Hypothesis testing assesses whether data support a given hypothesis rather than being an effect of random fluctuations or some other process described by an alternative hypothesis.

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Testing whether a seasonal dip in a time series this year is abnormal compared to previous years

Let's say I have sales data for each month of the year for the last few years. Sales tend to dip in the summer, and I want to determine if the dip this year (or for a given month) is abnormal. ...
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8 views

Using Levene Test for multiple dependent variables between multiple groups in R

Could you help me? I have been looking everywhere for an answer to this question. It does not seem as straightfoward as running ANOVAs in R. I want to test for equality of variances between four ...
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27 views

Test Statistic of Transformation

The two tests below seem to be the same to me. But when I tried an example and constructed the test statistics I couldn't see how they are the same. $H_0: \lambda=1~~~~H_a: \lambda\not=1$ $H_0: \ln(\...
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6 views

Analyzing several dependent variables using different tests

How to deal with a situation where assumptions of some tests are met only for few dependent variables? Can I use a different test for DVs for which assumptions of a test are not met? As an example, ...
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12 views

Two-Sample Hypothesis Test for Difference Between Two Proportions: Pooled vs Unpooled? How to Choose?

When are you supposed to use the pooled formula vs the unpooled formula? My understanding is that you use the pooled formula when testing a hypothesis where the null hypothesis is $H_0 = 0$ and the ...
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1answer
73 views

One-sided hypothesis test for correlation

In the textbooks I have access to (and that discuss hypothesis testing for correlation), I only met examples, where the null-hypothesis was $\rho=0$, and the alternative hypothesis was $\rho\ne 0$. My ...
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9 views

Zero-inflated model: non-finite value supplied by optim

So I have the following model predicting the presence of an animal on a certain spot. As a time unit quarter is initially used, but for one of the species of animals there is some (little) interesting ...
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35 views

How to do bayesian model comparison for control and treatment

I have a model for a biological experiment which has a typical bayesian structure, that is $\lambda \rightarrow X$. Now let's assume for control the parameters are $\lambda_1 \rightarrow X_1$ and $\...
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12 views

Kullback-Leibler divergence with sample data likelihood

I'm trying to get my head around the KB divergence in the context of the sample likelihood under two competing hypotheses, one optimal $H_0$ and one suboptimal $H_1$. Roughly speaking, I want to see ...
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16 views

Multiple Hypothesis Testing in Binary Text Classification

I've been checking several related questions about p-value correction and multiple hypothesis testing, but I've not figured out yet how and when to apply them in text classification problems We have <...
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55 views

Help Identifying the right statistical hypothesis test

I'm conducting a research which compares the ratio between two categories of words in 2 different text corpuses. Let's say I have corpuses A and B. I created 2 categories of words, Let's call them C ...
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11 views

p-value for non normalized data [on hold]

I'm working on a project where I want to apply the output of a neural network in conjunction with a greedy (prediction) algorithm. The project is segmentation of 3D volumes. The greedy algorithm ...
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1answer
5k views

40,000 neuroscience papers on fMRI might be wrong

I saw this article in the Economist about a seemingly-devastating paper [1] casting doubt on "something like 40,000 published [fMRI] studies." The error, they say, is because of "erroneous statistical ...
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1answer
42 views
+50

How to work out the relationship between error α and threshold η

Reading up on the Neyman Pearson Lemma, I have a question about how to obtain the probability for a type I error, $\alpha$, when we establish a threshold $\eta$ for the liklihood ratio $\Lambda(x)=\...
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1answer
30 views

How to compare data that fluctuates?

I want to build a chart to compare accessibility of N given front pages of different web sites. For getting the initial data I use AChecker tool which returns me a number of accessibility issues were ...
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1answer
24 views

Test for significance of variation in time series data

Suppose a DMV office runs driving tests. Every week a number of people take the driving test, some pass and some fail. Looking at this data set, we notice that the pass rate varies from week to week. ...
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1answer
13 views

interdependence of type 1 error and type 2 error in p-Value based hypothesis tests

Investigating a t-Test, I ran some "experiments", generating randomly distributed values around a given mean, and running a whole bunch of t-test (always with new data) for conditions where the null-...
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3answers
53 views

Why do we use $P_0$ instead of $\hat{p}$ for sample proportion Hypothesis Testing?

