# Tagged Questions

34 views

### Hypothesis testing with exponential family

I'm interested in running hypothesis tests for a variety of members of the exponential family with continuous support, for different values of the parameter/s, for a sample of n i.i.d random variables ...
33 views

### Generic test for unimodality given sample

Are there any generic tests to validate if a given sample follows a unimodal distribution, like a Gaussian, Cauchy, Student's t or a chi-square?
19 views

### Sampling distribution when testing an estimated hazard ratio against a population HR when also estimating its SE

I want to test a hazard ratio I estimated against some previously described. A Wald test seemed appropriate, utilizing the approximate normal distribution of the log hazard ratio. I therefore ...
280 views

### How do statisticians determine which distribution is appropriate for different statistical tests?

For example, the test statistic calculated for the ANOVA test is compared to an F-distribution, while a t-test comparing means compares the test statistic to a t-distribution.
20 views

### UMP test for one-sided hypotheses

Is it possible to identify a UMP test for one-sided hypotheses on $\theta$  for the case of an i.i.d. sample $(X_1, ..., X_n)$ of random variables $X_i \sim f_\theta (.)$ such that the ...
50 views

### Likelihood-ratio test for different distributions

I aim to discriminate between three populations by using a maximum likelihood classifier. The idea is that every population has a unique distribution $\hat{f_i} (x)$. The pdf $\hat{f_i}(x)$ has been ...
244 views

### Difference between null distribution and sampling distribution

I am asking this questions for clarifications on the terms between "null distribution" and "sampling distribution". I find that when some one says null distribution, actually they mean the same thing ...
117 views

### Hypothesis testing - is my distribution non random?

Say I have $n$ pairs of time series data. For each pair, I calculate a measurement which looks at the overlapping fraction of each time series pair, resulting in $n$ overlap values. EDIT : I define ...
123 views

### Continuous Kolmogorov-Smirnov test?

Is there something like a K-S test, but using an integral instead of a supremum? My thinking is that $\int_{-\infty}^\infty|F(x) - G(x)|dx$, where $F$ and $G$ are CDFs, will approximate zero if they ...
159 views

### Test whether variables follow the same distribution

If you want to test whether two variables follow the same distribution, would it be a good test to simply sort both variables, and then check their correlation? If it is high (at least 0.9?), then the ...
71 views

### What method can be used to test if three or more categorical sample data sets are from the same distribution?

I have three data sets like this: data1: {A, A, B, C, D, ..} data2: {A, B, B, C, E, ...} data3: {A, C, D, D, E, ...} How do I test if these three data sets are from the same distribution?
38 views

### Analysis of computer software performance

I am currently collecting data from a software system that draws conclusions about the nature of certain structures in medical CT chest scans. Structures in the chest can be classified into four ...
122 views

### Comparing sets of non-normal distributions

Apologies in advance if this question seems trivial -- I am a biologist and have little experience in statistics. I have six non-normal distributions (they're positively skewed): three are replicates ...
106 views

### Equivalent to K-S test on discrete data with uneven quantization

I have some data resulting from a simulation that consists of several groups, each containing a single real datapoint and a variable number of matched controls. I take the rank of each real value ...
62 views

### Stats test which test of the NULL that a distribution is uniformally distributed

I'm looking for a statistical test which tells the probability that a given sample comes from a uniform distribution. Shapiro test wether a sample comes from a normal distribution. I'm looking a ...
94 views

### t-test equivalent for samples, given a distribution of unknown form?

If there are two samples from a distribution whose form is not known, and which is certainly not normal, how can one ascertain the probability that, by random chance, their means/medians are ...
57 views

### Comparing two points corresponding to two different normal distributions

I have two multi variate normal distributions N1 and N2. Say two points p1 is from N1 and p2 is from N2. I want to get some statistical features from these two points. How can I do it? I need a ...
2k views

### How to get the expected counts when computing a chi-squared test?

I just have 1500 data points in excel. However, I want to do a chi squared test to prove if the data is normaly distributed. My question is: How to calculate the expected range for such a large data ...
2k views

### Test for bimodal distribution

I wonder if there is any statistical test to "test" the significance of a bimodal distribution. I mean, How much my data meets the bimodal distribution or not? If so, is there any test in the R ...
54 views

### How can you find the probability that an element is part of a sampled set?

Let's say I have a set of scalar values $V$ that I sampled from a set $S$. I want to test whether a given value $X$ could be a member of $S$ or not. I understand that if the values in $V$ are ...
299 views

### Comparison of entropy and distribution of bytes in compressed/encrypted data

I have some question which occupies myself for a while. The entropy test is often used to identify encrypted data. The entropy reaches its maximum when the bytes of the analyzed data are distributed ...
76 views

### Luck or skill in 3-person game

Two friends and I have been playing a game that is a combination of skill and luck. (as most games are). We assume that if the game was all luck and/or we all had the same skill level eventually the ...
144 views

### computing slope on heavy tailed lognormal distribution

I have a heavy tailed logNormal distribution and i want to know if it's possible to make a linear regression in order to compute RÂ˛ and slope for this data. I make my linear regression on computed ...
147 views

### How to compare a sample against some baseline data?

First let me describe the situation I'm dealing with: I'm looking at performance data for a software system. I have data for many versions of the software, including ongoing. For each version I have ...
233 views

