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.

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Is there a maximum sample size for a Kruskal Wallis test?

I am performing a Kruskal Wallis test for very big sample sizes (100 000+ numbers). While the distributions seem similar on the figures, the test says there is a significant difference between the two distributions. This is making me think that the…
Jellyse
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Help with finding reason behind weighting factor

I am trying find a solution to figure out a formula for how a specific weighting factor was decided. I am trying to determine a rarity ranking amongst the species based on traits that it has. My sample set is a total of 9971 species: Trait…
kapnoj
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Probability Density Function of sum of sgn function

Let $B=\{x\in \mathbb{R}: -1 \leq x \leq 1 \}$. Let $x,y \in B^{n}$ compute the probability density function of $$d_S(x,y)=\sum^{n-1}_{i=0}|sgn(x_i)-sgn(y_i)|$$. Consider $x_i,y_i$ independent and uniform distributed. Is there any way for this value…
juaninf
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What is the maximum amount of shuffled a deck of cards can be?

I had this question pop into my head a few days ago and I've been thinking about it since. It has a fairly simple set up: you have 52 cards. Take the amount of "shuffling" to be the average distance between where each card started, and where it…
JayZenvia
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Marginal distributions of a multi-variate q-Gaussian distribution

The multi-variate q-Gaussian distribution in $N$ dimensions takes the following form: $$G_{q,\sigma}(X) = \frac{1}{\sigma^N K_{q,N}}\left( 1 - \frac{1-q}{(N+4)-(N+2)q} \frac{\|X\|^2}{\sigma^2} \right)^{\frac{1}{1-q}}$$ It appears that the marginal…
Cedric H.
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Can somebody explain to me why student's t-distribution approaches the standard normal distribution as the degrees of freedom goes to infinity?

Been studying statistics lately. Been reading about the t-distribution and how as the degree's of freedom approaches infinity this distribution approaches the standard normal distribution. Can somebody give me an intuitive explanation of why this…
user637978
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How can I determine the efficiency of a vaccine in the following situation?

In a country of 20 mil. people, 25% of the inhabitants are fully vaccinated anti Covid-19 and 75% not vaccinated at all. It was noticed that, in the last weeks, 82% of the people found positive, after being tested, never received the vaccine and…
Robert Werner
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Is it okay in this case to average averages?

I have 5 years of data giving the salaries for each department in an organisation shaped roughly like this (with the number of employees and salary changing each…
tmnsnmt
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Find standard deviation of two different sets of numbers when combined

A set of 10 numbers has a mean of 10 and a standard deviation of 2.0 another set of 10 numbers have a mean of 4 and a standard deviation of 3.0 find the standard deviation of the 20 numbers
Lim LS
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Using a t-test vs. a z-test

The mean weight of the average man is 166 pounds. One can create a hypothesis test to decide whether the mean weight of men in a workout club is above the average. $H_0:\mu\leq166$ versus $H_1:\mu> 166$. The 25 people in the club have a mean weight…
ernesto
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how to find the maximum and minimum of standard deviation given Xmin, first quartile, median, third quartile and x max.

Suppose a box and whisker diagram was given with no data of mean and standard deviation. I am able to find the range of Mean(NOT sure if it is correct) as $\frac{(Xmin+Q1+Q2+Q3)}{4}$$
Jack Koo
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How to forecast revenue with my data?

I work for a law firm and I want to know whether I can accurately predict our future revenue based on data I've pulled from our SQL Server database. Here is the information that I know based on some queries: It takes on average, 333 days from the…
Ryan
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Law of Total Variance Using Three Different Variables

I have 3 random variables; X,Y, and Z. I am pretty familiar with law of total variance for two variables; $Var(X) = E[Var(X|Y)] + Var[E(X|Y)]$. (I'm sorry if the words are messy). Recently, I read some papers, which state law of total variance using…
imands
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Calculating error for a specific physics experiment

I asked a question for a project I am supposed to do and have changed my topic. Now I will use results from a physics lab I did. It is to estimate the value of $g$, the gravitational acceleration using a ramp and frictionless cart. I want to…
ernesto
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Determine variance using delta method for determined estimators

How do you determine the derivative of an average to use the delta method to approximate the variance of an estimator? For example for the problem above, I came across the estimators $\hat{\theta}=\frac{1}{\bar{X}}-1$ and…
ernesto
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