Questions tagged [hypothesis-testing]

Hypothesis testing assesses whether data are inconsistent with a given hypothesis rather than being an effect of random fluctuations.

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1answer
571 views

How to calculate sample size for a one-sided test on a rxs contigency table

I work quite often with Google's Website Optimizer, essentially it allows you to make small changes to a site to determine if they have an effect on the ratio of clicks to a web page to sales. The ...
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1answer
210 views

How different random number generators can be more similar than identical ones?

I have 6 random number generators. They are "black boxes", i.e. I do not know if they are the same or different. For example I do not know if they provide the same arithmetic averages and/or root mean ...
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105 views

Testing a model with truncated data

This is probably a simple question. I'm studying events which have N outcomes, of which exactly one is correct. N is very large, more than a billion (and is known). There are many possible events, ...
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Changing null hypothesis in linear regression

I have some data that is highly correlated. If I run a linear regression I get a regression line with a slope close to one (= 0.93). What I'd like to do is test if this slope is significantly ...
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1answer
131 views

How to compare vitamin D and glucose levels between patients and controls?

I want to test the hypothesis of a decreased level of vitamin D in diabetic subjects. For this I have recorded blood glucose and vitamin D levels in 40 cases and 40 controls. What kind of ...
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1answer
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What is explosive variable?

I'm trying to understand the following claim: if the $t$-statistic is greater than zero, it indicates that the variable is explosive... but does that mean it has unit root? In the context of ...
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What are examples where a “naive bootstrap” fails?

Suppose I have a set of sample data from an unknown or complex distribution, and I want to perform some inference on a statistic $T$ of the data. My default inclination is to just generate a bunch of ...
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Can a small sample size cause type 1 error?

I've learnt that small sample size may lead to insufficient power and type 2 error. However, I have the feeling that small samples just may be generally unreliable and may lead to any kind of result ...
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1answer
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Geometric mean and standard deviation

standard deviation (std) can be used when arithmetic mean is the right statistic. What is the equivalent of std when geometric mean is the right statistic?
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Can chi square be used to compare proportions?

I've read that the chi square test is useful to see if a sample is significantly different from a set of expected values. For example, here is a table of results of a survey regarding people's ...
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How to test if the mean equals the median?

Suppose you wish to test the hypothesis that the mean of a distribution equals the median, given some samples drawn from the distribution. How would this be done? I am guessing that the test statistic ...
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2answers
297 views

After the fact hypothesis testing

I'm not really a statistician, but rather in need of statistical guidance, so I hope this is not too much of an off-topic question. I'm writing a master's thesis (computational linguistics/NLP), and ...
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Checking if two Poisson samples have the same mean

This is an elementary question, but I wasn't able to find the answer. I have two measurements: n1 events in time t1 and n2 events in time t2, both produced (say) by Poisson processes with possibly-...
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8k views

What is a good introduction to statistical hypothesis testing for computer scientists?

I was recently exposed to some statistical hypothesis testing methods (e.g. Friedman test) at work, and I would like to increase my knowledge on the topic. Can you suggest a good introduction to ...
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788 views

STFT statistical analysis

I am using the evolfft function in the RSEIS R package to do a STFT analysis of a signal. The signal is one hour long and it ...
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4answers
6k views

What test to compare community composition?

Hope this newbie question is the right question for this site: Suppose I would like to compare the composition of ecological communities at two sites A, B. I know all three sites have dogs, cats, ...
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Multivariate grouping: clustering, anova, tukey

I have multiple variables (here: weight, horizontal diameter, price and dummy) related to different factors (here: Apple, Orange, Banana and Avocado): ...
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1answer
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Interpretation of the Granger causality test [duplicate]

I would like to clarify how the Granger causality can/should be used in practice, and how to interpret the statistical significance given by the test. Also, I would like to fill this table with ...
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1answer
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In R, fisher.test returns different results if I use vectors vs contingency table

Using R, I noticed that I get different results if I use fisher.test() with raw data (as factors) versus a contingency table. The documentation states that ...
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3answers
8k views

Hypothesis testing on zero-inflated continuous data

I would greatly appreciate your advice on the following problem: I've got a large continuous dataset with lots of zeros (~95%) and I need to find the best way to test whether certain subsets of it ...
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852 views

How to compare the effectiveness of medical diagnostic techniques?

A pathologist friend came to me for help with the following question for a research project. The goal is to compare the effectiveness of three different diagnostic techniques. The data set is as ...
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3answers
6k views

ANOVA-like test for bounded variables (percentages)

I'm interested in determining whether two or more groups of data share the same mean, and it seems like the ANOVA framework is a good way to approach this. However, ANOVA assumes residuals are ...
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3answers
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Has anyone solved PTLOS exercise 4.1?

This an exercise given in Probability Theory: The Logic of Science by Edwin Jaynes, 2003. There is a partial solution here. I have worked out a more general partial solution, and was wondering if ...
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1answer
358 views

Statistical analysis of competition data

I'm comparing scores for two small groups of individuals that competed in a tournament, and I'm being told that the comparison calls for a Mann-Whitney U test. It feels wrong to me, though: my two ...
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What method is preferred, a bootstrapping test or a nonparametric rank-based test?

I want to perform a single-tail test on a single sample of real numbers (N~100) against an expected value. The population is known to be not normally distributed. So from what I've read about stats, I ...
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1answer
261 views

Designing a stopping rule using a hypothesis test

I am working on a stopping rule for an optimization algorithm that produces an upper bound and lower bound for the objective value of an optimization problem. In my case, the lower bound is ...
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1answer
376 views

How can I test $H_0:\sigma^2_1=\sigma^2_2$?