### Can I use a likelihood ratio test when the error distributions differ?

This question might sound simple, but in fact I am absolutely unsure whether it is allowed to use an LRT for model comparison when the error distributions differ. For example, can I compare a model ...
330 views

### Nonparametric test statistics for non-equal sample sizes

If I have two samples, with one 30-times larger than the other, which nonparametric test statistics should be considered for checking the null of equal distribution? I am using Kolmogorov-Smirnov ...
369 views

### How to set the non-centrality parameter of the chi-squared distribution in terms of sample size for a power calculation

I am doing some problems on hypothesis tests on the variance, using a $\chi^2$ distribution. I need to find the power of the test, and I tried to write my own code in R. I don't know how to express ...
318 views

### Null hypothesis rejection with Kolmogorov-Smirnov

I want to compare two samples with a Kolmogorov-Smirnov test. Wikipedia states the null hypothesis is rejected at $\alpha$ if: $\sqrt( \frac{nn'}{n+n'}) D_{nn'} > K_\alpha$ where $n$ and $n'$ are ...
163 views

### Conservativeness of tests based on a discrete random variables

For discrete test statistics, the distribution of the corresponding $p$-value is discrete and stochastically larger than the uniform distribution. Hence the corresponding hypothesis test based on the ...
329 views

### Is there any test for a null hypothesis of non-normality?

I'm currently looking for a test having for null hypothesis that the sample does not come from observing a normally distributed random variable. In other words, I'd like to know if there's a test ...
180 views

### What test should I choose if I want to see if two groups are different from each other in many categories?

I am currently analysing data of a big webshop with over 31,000 vendors selling goods, i.e. each vendor is selling items over the webshop. The cool thing is that we know the gender of these vendors ...
360 views

### Test for a logistic distribution in R

I have a set of data and I'd like to know whether this data set has a logistic distribution. When I made a histogram of my data set it seems to have a logistic distribution, but to be sure I'd like to ...
458 views

### Kolmogorov-Smirnov Test Alternatives

I'm comparing 2 data sets from nearby locations to see if they differ significantly in air quality. I cannot perform any paired tests because the data at one location does not necessarily correspond ...
2k views

### What are the standard statistical tests to see if data follows exponential or normal distributions?

What are the standard statistical tests to see if data follows exponential or normal distributions?
103 views

### How to test that a set of distributions are located in a given order?

I have a set of population distributions; I obtained them empirically, computing histograms from very large populations (about 1 million per distribution). The population distributions might not have ...
119 views

### Estimate density from neighbor distances

Assuming I have a data set of known size, and there is one object that I want to test for being in an approximately uniform distributed region of the data set. For the query object, I know the $k$ ...
504 views

### Testing data against a known distribution

I asked a question similar to this a while ago, and the general answer was "your question is too vague". So let me try again with a little more detail... I have written a program which generates ...
70 views

### Weighting a control group

In reviewing some market research, I came across a study which decided to weight the results/outcomes of the control group so the distribution of participants in the control sub-groups (0,1,2,3,4,5 - ...
91 views

### Testing samples against a distribution

Suppose I have some data sitting in front of me, which is supposed to be sampled from a specific distribution. How would I go about testing whether it is from that distribution? I've seen several ...
130 views

### What statistical tests should be applied to the attached distributions?

In the attached images (bottom of this post), I wish to compare the plotted distributions as follows. Each plot shows two distributions labelled 'Forwards' and 'Backwards'. For each attached example, ...
826 views

### Comparing two discrete distributions (with small cell counts)

I need to compare sample distributions with theoretical ones, which is typically done with a chi-squared test. The problem is that I have distributions where one or more cells have low values, and ...
48 views

### Which is the correct hypothesis test formulation for this problem?

The problem I am working on can be formulated as follows: $S$ is the set of events $X_i$'s where each $X_i$ has occured different number of times. Also, if you think this process in turns; in each ...
184 views

### Pre-post distribution comparisons

I have a study looking at classroom socialization. Students named the top other students they wanted to read a book with before and after treatment. There was also a control group that received no ...
624 views

### Test for significant difference in ratios of normally distributed random variables

Related to Analysing ratios of variables and How to parameterize the ratio of two normally distributed variables, or the inverse of one?. Suppose I have a number of samples from four different ...
4k views

### How to test whether a sample of data fits the family of Gamma distribution?

I have a sample of data which was generated from a continuous random variable X. And from the histogram I draw using R, I guess that maybe the distribution of X obeys a certain Gamma distribution. But ...
435 views

### Proper use and interpretation of chi-squared test

Please help me understanding basic features of chi-squared test for distribution comparison. As far as I understand, if we draw two samples from the same distribution, and treat one sample as ...
671 views

### Using Kolmogorovâ€“Smirnov test

A newbie question (please provide detailed answers): I am trying to use the Kolmogorovâ€“Smirnov test. I managed to calculate the difference between the empirical points and the theoretical distribution ...
117 views

### Testing that a sample corresponds to an arbitrary distribution

I'm writing a set of unit test for a function that draws random numbers from an arbitrary distribution, defined as a PDF (example of such a function can be seen here). I am confused about the proper ...