Linked Questions

0
votes
1answer
103 views

Confidence interval deeper explanation? [duplicate]

I have some data on a drug where doctors are trying to find out based on collected data how many patients get heart disease because of a drug. The output is the following: 95%CI 1.72(1.28-2.30) for ...
0
votes
1answer
37 views

Difference in CI Interpretations? [duplicate]

So the interpretation of a 95% CI is that there is a 95% probability that the CI contains the true parameter value, but not that there is a 95% probability that the true parameter lies in the CI? Can ...
405
votes
14answers
249k views

Bayesian and frequentist reasoning in plain English

How would you describe in plain English the characteristics that distinguish Bayesian from Frequentist reasoning?
93
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12answers
15k views

What, precisely, is a confidence interval?

I know roughly and informally what a confidence interval is. However, I can't seem to wrap my head around one rather important detail: According to Wikipedia: A confidence interval does not ...
42
votes
16answers
6k views

The Monty Hall Problem - where does our intuition fail us?

From Wikipedia : Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who ...
87
votes
7answers
12k views

Are there any examples where Bayesian credible intervals are obviously inferior to frequentist confidence intervals

A recent question on the difference between confidence and credible intervals led me to start re-reading Edwin Jaynes' article on that topic: Jaynes, E. T., 1976. `Confidence Intervals vs Bayesian ...
31
votes
5answers
7k views

What do confidence intervals say about precision (if anything)?

Morey et al (2015) argue that confidence intervals are misleading and there are multiple bias related to understanding of them. Among others, they describe the precision fallacy as following: The ...
23
votes
5answers
20k views

Now that I've rejected the null hypothesis what's next?

I've time and again rejected or failed to reject the null hypothesis. In the failure to reject case, you conclude that there isn't sufficient evidence for rejection and you "move on" (i.e., either ...
2
votes
1answer
10k views

Confidence intervals for regression interpretation

I have done linear regression and plotted the data, the regression line and also the confidence interval (for 95% confidence). However it seems that most of the data points fall outside the ...
11
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3answers
6k views

What does a confidence interval (vs. a credible interval) actually express? [duplicate]

Possible Duplicate: What, precisely, is a confidence interval? Yes, similar questions have been asked before, but many of the answers seem contradictory and don't address my issue. (Or my ...
4
votes
3answers
7k views

Hypothesis testing for a correlation that is zero or negative

I would like to test for a correlation that is zero or negative using the following hypothesis test: $H_0: p>0$ (Null hypothesis: the correlation is positive) $H_A: p\le0$ (Alternative hypothesis: ...
6
votes
2answers
1k views

Interpreting a confidence interval.

If someone asks me to interpret the confidence interval (say at the level of a first graduate course in statistics) -- are there typical templates for such an interpretation. By typical templates I ...
4
votes
4answers
1k views

Expected value of small sample

I've got product ratings for a few thousand products. The number of ratings for each product varies from zero to about fifty. I want to find the expected value of product rating for each product. If ...
6
votes
2answers
2k views

Putting a confidence interval on the mean of a very rare event

I'm simulating an extremely rare event (the detection of weighted photon packets in a highly absorbing material). For example, I may simulate the transmission of 1e9 photons and only detect 10 of them ...
5
votes
1answer
2k views

Confidence interval for Uniform($\theta$, $\theta + a$)

I am encountering a difficulty with the following task. Have I made a mistake, or is this an inherent flaw in the notion of confidence intervals? (Other such flaws exist.) Consider a random sample $...
4
votes
2answers
311 views

Does a confidence interval carry some extra error for non perfectly normal distributions?

I'm not trying to nitpick but I always want to make sure with stats that I clearly understand the delimitation between exact/theoretical measurements and "real life" measurements. Let's say for ...
2
votes
3answers
1k views

Multiple testing and logistic regression

I want to perform a number of univariate regressions with different symptoms (e.g. fever, cough, sneezing) as the response variable and one categorical variable (which is always the same each time) as ...
2
votes
1answer
863 views

What is the fundamental confidence interval fallacy? [duplicate]

Beginner question here. I've read (see this paper) that when computing confidence intervals if you get a given interval with a confidence level of 95%, then it is a fallacy to think that the true ...
0
votes
0answers
368 views

Interpreting confidence intervals

Suppose I have a $95 \%$ confidence interval for $\mu$ with population variance $\sigma^{2}$ known. It will be of the form $$[\bar{X}-1.96 \sigma/\sqrt{n}, \bar{X}+1.96 \sigma/\sqrt{n}]$$ The ...
3
votes
2answers
117 views

Pick a card, any card: understanding the frequentist interpretation of a confidence interval

I've been trying to wrap my head around the oft-quoted misconceptions surrounding the frequentist interpretation of a confidence interval. There are many questions on Cross Validated and many ...
1
vote
0answers
160 views

Confidence Interval for the Population

My (basic) understanding of a 95% confidence interval is that it is the interval within which the sample mean would fall 95 times should you take 100 random samples from the population. My query is ...
0
votes
0answers
23 views

Confidence intervals: how do we have to interpret them? [duplicate]

I have a very basic question regarding confidence intervals. I am confused between two interpretations of confidence intervals. Interpretation 1: If repeated samples were taken and the 95% ...