It seems that most people favor using $$t_{stat} = \frac{\hat{p}-p_0}{\sqrt{p_0(1-p_0)/n}}$$ instead of $$t_{stat} = \frac{\hat{p}-p_0}{\sqrt{\hat{p}(1-\hat{p})/n}}$$ when doing Hypothesis Testing ...
2
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1answer
31 views

In medical statistics, when to use $\chi^2$ and when to use Kruskal-Wallis H?

I am conducting a retrospective analysis on the effect of three different treatment option (intervention treatment) on a special type of cancer, so I have three groups: 1, 2, and 3. In the baseline ...
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0answers
8 views

correlation between score and variable across different methods

I am using three different Machine learning methods to segment images, with a score for each image. I would like to show that there is a relationship between the score and the image, rather than the ...
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0answers
41 views

Logistic regression: Is there a significant difference for probability p between groups of Bernoulli random variables?

Let $S_{I+1} = \{1,2,\cdots,I\}$. And assume that there are exactly $J$ observations $(x_j,s_j) \in \mathbb{R} \times S_{I+1}$ for each integer $j$ such that $1 \leq j \leq J$. For each $i \in S_{I+1}$...
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5 views

Pairwise significance test with different variances within sample

I'm trying to test the significance of changes in the sales volume from one year to another. For each store I know the sales in 2014 and 2015 each day and would like to do a pairwise significance ...
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1answer
22 views

Advance Methods of Understanding Significance of Customer Behaviors

I currently own a couple of websites and lately I've been implementing some feature changes - I've noticed some changes in website traffic and I was wondering what some of the more sophisticated ways ...
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13 views

Binomial Hypothesis Test Segmentation For Webpage A/B Testing

My Question: Is page1 performance better or worse than page2 performance? Which page would you switch traffic to? More Context ...
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2answers
58 views
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135 views

Not able to understand the intuition behind $z$-test, $t$-test

I am not able to understand and appreciate the basic intuition behind need of this whole hypothesis testing framework, different kinds of tests, looking up tables, significance level etc etc. Why can'...
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13 views

Anova with order between treatments

I want to analyse a regression model with categorical explanatory variable. to be accurate, the model is as follows: $y_{k,j}=\mu_k+\epsilon_{k,j}$ where $k$ is the number of different effects $(k&...
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3answers
63 views

Number of false positives after Bonferroni or FDR

Let's say I am doing 100,000 tests. If the tests are independent, at an alpha of 0.05, we would expect (on average) 5000 of these tests to be false positives. The Bonferroni method would penalize ...
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29 views

Binomial modelling, testing and Bonferroni

I am currently trying to validate an implementation that is supposed to randomly assign a certain number of tags to users who enter a platform. The variable of interest here for me is the sum of all ...
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0answers
11 views

Is chi square test appropriate for testing frequencies of modifications?

I have a lot of sequence reads from next generation sequencing that I'm converting to a sequence of number of Stops, sorted by position on a specific gene. Such a sequence can look like: 0 0 0 0 1 0 ...
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12 views

Hypothesis Test for Inferring a User's Interest

I am dealing with the following information retrieval problem. A user uses a search engine and the results that are given all belong to distinct categories - say category 1, category 2, and category ...
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0answers
20 views

Likelihood Ratio Test p-value for three parameters in r

I have a function with 3 unknown parameters (theta1, theta2, theta3), defined as: ...
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0answers
15 views

multiple paired-sample t-test and Bonferroni Adjustment

I have 4 questionnaires: A,B,C,D. I also have another 4 items ($i_1,i_2.i_3,i_4$) that each measures some aspect of acceptability or feasibility of the questionnaires, which were answered following ...
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40 views

What statistical test can I use?

