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Questions tagged [p-value]

For questions related to p-value. In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.

In general, p-value is the probability of obtaining a real-valued test statistic at least as extreme as the one actually obtained.

In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.

Consider an observed test-statistic $t$ from unknown distribution $T$. Then the p-value $p$ is what the prior probability would be of observing a test-statistic value at least as "extreme" as $t$ if null hypothesis $H_{0}$ were true.

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117 questions
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Two definitions of p-value

According to Casella-Berger (2002) the definition of p-value (def. 8.3.26, §8.3.4, p. 397) is: A p-value $p(X)$ is a test statistic satisfying $0 \le p(x) \le 1$ for every sample point $x$. Small values of $p(X)$ give evidence that $H_1$ is true. A…
user1868607
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What is $p$-value?

Tell me about this $p$-value in relatively simple but not too simple terms. I've been reading many academic publications of late and come across it quite a few times without having a clear idea what it means. It's something about probability,…
Sergey Zolotarev
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Hypothesis test, finding p-value

A coin has a probability of getting tails of $\theta$ unknown. We would like to do the following hypothesis test over the value of $\theta$: $$\begin{cases}H_0 : \theta=0.5 \\ H_1 : \theta > 0.5 \end{cases}$$ Suppose we flipped the coin 5 times and…
Moria
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Finding the $p$-value from Bernoulli hypothesis test

So I'm told that $X_i \sim Bern(p)$, $Y = \sum_{i=1}^N X_i$ and $H_0: p \geq 0.5$ vs $H_1: p < 0.5$ with $\alpha = 0.05$. I have to find the $p$-value at $n=30$ and $y=5$. I'm not sure if this correct, but I figured the $p$-value was simply: $$P(Y…
doctopus
  • 491
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Testing goodness of fit using Kolmogorov-Smirnov test

I want to check if two probability distributions (experimental and theoretical) are same. The distributions are not normal distributions so I decided to use KS test. I used the MATLAB function KStest2 and got p-value = 1! Now, it means that I can't…
cat's eye
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Is it possible to put inequality to null hypothesis?

Based on a sample of i.i.d. Normal random variables $X_1, . . . , X_n$ with mean µ and variance $σ^2$, propose a test with asymptotic level 5% for the hypotheses: $$ H_0: µ > σ$$ $$ H_1: µ \leq σ$$ What is the p-value of your test if the sample has…
student
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Are the null hypothesis and alternative hypothesis mutually exclusive?

I am having a little bit of trouble understanding the concept of p-values. On the one hand, we are saying that the null hypothesis is a hypothesis we set, and the alternative hypothesis is something we would like to prove. In that case, how does it…
user796478
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Finding p-value with decimal degree of freedom

I am learning Welch's t-test and I successfully found that, in a two sample test, $t=2.968$ and the degree of freedom is $5.1$. I then go to an online p-value calculator for the p-value at 0.05 significance level. The results are as follows. The…
Am_2099
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Autocorrelation of p-values after $n$ observations

For $i = 1, 2, \dots$, let $X_i \sim N(0, 1)$ and $Y_i \sim N(0, 1)$, with all observations independent of each other. Suppose that after observing $X_1, \dots, X_n, Y_1, \dots, Y_n$ we calculate the equal-sample-size equal-variance $t$-statistic…
Alex
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misinterpretation of the P-value?

Sorry, if question is meaningless but I have started to learn concept of P-value and confused to interpret that, if actual results are in favour of hypothesis but p-value are against it then what statistics we should go with? For an example - Let's…
Bits
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Finding the $p$-value of a test with exponential data

My problem Assume that $X$ is exponentially distributed such that $X\in\operatorname{Exp}(\lambda)$. Let $H_0$ be $\lambda=3$. We want to test $H_0$ against the alternative $H_1$: $\lambda=1$ and reject $H_0$ if we observe a great value $x$ for…
August Jelemson
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How to calculate $p$-value in a clinical trial

I'm trying to verify the $p$-value mentioned in this article: $8\%$ ($n=\frac{1}{13}$) of mavrilimumab-treated patients progressed to mechanical ventilation by Day $28$, compared to $35\%$ ($n=\frac{9}{26}$) of control-group patients who progressed…
Caner
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Statistics, Hypothesis and P-value - Check my answers

I am trying to solve a question but stuck with the steps. I can not find any similar questions. With help of some online resources to calculate some parts of the question but I can see that is not enough. I know my approach has lack of information…
programminglearner
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Understanding exact tests for clinical trial data

A clinical trial is done with 400 persons suffering from a particular disease, to find out whether a treatment is better than placebo. They are randomised to receive treatment or placebo (200 participants each). The outcome studied is how many get…
Adhish
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Calculating the P-value of a T-distribution.

Learning some statistics here and in the chapter of Linear Regression I wanted to prove the values that I get on summary() from a created model. My summary() output is: Call: lm(formula = Price ~ Taxes + Size, data = HousePrices) Residuals: Min…
Patrick Vibild
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