## 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

## Compare a panel versus a reduced panel

I am facing a sort of situation I never encountered so far. Basically I would like to compare a set of data from a panel versus a set of data from the same panel but reduced (see picture) My point is to see whether the mean from the reduced panel is significantly different to the … Read more

## Independence of points from same underlying function

I have a function y=sin(x) I sample the points xi={0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1} and yi=sin(xi)+ϵ  ϵ∼iid Normal Now given only the set {xi,yi} I want to uncover the underlying functional form f(x) given as y=f(x)+ϵ    ϵ∼iid Normal My question is : ARE yi‘s independent ? My intuition is that y1 and y2 are not independent. This is because given a new x … Read more

## Test for monotonic trend in group means

I have dozens of groups of an observed variable. The number of observations in each group varies and the variance between groups is different. The mean of each group is the variable of interest. The groups have a rank 1,2,…,k. I need a test of whether the mean increases, decreases, or stays the same as … Read more

## Are there any quantitative metrics for how representative a sample is?

I’m interested in selecting a sample that is representative of a population. Additionally, I want to be able to quantitatively measure the representativeness of a sample. For example, is there a way to determine, for a sample size n, where n is some fraction of the population size x, how representative the sample is? Can … Read more

## Centrality measures and interpretation

I am new to graph theory and I have some questioning. First of all, how can I determine the significant of two different degree centrality means and two different closeness centrality means? For example, I have a network of international organizations which are public or private, but I don’t know how to determine if the … Read more

## Calculating significance of distribution

I have the following type of data: Age Type 3 A 3 A 3 A 4 A 4 B 4 A 5 A 5 A 5 B 6 A 6 C 6 B 7 A 7 C 7 B Explanation of the data: essentially, this represents different types of outputs produced by a single child … Read more

## Which Significance Test?

Which Significance Test? I have a population of 4,780 users who answer 50 questions from a personality test. The responses are tabulated into a score for each of the four personality types that all add up to 50. Given that I have statistics for an individual and statistics for the 4,780 user population is there … Read more

## Significance Testing with Model Error

My set up is the following: I have a group of people, initially whose gender I do not know. I predict the gender of each individual with a gender prediction model and put them into Male and Female group. I know the accuracy/error of this model. My test statistic is % of people that like … Read more

## How do I test for differences in cost per acquisition (CPA) in an A/B test?

How would I go about testing for differences in cost per acquisition (CPA) in an A/B test? I’m a huge novice and am unsure if I would use some kind of t-test or chi-square test (or neither) to compare the proportion of cost per acquisition in group A to cost per acquisition in group B. … Read more