Questions tagged [standard-error]

For basic questions in statistics involving the properties or use of standard error of the sample points present in a simple random sample.

0
votes
0answers
130 views

Gap correction between two curves

I have two curves like this : I would like to be able to calculate the gap between these two curves according to the Y value. For example: In my example Y < 5, error between the two curves is ...
1
vote
1answer
46 views

What is the best measure of error for a data set where each point is the mean of 3 quick readings?

I have an experiment that relies on measuring temperature as a function of a given condition. I change the condition, allow the temperature to stabilize as much as possible, then take 3 measurements ...
1
vote
0answers
14 views

Should I use $\sigma_x^{-2}$ or $\left(\sigma_x/x\right)^{-2}$ as my weights when fitting simulation data? My intuition tells me to use the latter.

I have simulated a set of probabilities $\{p_n\}$ by the hit-or-miss Monte Carlo method. Specifically, my program checks whether or not an $n\times n$ matrix has a certain feature or not; say that, ...
0
votes
0answers
152 views

Bivariate Normal Distribution Standard Error

Data from a large population indicate that the heights of mothers and daughters in this population follow a bivariate normal distribution with correlation 0.5. Both the mothers and daughters have a ...
1
vote
2answers
64 views

How to obtain the standard error of measurements that already have error bars?

Suppose I make three measurements: 9, 10 and 11. Let's say there is no uncertainty associated with these values because they are counts. Numbers of children in a class say. I want to know the average ...
1
vote
3answers
78 views

Standard error. Why does it get more accurate as N gets bigger?

I came across this quote about the Standard Error in the OpenIntro Statistics book: We required a large sample in Chapter 4 for two reasons: 1. The sampling distribution of x tends to be more ...
0
votes
1answer
2k views

How can we calculate the standard error from a single sample?

Say we sample 19 dolphins for mercury levels. Say the summary of the sample is here: So the mean is 4.4 and the sample's standard deviation is 2.3 From this, why do we say the standard error (which ...
0
votes
1answer
34 views

Error term in an infinite series

Well, I've the following series: $$\frac{1}{\left(1+\epsilon\cos\left(x\right)\right)^2}=\sum_{\text{k}=0}^\infty\epsilon^\text{k}\left(1+\text{k}\right)\cos^\text{k}\left(x\right)\tag1$$ This ...
3
votes
2answers
166 views

Are the statements about the confidence interval correct?

We have a 90%-confidence interval. I want to check if the following statements are correct. If double the sample, the possibility that the value that we are looking for is out of the confidence ...
2
votes
0answers
345 views

Standard Error of weighted mean estimate

$X$ is a random variable with unknown distribution. A number of experiments are conducted to estimate $X$. Each experiment has a different reliability measure in estimating $X$. These $n$ experiments ...
6
votes
3answers
3k views

Why do you use n-1 in Standard error of the mean but n in hypothesis testing

When you divide in hypothesis testing you use the formula: $$ \frac{\bar X-\mu}{s/\sqrt n} $$ but the standard error of the mean is: $$ \frac s{\sqrt {n-1}} $$ Why don't you use $n-1$ when ...
0
votes
0answers
29 views

derivation of standard error - Why can we assume all variances can be the same?

I'm learning how to derive standard error of the mean mathematically. I understand that standard error is the square root of the variance of the mean: $SE =\sqrt {Var((x_1+x_2+...+x_n)/n}$ And ...