# Tagged Questions

1answer
18 views

### Measuring variation of one data set with respect to another data set

Each of the points in the plot below is a mean of 1000 samples. The standard deviation of a point on the RED line is "small" in that it is smaller than the difference between the mean of the RED line ...
1answer
91 views

### What does it mean for variances to be equal?

What does it mean for variances to be equal? Is this the same as the variance to follow a normal distribution?
1answer
54 views

### Variance of a sample - proof

On page 72 of Introductory Statistics, A Conceptual Approach Using R (Routledge, 2012), the authors first compute the variance of a sample of size $n$ using: ...
0answers
87 views

### Setting intercept to zero: Will this change both standard deviations and the error term?

After running a single regression with a forced zero intercept, I understand that $\beta$ (slope(s)) will change as $\alpha$ (intercept) will be set to zero. Easy. $\rho = \beta(\sigma_x / \sigma_y)$ ...
1answer
20 views

### Demand with different Measurement

Weekly's demand of a product has a probability function ...
1answer
82 views

### Quantifying heterogeneity

I have been trying to quantify the heterogeneity of a given variable. I'd like to say that the distribution in calcite concentrations, for example, is more heterogeneous in one rock formation than ...
1answer
72 views

### Estimating the population variance [duplicate]

I'm trying to understand the emphasized phrase in the following passage: The usual method of determining the probability that the mean of the population lies within a given distance of the mean of ...
1answer
230 views

### Standard deviation of binned observations

I have a dataset of sample observations, stored as counts within range bins. e.g.: min/max count 40/44 1 45/49 2 50/54 3 55/59 4 70/74 1 Now, ...
0answers
22 views

### Variance of superset from variance of subsets [duplicate]

Let's say I want to estimate $var(A)$ of a list of numbers $a_i \in A, i\in [0,N]$. However, I only have the variance of the non-overlapping, and complete ($B \cup C = A)$ subsets $B$ and $C$. ...
3answers
275 views

### How to quantify the effect of an independent variable on the standard deviation of the dependent variable?

My independent variable changes the variation in the dependent variable. The mean doesn't matter, just the variance. Bartlett and Levene's tests indicate a small p-value and thus significant ...
2answers
173 views

### Population Variance and Sample Variance

How is it that lowering the number of frequence,$n$ by $1$ in the for formula for Population and Sample Variance account for the discrepency of using sample rather than population. I mean how is ...
0answers
80 views

### Prove one assumption in confidence interval for difference in means

How to prove that $\sqrt{( s_1^2 / n_1 + s_2^2 / n_2)}$ converge in probability to $\sqrt{( \sigma_1^2 / n_1 + \sigma_2^2 / n_2)}$? $s^2$ converge in probability to $\sigma^2$, when n goes to ...
1answer
195 views

### Combining and ranking standard deviations

I am trying to take three independent indicators and combine them into a single composite measure. For discussion, let's say that this is a composite measure for 'economic performance', and that the ...
0answers
84 views

### Why does GARCH use squared residuals?

Take GARCH(1,1). Suppose the mean equation is: $$y_t = \mu + \epsilon_t = \mu + z_t\sigma_t$$ with $z_t \sim N(0,1)$, $\epsilon_t \sim N(0,\sigma_t)$. Then the univariate GARCH(1,1) variance ...
1answer
463 views

### Variance of a bounded random variable

Suppose that a random variable has a lower and an upper bound [0,1]. How to compute the variance of such a variable?
1answer
138 views

### Variance or standard deviation from a value other than the mean

Is there a term(s) for calculating the variance or standard deviation from a value other than the mean? Example: If I have a set of estimates for jelly beans in a jar, calculating standard deviation ...
1answer
105 views

### Are $\sigma_{70\%} = cte * \sigma /\sqrt{N}$, & $\sigma_{\bar x_{70\%}} = cte * \sigma /\sqrt{N}$ valid with non-normal distributions?

