Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

37109 questions
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Exact interpretration of p-value and significance of test

First question: Let's say we have a hypothesis test: ${ H }_{ 0 }:u=100$ and ${ H }_{ 1 }:u\neq 100$. The sample has a size of 10 and gives an average $u=103$ and a p-value = 0.08. The level of significance is 0.05. I'm asked the following question…
XCoder
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Largest possible mean deviation

In a data set with 12 numbers, and the lowest and largest numbers can be 0 and 10, what are the numbers in the set to get the largest mean deviation. The mean deviation is obtained by: Finding the mean of all values Finding the distance of each…
Joey Tellor
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For what value of $n(=m)$ will the resulting interval have width at most $0.1$ irrespective of the results of the sampling?

Using the traditional formula, a $95\%$ CI for $p_1 - p_2$ is to be constructed based on equal sample sizes from the two populations. For what value of $n ( = m)$ will the resulting interval have width at most $0.1$ irrespective of the results of…
Danny
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Matthews Correlation Coefficient yielding values outside of [-1,1]

(Note, this question has been cross-posted on the Cross-Validation site, which I wasn't aware of at the time of initial posting). I'm using the formula found on Wikipedia for calculating Matthew's Correlation Coefficient. It works fairly well, most…
Isaac
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Is it possible to estimate true standard deviation from averaged data?

I want to use some field collected data to form a Gaussian/Normal distribution model. Then use this model as the input to a simulation software. Then increase the mean and the standard deviation to see the effects. I know how to compute the mean…
David293836
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$5\sigma$ and population standard deviation

Does $5\sigma$ represent a data point that is five standard deviations from the mean? If so, suppose we come across data that is for some reason $4$ or $5$ standard deviations from the mean. Could this be determined using the $\textit{population…
CuriousGeorge119
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Factor Analysis versus Mean of Items

I am looking to measure attitudes of respondents based on a 7-point Likert scale with 8 items. However, I need to summarize these attitudes into a single score. Originally, I performed a factor analysis, only keeping a single dimension (Kaiser's…
user167428
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second derivative of the logarithmic student t-distribution

I would like to determine the second derivative of the log t-distribution. Results are given in this paper http://faculty.chicagobooth.edu/drew.creal/research/papers/crealKoopmanLucas2012_univariateVolatility.pdf at page 4, chapter 2.2. I got the…
Julia
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How to extract an individual's (normalized) contribution from a group?

To make this concrete assume you have two teams playing against each other. Each team can only have n players on the field, and may be substituted for a different player at different times during the game (say hockey or basketball). You have a list…
B Dam
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Choice of the ridge parameter using leave-p-out estimation of the risk

The context of my question is the kernel ridge regression (in the field of Statistics). The question is to find a closed formula for $\lambda^{*}$ \begin{align*} \lambda^{*}=\underset{\lambda >O…
user166890
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How to get a good approximation or exact value to the average of a group of numbers without storing the numbers in memory?

I am not sure if this is possible, plus I am running on no sleep, so here is what I am asking. Assume I have a list of random numbers. In this instance we will have a list containing $[5, 4, 3, 2, 1]$. I want to retain as little data about these…
TheKobra
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What is the distribution of sum of a Rayleigh and a Log-logistic distributed independent r.v.?

Let Z = X + Y. X follows the Rayleigh distribution given by \begin{equation} f_X(x;\sigma_1) = \frac{x}{\sigma_1^2}\exp\left(-\frac{x^2}{2\sigma_1^2}\right), \; x \geq 0 \label{RayleighPDF} \end{equation} and Y follows the Loglogistic…
Shen Chiu
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Similar to Kruskal-Wallis Test for multidimensional vector

I need to do the similar kind of test as Kruskal-Wallis Test but for the multidimensional vector. Would you please kindly suggest such kind of test or provide some references for N-d case. Thank you for your help. Best Regards.
Tom
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Is my coin fair -- only 11 trials

My task was to flip my penny $11$ times and record the number of successes (heads) and then determine with $99\%$ confidence whether the coin is fair or foul. my $\hat{p}$ is $0.45$, thus $\hat{q}$ is $0.55$. What I calculated: $99\%$ confidence…
user163862
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Difference of sums or sum of differences this is the question

If you have a bunch of paired measurements, let's say you measured peoples weights before and after holidays (AND you are assuming these are samples from an underlaying Gaussian distribution) what is the correct thing to do, to calculate the…
Ali
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