# Tagged Questions

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### Difference estimate & confidence intervals for $\chi^2$ test between 2 proportions

I am using a chi-sq test between two proportions (http://statistic-on-air.blogspot.com/2009/07/comparison-of-two-proportions.html). I am using this over the z-test for proportions because I do not ...
47 views

### scale estimate for positive and negative data

I have 2 datasets (nonpaired), P1 & P2, and I want to know 'scale parameter' of one to the other, aka P1=a*P2. As both datasets are highly nonnormal, I am performing a Mann-Whitney Test on the ...
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### Decision rules based on amount of overlap between Bayesian probability intervals

My research hypothesis is that an intervention, I, results in greater scores than the control,C. If the intervals for these two don't overlap, I know I can make a clear-cut statement either accepting ...
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### Which is better? Hypothesis Testing or Confidence Interval

I am currently during my final year of schooling. I am curious to know (and I want to put this in my Math assignment), what is better 1-tailed Hypothesis Testing, where you see if a claim is ...
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### Does it make sense to compute confidence intervals and to test hypotheses when data from whole population is available?

Does it make sense to compute confidence intervals and to test hypotheses when data from whole population is available? In my opinion, the answer is no, since we can accurately compute true values of ...
157 views

### How do I calculate confidence intervals for a linear combination of coefficients of a logistic regression?

I want to test a series of hypotheses on linear combinations of coefficients for logistic regression on categorical count data implemented as a GLM model. I know how to do linear combinations under ...
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### Testing if a vector is in a population of vectors

Suppose that I am concerned with objects that are described by N 2D points. These points all have equal importance to me. I begin with a large number R of such objects, each with its corresponding ...
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### Inverting a hypothesis test: nitpicky detail

First timer here. I'm reviewing a section of Casella and Berger on inverting a hypothesis test to get a Confidence Interval (CI), and came across a proof which I believe is missing a tiny piece. ...
288 views

### Ratios of means - statistical comparison test using Fieller's theorem?

I would really appreciate any suggestions with the following data analysis issue. Please read till the end as the problem at first may appear trivial, but after much researching, I assure you it is ...
43 views

### Duality between acceptance region of testing and confidence region in terms of optimality?

The duality theorem between acceptance region of testing and confidence region is about their validity (i.e. satisfying the significance level of the former and the confidence level of the latter sum ...
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### In testing, do we need to make the area of an acceptance region as small as possible?

One criterion to access a confidence interval is that the smaller its area, the better. For hypothesis testing, I was wondering if it is also that the smaller the area of the acceptance region, the ...
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### How do you construct confidence interval (by the method of pivots)?

From a note Many derivations of confidence intervals can be described in terms of ... (pivot). ... The best choice is often suggested by looking at what statistic a good hypothesis test ...
157 views

### One sided confidence interval for hypothesis testing

I'm having a hard time understanding how to use confidence intervals for hypothesis testing. I've seen examples to reject a null hypothesis, but don't understand how to use a one-sided confidence ...
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### Standard Error used in Hypothesis Testing and Confidence Interval construction

In the excellent Practical Statistics for Medical Research Douglas Altman writes in page 235: "Because the standard error used for calculating the confidence interval differs from that used in ...
325 views

### Test for multinomial distribution

I have a sample of animals and a categorical variable of $L$ behaviors $i=1,...L$. I computed the proportions of this sample corresponding to each behavior category $p_{i}$, $\sum p_{i}=1$. Can I ...
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### 95% CI that contradict a paired samples t-test

I conducted a paired samples t-test to analyse the effect of an exercise intervention on blood pressure measurements. The test demonstrated a significant p-value. However, when I have calculated 95% ...
811 views

### What is the connection between credible regions and Bayesian hypothesis tests?

In frequentist statistics, there is a close connection between confidence intervals and tests. Using inference about $\mu$ in the $\rm N(\mu,\sigma^2)$ distribution as an example, the $1-\alpha$ ...
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### Understanding hypothesis testing, confidence intervals and frequencies

Sorry if this is a silly question but I seem to be mixing a few things together and would love if someone could straighten it all out for me. Please correct me! This is somewhat related to my post ...
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### Help required with using the correct model for sampling

I regularly encounter the following scenario: I am presented with a set, $\mathcal{S}$, of $i$ items. I am assured that $d$ of the $i$ items possess a particular property, $d'$ - and that the rest, ...
221 views

### Binomial mid-p value

I've been under the impression that the mid-$p$ values generally control the Type I error, and consequently confidence intervals based on mid-$p$ values control the coverage. However I have checked ...
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### Are rejection regions always open/closed?

Does there exist any agreement on what must rejection regions look like topologically? If we identify the region of "acceptance" with the corresponding confidence interval (or confidence region in ...
2k views

### Relation between confidence interval and testing statistical hypothesis for t-test

It is well known that confidence intervals and testing statistical hypothesis are strongly related. My questions is focused on comparison of means for two groups based on a numerical variable. Let's ...
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### How can I (or should I) test that observation A tends to be greater than observation B for each subject?

I measured 2 sediment parameters in multiple lakes. The organic matter content at the sediment/water interface surfOM and the mean organic matter content of the ...
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### What is the equivalent confidence interval for a directional hypotheses?

Testing the null hypothesis $H_0: \theta = 0$ against the alternative $H_1: \theta \neq 0$ is equivalent to constructing a confidence interval and checking whether or not zero belongs to it. But what ...
4k views

### What is the relationship between a p-value and a confidence interval?

Following from this question on the difference between confidence intervals and hypothesis testing, I would love to have a simple example to better understand the the relationship between confidence ...
10k views

### What is the difference between confidence intervals and hypothesis testing?

I have read about controversies regarding hypothesis testing with some commentators suggesting that hypothesis testing should not be used. Some commentators suggest that confidence intervals should ...
2k views

### 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 ...