Linked Questions
10 questions linked to/from Formal definition of p-value
14
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5
answers
2k
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Does p-value ever depend on the alternative?
Our tag definition of the $p$-value says
In frequentist hypothesis testing, the $p$-value is the probability of a result as extreme (or more) than the observed result, under the assumption that the ...
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7
votes
3
answers
1k
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Why does $\mu > 0$ (or even $\mu > \epsilon$) "seem easier” to substantiate than $\mu \neq 0$?
Consider a random variable $X$ following a normal distribution $N(\mu,\sigma^2)$. Suppose that we have drawn iid samples of $X$, obtaining a data set with a sample mean $\bar{x}>0$.
We want to test ...
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3
votes
2
answers
380
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Relationship of significance level and p-values
In a hypothesis test, the null hypothesis $H_0$ is rejected in favor of $H_1$ if $|\bar X|>\mu$.
When tests found that $\bar x$ is the mean of the samples, a p-value is computed using
$$
p=\Pr(|\...
- 6,917
9
votes
5
answers
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Why is the p-value defined the way it is (as opposed to a more intuitive measure)?
As I understand it the p-value for some hypothesis H and some test-statistic T is defined as the probability of observing a test-statistic T' which is at least as extreme as T, conditional on H being ...
- 71.8k
15
votes
4
answers
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Difference/relationship between power and significance
What is the conceptual difference between statistical power and statistical significance?
Are they the same? Is one used for the other?
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6
votes
6
answers
3k
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Comparing two, or more, independent paired t-tests
Can we compare the results from two, or more, independent paired t-tests?
For example: I want to test if drug 1 and drug 2 are effective to reduce weight. I have a control group (that will consume a ...
- 71.8k
23
votes
3
answers
66k
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How can I get a significant overall ANOVA but no significant pairwise differences with Tukey's procedure?
I performed with R an ANOVA and I got significant differences. However when checking which pairs were significantly different using the Tukey's procedure
I did not get any of them.
How can this be ...
- 71.8k
2
votes
1
answer
2k
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Which statistical analysis should I perform if the data sets are not normally distributed?
I am doing an experiment where there are two independent groups; one is the group of "infected" patients another is the group of "sepsis" patients. I am comparing "platelet monocyte aggregates(PMA)" ...
- 71.8k
2
votes
1
answer
4k
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R Tukey HSD Anova: Anova significant, Tukey not? [duplicate]
i created a simple anova with three groups in R and get a significant Result. After that i do a Tukey HSD Test and now nothing is significant. How can that be?
Pr(>F): 0.0316
Group | p adj
1 - 2 ...
- 71.8k
9
votes
1
answer
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Surprising behavior of the power of Fisher exact test (permutation tests)
I met a paradoxical behavior of so-called "exact tests" or "permutation tests", the prototype of which is Fisher test. Here it is.
Imagine you have two groups of 400 individuals (e.g. 400 control vs ...
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