The expected value of a random variable; or a location measure for a sample.
9
votes
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 ...
46
votes
4answers
4k views
Which “mean” to use and when?
So we have arithmetic mean (AM), geometric mean (GM) and harmonic mean (HM). Their mathematical formulation is also well known along with their associated stereotypical examples (e.g., Harmonic mean ...
6
votes
4answers
1k views
Averaging correlation values
Let's say I test how variable Y depends on variable X under different experimental conditions and obtain the following graph:
...
22
votes
3answers
3k views
Difference between standard error and standard deviation
I'm a beginner in statistics. I'm struggling to understand the difference between the standard error and the standard deviation. How are they different and why do you need to measure standard error? ...
4
votes
2answers
2k views
How should one interpret the comparison of means from different sample sizes?
Take the case of book ratings on a website. Book A is rated by 10,000 people with an average rating of 4.25 and the variance $\sigma = 0.5$. Similarly Book B is rated by 100 people and has a rating of ...
19
votes
11answers
14k views
Why is median age a better statistic than mean age?
If you look at Wolfram Alpha
Or this Wikipedia page List of countries by median age
Clearly median seems to be the statistic of choice when it comes to ages.
I am not able to explain to ...
27
votes
6answers
3k views
Is Amazon's “average rating” misleading?
If I understand correctly, book ratings on a 1-5 scale are Likert scores. That is, a 3 for me may not necessarily be a 3 for someone else. It's an ordinal scale IMO. One shouldn't really average ...
11
votes
8answers
5k views
Can the standard deviation of non-negative data exceed the mean?
I have some triangulated 3D meshes. The statistics for the triangle areas are:
Min 0.000
Max 2341.141
Mean 56.317
Std dev 98.720
So, does it mean anything particularly useful about the standard ...
0
votes
2answers
253 views
Significance tests
I have two sample means from two different samples. I purport that the true population means are identical.
$H_{0}$: $\mu_{1}=\mu_{2}$ and
$H_{1}$: $\mu_{1}\ne\mu_{2}$
What significance test would I ...
7
votes
3answers
303 views
Is it appropriate to plot the mean in a histogram?
I have a Really Stupid Question:
Is it "okay" to add a vertical line to a histogram to visualize the mean value?
It seems okay to me, but I've never seen this in textbooks and the likes, so I'm ...
7
votes
2answers
297 views
How can I test $H_0:\sigma^2_1=\sigma^2_2$?
I have a few hundred estimates of a parameter calculated from two different models and I would like to know if these parameters have different variances.
What is a straightforward test for comparing ...
5
votes
1answer
420 views
Why are cumulative residuals from regression on stock and index returns mean reverting
In the paper
M. Avellaneda and J. H. Lee, Statistical arbitrage in the U.S. equities market, July 2008,
in the Appendix on page 44, I have some questions.
First he runs the regression of ...
9
votes
2answers
2k views
How do I calculate a confidence interval for the mean of a log-normal data set?
I've heard/seen in several places that you can transform the data set into something that is normal-distributed by taking the logarithm of each sample, calculate the confidence interval for the ...
8
votes
3answers
293 views
Mean$\pm$SD or Median$\pm$MAD to summarise a highly skewed variable?
I'm working on highly skewed data, so I'm using the median instead of the mean to summarise the central tendency. I'd like to have a measure of dispersion
While I often see people reporting mean ...
3
votes
2answers
7k views
How to calculate the truncated or trimmed mean?
How can I calculate the truncated or trimmed mean? Let's say truncated by 10%?
I can imagine how to do it if you have 10 entries or so, but how can I do it for a lot of entries?
2
votes
2answers
315 views
Question on confidence interval
My mean is 3.454992884900722e+008, and my confidence intervals from three distributions (when compared to the given mean) are:
CI for dist. 1: 1.0e+008 * ...
1
vote
1answer
244 views
Comparing 2 independent non-central t statistics
One estimate of the 'quality' of a portfolio of stocks is the Sharpe ratio, which is defined as the mean of the returns divided by the standard deviation of the returns (modulo adjustments for risk ...
6
votes
2answers
392 views
Difference in means in multiple-choice poll
Let's say that N randomly chosen persons where asked a question where the answer could be in either of X categories. For example, 500 persons where asked which of the top 5 political parties they ...
5
votes
2answers
235 views
One component in PCA is always the mean vector in two-dimensions but not three
I've been testing PCA via SVD to decompose a simple time series data matrix, $X$. I have two signals $x_1(t)$ and $x_2(t)$ in a data matrix where $M$ rows represents each timepoint sample and each ...
5
votes
1answer
842 views
Two sample t-test for data (maybe time series) with autocorrelation?
I am new to statistics, so pardon any mistakes in my question.
I have two time series $X_i$ and $Y_i$. Assuming that they're stationary AR(1) processes with possibly different means, how do I test ...
3
votes
1answer
70 views
Finding a linear relationship without linear model
(If this doesn't make sense it is because I am inexperienced at statistics)
Assume I have a broad universe of actions $A$ I could pursue, and for each $a_i \in A$ there is an associated ...
3
votes
2answers
1k views
Calculating mean age from grouped census data
I hope you can
help me with a question regarding calculating mean age from grouped census data. If the
age categories used were [0–4], [5–9], [10–14], and [15–19] years,
how would you calculate the ...
3
votes
2answers
1k views
Why (or when) to use the log-mean?
I am looking at a scientific paper in which a single measurement is calculated using a logarithmic mean
'triplicate spots were combined to
produce one signal by taking the
logarithmic mean of ...
2
votes
1answer
133 views
Is it typical for group means of composite z-scores to have means with values of the same magnitude but opposite signs?
I developed a composite score by converting four items to z-scores, then I summed up the z-scores to form a composite measure.
However, when I've calculated means to compare finding for two ...
1
vote
1answer
77 views
Reason for taking the mean of experimental observations
Whenever we do some experiment in Physics, e.g. measure Planck's constant, we take the mean of several experimental observations. This seems to be the most obvious way to report a result.
Is there a ...
0
votes
1answer
103 views
Regression on means of log-transformed variables
Suppose that I want to study the relationship between two variables $Y$ and $X$ using the linear model $Y \sim X$. Unfortunately, both $Y$ and $X$ are not normally distributed, say they are both ...
0
votes
1answer
241 views
Mean and variance of a normally distributed random number created from the average of a set of uniformly distributed random numbers
An old-fashioned way of generating normally distributed random numbers entailed setting each normally distributed random number equal to the average of a set of uniformly distributed random numbers, ...
