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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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why should the p-values be uniform when the null is true?

I am reading about the False Discovery Rate and Bonferroni and I found in various places that under H0 (true null) the distribution of p-values (for the test that rejects H0) should be uniform. Can someone tell me why it would be the case? Thanks!
ℕʘʘḆḽḘ
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Diagram ( histogram and box chart interpretation)

Which diagram motivation corresponds best to variable B? (I) A box diagram reveals a deviating observation (II) A histogram makes the skewness in the distribution clear (III) None of the above alternatives Diagrams My thinking: Even though it is…
hannesbjörk
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Calculating the p-value for two events

can anyone help me with that problem? The school newspaper claims that 35% of students have credit card debt. You think it’s different. We simple random sample “M” students and “H” say that they have credit card debt. M=104 H= 30 Is there sufficient…
Hassan Othman
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Using the Fisher–Neyman factorization theorem to show that $\left(\sum_{i = 1}^n Y_i, \sum_{i = 1}^n Y_i^2 \right)$ is a sufficient statistic

I want to use the Fisher–Neyman factorization theorem, of the form $L(\mu; \mathbf{y}) = g(T(\mathbf{y}), \mu) \times h(\mathbf{y})$, to factor $\exp{\left\{ \dfrac{1}{2 \mu} \left( \sum_{i = 1}^n y_{2i}^2 - \sum_{i = 1}^n y_{1i}^2 \right) + \left(…
The Pointer
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could t-test be used to calculate how much differences for two statistics?

We know t-test could be used to test whether two statistics has significant differences. My question is, could t-test be used to test how much differences are two statistics? For example, whether t-test could answer question like "two statistics has…
Lin Ma
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Confidence interval variance among a set of groups,

A psychiatrist is interested in finding a 90% confidence interval for the tics per hour exhibited by children with Tourette syndrome. The data below show the tics in an observed hour for 13 randomly selected children with Tourette syndrome, with…
Thomas Hood
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showing that $S=\sum^n_{i=1} \ln(X_i)$ is a complete sufficient statistic

We have a random sample $X_1,X_2,\ldots,X_n$ from a probability with density: $$ f(x)=\theta x^{-(\theta +1)} $$ given that $x>1$ and $0$ else. now the question is: Show that $S=\sum^n_{i=1} \ln(X_i)$ is a complete sufficient statistic and use this…
WiseStrawberry
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From two machines that automatically pack coffee, samples of 64 bags have been extracted in each one of them

From two machines that automatically pack coffee, samples of 64 bags have been extracted in each one of them. The probability distribution of the weight of each bag for both populations has identical means and standard deviations of 6.4 grams and…
Isabel
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Law of Iterated Expectations $\operatorname{E}\left[XYZ\right]=\operatorname{E}\left[\operatorname{E}\left[XYZ \mid X,Y\right]\right]$

my doubt is actually pretty simple. Considerer three random variables $X,Y,Z$. I wonder if I can use the LIE to do this: $$\operatorname{E}\left[XYZ\right]=\operatorname{E}\left[\operatorname{E}\left[XYZ \mid X,Y\right]\right]$$ Or the only way to…
Jackaba
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goodness-of-fit test for categorical data with small expected frequencies

I have a categorical data set with 8 categories and I want to test my data against a theoretical "ideal" distribution. Usually I think a chi square test does this just fine; however, some of my theoretical probabilities are small and therefore my…
David
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Simple application of survival function of noncentral chi square distribution

Im looking for a new(ish) paper that is an application (with a simple setup and background) of the survival function of a noncentral (or with noncentrality parameter 0) chi square distribution. I want the given probability to have some applied…
Robert
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Finding true proportion and comparing it to the level of significance?

I'm currently taking a statistics course and am a little confused about this question. I've found true proportions before, but usually I'm given numbers, rather than just percentages. So, I'm very confused about the following question. Any help…
larn
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How to tackle a statistics problem given a random variable X?

I'm having trouble getting an overall grasp of certain aspects of statistics, namely knowing when to use which formula/approach to solve a problem. Let's consider a random variable X, after you determine whether the random variable is continuous or…
user1766888
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Is K-W test statistics a U statistics?

The K-W H test statistic is given by $$ H=(N-1) \frac{\sum_{i=1}^{g} n_{i}\left(\bar{r}_{i \cdot}-\bar{r}\right)^{2}}{\sum_{i=1}^{g} \sum_{j=1}^{n_{i}}\left(r_{i j}-\bar{r}\right)^{2}} $$ If the data contain no ties $$ H=\frac{12}{N(N+1)}…
Happy Superman
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standard error for ratio of two poisson random variables

I'm collecting data for two Poisson random variables, that are completely independent of each other. My current analysis method yields 95% (or 90% or other) confidence intervals for the two $\lambda_1$, $\lambda_2$ for the two Poissons. My question:…
user635185
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