Tagged Questions

3
votes
0answers
163 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 ...
-1
votes
0answers
29 views

Method to evaluate a multiple choice type survey [closed]

I have designed a survey that asks survey takes a set of question based on a video. There are many such videos and each video has three questions. Questions have four options each. I need to evaluate ...
1
vote
0answers
18 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 ...
1
vote
0answers
38 views

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 ...
0
votes
0answers
26 views

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 ...
0
votes
1answer
112 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 ...
1
vote
1answer
125 views

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 ...
2
votes
1answer
208 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 ...
2
votes
1answer
272 views

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% ...
20
votes
6answers
655 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 $1-\alpha$ ...
1
vote
1answer
97 views

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 ...
1
vote
1answer
73 views

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, ...
0
votes
0answers
55 views

What are origin/rationales for standard training vs. test data splits?

In experiments on supervised learning using a held out test set, one commonly sees allocations of labeled examples ranging from 50% training/50% test up to 80% training/20% test. These proportions ...
4
votes
0answers
178 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 ...
1
vote
0answers
75 views

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 ...
9
votes
3answers
1k 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 ...
5
votes
2answers
86 views

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 ...
1
vote
1answer
93 views

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 ...
4
votes
2answers
2k 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 ...
5
votes
3answers
7k 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 ...
32
votes
2answers
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 ...
3
votes
1answer
573 views

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?
3
votes
1answer
227 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 ...