I have a few hundred estimates of a parameter calculated from two different models and I would like to know if these parameters have different variances. What is a straightforward test for comparing ...
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1answer
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Test equivalence of non-nested models

Let's say $y$ is a linear function of $x$ and a dummy $d$. My hypothesis is that $d$ itself is like a hedonistic index of a vector of other variables, $Z$. I have support for this in a $MANOVA$ of $Z$ ...
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What is the difference between Z-scores and p-values?

In network motif algorithms, it seems quite common to return both a p-value and a Z-score for a statistic: "Input network contains X copies of subgraph G". A subgraph is deemed a motif if it ...
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495 views

What kind of distribution is this “almost” uniformly distributed data for calls/week?

My supervisor asked me to find out which distribution represents a particular situation. I have a VoIP generator that generates calls "uniformly" distributed between callers. This means that the ...
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2answers
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Comparing a mixed model (subject as random effect) to a simple linear model (subject as a fixed effect)

I am finishing up some analysis on a large set of data. I would like to take the linear model used in the first part of the work and re-fit it using an linear mixed model (LME). The LME would be very ...
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1answer
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Chow test or not?

I am trying to set up an automatic screen to detect structural breaks in large numbers of time series. The time series are weekly and represent behaviour of customers. I have set up a Chow test. I ...
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Why is the null hypothesis always a point value rather than a range in hypothesis testing?

This is somewhat related to another question that I asked. The question I have is, when doing hypothesis testing, when the alternative hypothesis is a range, the null hypothesis is still a point value....
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2answers
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Hypothesis test for whether correlation coefficient is greater than specified value?

I want to test whether a correlation coefficient is greater than 0.5. What should the null and alternative hypothesis be? Should I do a two tailed test or one tailed test? Thanks
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One-sample-dispersion-test for Poisson parameter

Revised Version Situation: We have a sample of size $r$. Then, we count how many out of these $r$ to be "success". Let $X=$ the no. of the "successes" and say $X$ follow Poisson dist. Goal: To test ...
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1answer
125 views

Hypothesis testing on values that are functions of multiple distributions

I have a hypothetical experiment where I am comparing scores on some measure at 1 year to scores on the measure at 4 years. I use a non-paired t-test to see if there is a significant difference ...
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1answer
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Scrambling and correlation in low discrepancy sequences (Halton/Sobol)

I am currently working on a project where I generate random values using low discrepancy / quasi-random point sets, such as Halton and Sobol point sets. These are essentially $d$-dimensional vectors ...
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Justification of one-tailed hypothesis testing

I understand two-tailed hypothesis testing. You have $H_0 : \theta = \theta_0$ (vs. $H_1 = \neg H_0 : \theta \ne \theta_0$). The $p$-value is the probability that $\theta$ generates data at least as ...
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1answer
130 views

Terminology question concerning regression

hopefully you can help me with the meaning of the following, I don't really understand the terminology: "regression of a vector of ones on the matrix $W$", where $W$ is something like $(W_t)' = (...
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1answer
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Pivotal quantities, test statistics and hypothesis tests

We are learning pivot functions, test statistics, and hypothesis testing at university but it makes no sense. I've tried reading my text book/notes, going through examples, etc., but the concepts seem ...
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1answer
132 views

Construct probability that measurement belongs to one of two sets

We are dealing with a measurement apparatus that is cursed by noise and are trying to find out if a measurement was noise or an actual measurement. Assume we have a beam of light incident on an ...
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1answer
530 views

Moving from conversion rates to sales volume in A/B tests

there is a short introduction to AB Tests in this question or here at 20bits. We are currently testing different versions of landing pages and are using the conversion rate (e.g. 4% vs. 5%) to track ...
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2answers
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How to estimate a critical value of Spearman's correlation for n=100?

I have searched a lot, and I can only find tables that show critical values up to n=30. Can someone provide, or point me to, a simple method of estimating this value for different $\alpha$?
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1answer
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Two sample t-test for data (maybe time series) with autocorrelation?

I am new to statistics, so pardon any mistakes in my question. I have two time series $X_i$ and $Y_i$. Assuming that they're stationary AR(1) processes with possibly different means, how do I test ...
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2answers
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Which non-parametric test can I use to identify significant interactions of independent variables?

I have an experiment producing results (dependent variables) that don't pass tests of normality, thus I am testing hypotheses using non-parametric tests. My DVs are continuous, while my factors (...
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1answer
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Is there any difference between the terms “paired t-test” and “pairwise t-test”?

What is paired t-test, and under which circumstances should I use paired t-test? Is there any difference between paired t-test and pairwise t-test?
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1answer
230 views

Appropriate test to compare online voting data

The data I want to analyze consist of set of votes similar to the voting system here on stackexchange. Votes are binary, i.e, items can receive up- or down-votes. The data have been gathered in an A/B ...
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2answers
813 views

Difference between two slopes

I have a dataset with yearly levels of corruption in a number of countries, as well as whether they changed their government that year. ...
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1answer
213 views

Location test under a bounded non-stationarity?

Suppose I draw $n$ observations $X_1,X_2,\ldots,X_n$ independently from a distribution where $X_i \sim \mathcal{N}(\mu_i,\sigma^2)$, where the mean is assumed to be Lipschitz: $\left| \mu_i - \mu_{i+...
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4answers
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Justifying normal approximation of experimental data

Background: In connection with the question here I came upon a more interesting question. I believe the question is large and distinct enough to have it's own thread. Of course I might be mistaken, ...