I'm currently trying to test the effect of pH on the growth of three different types of grasses for my dissertation and didn't account for number of replicates being used (statistically dumb). Here is ...
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0answers
35 views

Applying the $\chi^2$ test of independence: why $(observed - expected)^2 \over expected$?

In the $\chi^2$ test of independence, the test statistic is defined over the contingency table as such: $\chi^2 = \sum_{cells} \frac{(observed - expected)^2}{expected}$ Why is it defined like that? ...
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0answers
24 views

Test for difference of spatial/temporal distribution

I have the data of the average hourly consumption of electric power in 50 districst of a city, for the days of 2 months: ...
11
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2answers
98 views

Using lm for 2-sample proportion test

I have been using linear models to perform 2-sample proportion tests for a while, but have realized that might not be completely correct. It appears that using a generalized linear model with a ...
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21 views

Difference in mean change between groups - which statistical test to use?

I have three groups for which I have baseline and final measurement values (and intermediate, but that doesn't really pertain to this question). I want to use a statistical test on the mean change ...
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0answers
20 views

Weights in Welch's t-test

I am familiar with Welch's t-test, but I would like to use weighted means in the data. Is anyone familiar with a t-test with unequal variances, and how I can manually calculate a t-statistic and ...
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0answers
39 views

y and x axes coupled by two experimental measurables, how to determine if the trend is due to the coupling or not?

If, in a plot of $y$ versus $x$ where $y=f(a,b)$ and $x=g(a,b)$ such that $f{\ne}g$, a clear trend arises, how can one show that the trend is either a) probably due to the axes sharing the variables ...
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10 views

Comparing 2 sets of distributions

I have a data set where I have 2 groups of samples, each with 5 samples within each group. Each sample has a distribution of particle sizes within it (500 or more items in each distribution). How do I ...
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0answers
8 views

Testing paired binary data for independence

I have run an experiment where I apply two treatments to a subject. Each treatment has a binary success outcome. My results look something like: ...
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0answers
15 views

Which test can I use to compare two count data means with a lot of zeros?

Suppose I have two count datasets, lets say the count of tigers across different years at two places. Now for most of the years we have 0 tiger sightings. For eg. ...
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1answer
22 views

Statistically significance test to compare a ML classifier to a group of experts?

I am working on a medical data set of 60 test samples and I have the decisions of 45 medical experts for them over 5 diagnostic classes. How should I do hypothesis testing to show that the classifier ...
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0answers
11 views

Which ANOVA model should I use?

I have a data set containing root, shoot, and seedling growth measurements from 5 treatment groups (at different concentrations, 3 replicates) including control. There were no separate control groups ...
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1answer
25 views

What do you expect a 2-sample t-test for the same two samples to return?

I am using scipy in Python and the following return a nan value for whatever reason: ...
8
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2answers
194 views

How to define a Rejection Region when there's no UMP?

Consider the linear regression model $\mathbf{y}=\mathbf{X\beta}+\mathbf{u}$, $\mathbf{u}\sim N(\mathbf{0},\sigma^2\mathbf{I})$, $E(\mathbf{u}\mid\mathbf{X})=\mathbf{0}$. Let $H_0: \sigma_0^2=\...
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0answers
9 views

A/B Test: Determine if a Lift in Measured Sales is Significant

I am no stats expert so any assistance will be greatly appreciated. I’m working on a post-campaign analysis to determine if any measured sales lift (sales lift per audience) is significant between ...
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0answers
17 views

Multiple hypothesis testing for bivariate correlation

I am doing bivariate correlations (Pearson) comparing 140 different variables against each other. I was wondering if there is any risk of false positives (or that MHT has an effect here) in terms of ...
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0answers
18 views

What nonparametric test should I use?

I am having two groups of data (unpaired, different sample size N) that I need to compare in non-parametric way. I would like to use median. I read about median test, but I am not sure if that is the ...