My working population is non normally distributed and from time to time I need to take a sample of it. Sometimes my sample exists of 100 units, at other times of 150 units. Of my sample I calculate ...
6answers
36k views

### What's the difference between variance and standard deviation?

I was wondering what's the difference between variance and standard deviation? If you calculate it its is clear that you get the standard deviation out of the variance... But what does that mean in ...
2answers
190 views

### Size of the data set for measuring variation

This might be a simple question but I am unable to find a solution on the web. I would like to measure variation of some numerical data. What is the minimum number of values I should use for measuring ...
0answers
1k views

### What does a squared coefficient of variation signify?

The coefficient of variation is defined as the ratio of S.D to mean, a dimensionless number which on multiplication by 100 gives the percentage of dispersion with mean. But when we square this ...
0answers
138 views

### How do I test whether differences in populations are significant?

I'm working on a large database. I want to explore whether certain batch jobs run in more or less time after a change was than they did before the change. There are about 90 distinct batch jobs. They ...
0answers
135 views

### Is 2-sigma limit applicable as a measure of variance to a distribution?

There is a paper that uses something like the 2-sigma limit to check if a quantity is more-or-less constant. More specifically in this paper on Text Detection (Sec. 3.2 3rd para last line) this limit ...
1answer
83 views

### Estimate variance of sub-sets from overall variance

I am looking for a way to estimate the variance of a summed sub-set based on the variance of those sums. Si = sum( Ai ) S = { S0...Sn } V = variance( S ) That ...
2answers
1k views

### Maximum value of coefficient of variation for bounded data set

In the discussion following a recent question about whether the standard deviation can exceed the mean, one question was raised briefly but never fully answered. So I am asking it here. Consider a ...
5answers
5k views

### Understanding “variance” intuitively

What is the cleanest, easiest way to explain someone the concept of variance? What does it intuitively mean? If one is to explain this to their mom or child how would one go about it? It's a concept ...
1answer
1k views

### Comparing standard deviations between variables with very different ranges

I have a number of variables for which I want to compare the standard deviations. Each of these variables is actually the data for a particular wavelength of light, and I want to produce a plot ...
1answer
219 views

### Bound on variance of sum of variables

Suppose I have two finite sets of data A and B, with equal length n. What's the best upper ...
1answer
109 views

### How should I characterize the “typical” variance of a large collection of variables?

For an experiment I'm analyzing, I took many measurements of many different values. (To make it concrete, let's pretend I measured the height of people from many different age groups -- I have the ...
1answer
95 views

### Relationship between number of replications and the standard deviation of entry means

I'm working at a plant breeding company. During some spare time I recently did some exploring of our data (yield trials), mostly just out of curiosity and wanting to learn R better. I started by ...
1answer
65 views

### Computing descriptives statistics for sites and locations based on literature search with sites having varying numbers of time points

I've collected a data set from the literature. These data are largely binomial: they are clutch sizes of a bird that lays only 1 or 2 eggs in most areas, and in some areas will lay 3. However the only ...
2answers
2k views

### When would it be appropriate to report variance instead of standard deviation?

I have conducted an analysis in which I have modeled different variance components. When reporting the results in a table, it is much more concise to report standard deviations instead of variances. ...
1answer
5k views

### How to calculate the difference of two standard deviations?

Background I have two estimates of variance and their associated standard errors calculated from sample sizes of $n=500$ and $n=10,000$ the results are $\hat{\sigma^2} (sd_{\hat{\sigma^2}})$: ...
1answer
237 views

### Given sample size, group means, and misc. post-hoc range statistics, can you suggest a good way to estimate variance through simulation?

I previously asked this question about the validity of my solutions for for $SE$ given $n$, $\bar{X_i}$ and summary statistics from post-hoc multiple comparisons such as Fisher's $LSD$ and Tukey's ...
2answers
1k views

### Pitman's test of equality of variance and testing for regression to the mean: am I doing the right thing?

I have 2560 paired observations from an experiment in which participants provided two ratings for a set of objects, at two different points in time. Half of the objects in the set had the value of an ...
6answers
681 views

### Basic question regarding variance and stdev of a sample

Suppose there is a very big (infinite?) population of normally distributed values with unknown mean and variance. Suppose also that we have a sample, S, of n values from the entire population. We can ...
3answers
34k views

### What is the difference between a population and a sample?

What is the difference between a population and a sample? What common variables and statistics are used for each one, and how do those relate to each other?
1answer
422 views

### Variance components

I have a set of $N$ bodies, which is a random sample from a population whose mean and variance I want to estimate. A property of each body is being measured $m_i$ times ($m_i>1$) and different for ...