, $y_1(t),...,y_N(t)$ where $$y_k(t) = \dfrac{1}{M}\sum_{j = 1}^{M} x_j(t); \ \ k = 1,...,N.$$ I am ...
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Confidence Ellipsoids
I need help to understand and answer the following question.
I referred the following website to read about the confidence ellipsoids.
https://www.visiondummy.com/2014/04/draw-error-ellipse-...
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Pointwise standard error and confidence interval for a smoothing spline
I wish to generate confidence intervals for a smoothing spline using the pointwise standard error of $\hat{f}_\lambda(x)$. In particular, I am trying to construct the following interval: $$\hat{f}_\...
- 556
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2
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850
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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 ...
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140
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Computing the confidence interval for two samples but getting slightly different answers
Consider two samples $X_1,..,X_k$ and $Y_1,..,Y_m$ where $X_i \sim \mathcal{N}(\mu_x,\,\sigma^{2})\,$ and $Y_i \sim \mathcal{N}(\mu_y,\,\sigma^{2})\,.$ Say $k=m=100$ and $k+m=n$. Say that the ...
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1
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330
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Ratio of Standard Deviations from a Normal Distribution to an F Distribution
Apologies if the title is confusing, I couldn't think of a more apt title.
I have that $W_i$s are iid $N(\mu_a,\sigma_a^2)$ and independent of $Z_i$s which are iid $N(\mu_b,\sigma_b^2)$. This means
$...
- 367
2
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1
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225
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Can the variance of a U-statistic be of the order $O(\frac{1}{n^2})$?
It is not that easy to find estimators $T_n$ such that $\mbox{Var}[T_n] \sim O(n^{-B})$ with $B = 2$. In most cases, $B=1$.Here $n$ is the sample size. It seems, according to this paper on U-...
