# Questions tagged [mathematical-statistics]

Mathematical theory of statistics, concerned with formal definitions and general results.

4,378 questions
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### How do we prove this identity related to expectation and variance?

Prove that if $\textbf{a}$ is a vector of constants with the same dimension as the random vector $\textbf{X}$, then \begin{align*} \textbf{E}[(\textbf{X} - \textbf{a})(\textbf{X} - \textbf{a})^{\prime}...
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### What Statistical Method is Useful for Comparing Two Different Groups?

I'm working on a project and I want to know what statistical method would be useful to see if my hypothesis is true. The project I'm working on is Calculus Rentention. My hypothesis is: do students, ...
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### Variance Calculation Issue

I want to calculate variance for the given problem , i am confused when to use n or n-1 , if nothing is mentioned. also, what should i use in this case. please explain
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### Given two related ratios within a population, derive a third ratio (eg. redheads, non-redheads, and skin cancer)

If People X are N times more likely to have attribute A than non-X People X are P percent of the population then What percentage of A's are X? Example (the numbers are just for illustration). If ...
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### Calculating the variance and expected value of a multiple Coin Toss with Reward

I was wondering if you flipped 4 coin tosses, and you get 0.25 dollars for each coin that lands on tails and 0 dollars if it lands on head. How, would you calculate the variance and expected value.
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### Statistical test to check if sampling was not uniform

Given a set of real numbers $X$ and a subset $Y \subset X$, I would like to demonstrate that $Y$ is not a result of a uniform sampling from $X$. One solution that I thought recall this, that is: ...
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### Survival analysis with biased coins

Suppose I have five biased coins $c1, c2, c3, c4$ and $c5$ each with different probabilities of getting heads. Pr. heads for coin $c1=0.5$ Pr. heads for coin $c2=0.8$ Pr. heads for coin $c3=0.6$ Pr....
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### Statistical technique to assess change in drug events over time - Interrupted time series analysis?

I have a dataset of the number of drug related events (e.g. arrest, non-fatal overdoses) a population of individuals have had. My aim is to see if a certain policy intervention that occurred on 1 June ...
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### How to prove $P(a \geq b +c) \leq P(a \geq b) + P(c \leq 0)?$

How to prove $$P(a\geq b+c)\leq P(a\geq b)+P(c\leq0)?$$ Thanks.
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### Measuring the confidence of a delta

Hope this is the right place to ask this. I'm measuring a single quantity, A, multiple times and each time the value is expected to be different(inherent error in the system). Call them ...
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### Comparison of discrimination tests using, Thurstonian model and its d -values

The task is to measure two discrimination test methods "triangle test and tetrad". In both methods the possibility to guess correct is (1/3). In my study I used Chi square test to analyse data. ...
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### Multivariate Taylor series for moments of a random variable

In the expectation propagation for the generative aspect model, Minka uses Taylor series for the parameter estimation of the topics $p(w\mid a)$ eq 31. I am a little confused in the last equation. He ...
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### How is the L2 regularization derived? [duplicate]

I just proved to myself why the regularization is added rather than multiplied to loss function. I did so by taking the MLE formula... $$\operatorname{argmax}\sum \log(P(x_i\mid\Theta ))$$ and ...
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The question is, Suppose that a single factor experiment with four factors and six blocks is conducted and the error sum of squares is 500 and the sum of squares for the blocks is 250. The question ...
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### Why is ANOVA in R showing a different result than ANOVA from another source?

I am new to R and statistics both. I am trying to perform 2x2 ANOVA on an excel dataset where the 2 factors are Gender and Athletes and the dependent variable is Anger Expression. When I am ...
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### Hypothesis testing with 1 or 2 sample in ornithology

I am doing an experiment with birds. I have set up the experiment to measure how certain foods affect bird flying speeds. When I implement a control, for example food A, I want to claim that the ...
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### Deriving standard deviation from p-value and t-statistics

I have the results of a t-test for two groups, where the mean of one group is 3.4 units and the mean of the second group is 3.8. From the paired t-test, I know that t$_{17}$ = 2.8 and p = 0.013. Is ...
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### With few respondents on a 1 to 10 scale, is it better to use a weighted mean or the median?

I have survey data where ~20 respondents replied to some questions on a scale of 1 to 10. For the most part, none of the distributions are Gaussian. A set of questions look to find out a participants ...
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### normalize/standardize data

I hope someone here can point me on the right direction. I have the following dataset. I have fish adult and juvenile data that I want to compare side by side, however, the juvenile fish numbers are ...
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### Krippendorff's alpha getting low after restricting data

I am calculating inter-rater agreement for ~350 raters, each of who rated 100 items using Likert scale. The original scale has range [-3,3], using this python implementation, I got $\alpha=.35$, which ...
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### classify according to one variable and no classes

I have a problem, I think that is common but I don´t have idea about how to proceed. I am looking an elegant solution for it. I have N groups and two variables for each group. After that I have ...
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### How to know where to cut off a list of values?

Suppose I have a list of values like this one: ...
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### median survival derived from a mixture of exponential distributions

I recently got a very nice question... Let's say that we have one cohort, and we know the median survival of it. Then we split the cohort into two groups, and somehow we also know the median survival ...
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### Confusing problem statement of exercise 7.4.3 in Wasserman's All of statistics

I am reading chapter 7 of Larry Wasserman's All of statistics and working on the exercises in the end of this chapter. The exercise 7.4.3 (on p. 104) states: (Computer Experiment.) Generate 100 ...
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### Find the cause of periodic behaviour present in Google-search “war”

If you use Google Trends (a tool to illustrate the frequency of search terms) and search for the word "war" with USA as geographic region, you will be presented with the graph below showing monthly ...
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### Getting From Concentration Inequality to Interval Length

I've seen this used some times and I would like to ask what steps are taken on the way to getting there: E.g. assuming bounded variance, we can use Chebyshev concentration inequality: for any $t>0$...
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### ARIMA Model Ljung-Box Test Derivation

Initially I am aware of the fact that in order to analyse autocorrelations of residuals of ARMA(p,q) we apply Ljung-Box test and involve chi-square distribution (because autocorrelations are ...
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