## Parametric test for testing if two sets of samples came from the same normal distribution with unknown parameter?

Is there a parametric test to see if two sets of samples came from the same normal distribution with unknown parameter? Suppose I have one set of samples $X_1, X_2, \dots, X_m$ and another set of samples $Y_1, Y_2, \dots, Y_n$. Do we know a test to check if both of these were drawn from … Read more

## Test if one Poisson process’s rate is smaller than a given value

Suppose N(t) is a Poisson process with rates λ. Suppose I’ve been observing it for t∈[0,T] and recorded events. How can I test the null hypothesis λ<λ0, where λ0 is a given value? An obvious solution is to derive MLE of rates ˆλ and compare with λ0. But I don’t know how to calculate the … Read more

## when add-on test is necessary? better diagnosis strategy

Suppose there are two types of tests available. Test A: low-cost, but relatively less precise; Test B: high-cost, but more precise. Test B can be considered as the good standard with 100% accuracy. Suppose there is a group of patients with different sex, age, gender and race. The question is, which patient should be recommended … Read more

## Check of moments for pseudo random number generators using CLT

I’m trying to get to grips with my lecture notes but cannot understand the idea behind it. I’d really appreciate some help: “Generate a sequence of size $n$ from stated distribution. Consider an independent sample $X_1,X_2,X_3,..,X_n$ from pdf $f_x(x)$, with mean $\mu$ and variance $\sigma^2$. Then the CLT says that… (def. continued – I don’t … Read more

## Statistical test to see whether dataset represents reality or not [closed]

Closed. This question needs details or clarity. It is not currently accepting answers. Want to improve this question? Add details and clarify the problem by editing this post. Closed 5 years ago. Improve this question I have a dataset consisting data from 3 persons (2 male, 1 female) for a total of 56 days. Data … Read more

## Can we do a chi-squared test of independence on nominal(output) and ratio(input) data?

I have a data set with Age and Survival Status column. I have categorized the ages into Age Groups namely: 30-47 years old, 48-65 years old and 66-83 years old and have aggregated the Survival Status for the ages which fall in the same group. Survival Status can have the value as True or False … Read more

## Gini coefficients : compare two samples with different sample sizes

I’ve two samples representing the distribution of tumor cell clones in two patient. In sample 1 I’ve about 10,000 clones – each clone has a relative abundance (so the sum of the relative abundance of all clones in one sample is 1). For sample 2 I’ve about 1,000 clones. The number of clones are different … Read more

## When is the chi-squared test becoming virtually identical to a Fisher exact test?

I am conducting several hypothesis tests for caterorical variables, with several groups being compared. I routinely use the Fisher exact test in Stata, but occasionally it may get time consuming and computationally intensive, forcing me to switch to a standard chi-squared test. I do that assuming that the chi-squared test becomes virtually identical to a … Read more

## test two binomial distributions: overall successes > failures and proportion successes A≠B

Let’s say I have data from an experiment: 3 participants took part each of them was subject to two conditions. Condition A, and B. in Condition A, 3 trials could yield success or failure (depending on the performance) in Condition B, a variable number of trials could yield success or failure (also depending on the … Read more

## Finding UMPT for uniform distribution with varying support

$\textbf{Problem}$ Let $X_1,\dots,X_n$ be a random sample from $f(x;\theta) = 1 / \theta$, where $0 < x < \theta$. We want to test $H_0: \theta \leq \theta_0$ versus $H_1: \theta > \theta_0$. Obtain the uniformly most powerful test with size $\alpha$. You must describe how to calculate $\alpha$ to get a full credit. Here I … Read more