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Questions tagged [critical-value]

In hypothesis testing, a critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis. If the absolute value of your test statistic is greater than the critical value, you can declare statistical significance and reject the null hypothesis. (source: https://support.minitab.com/)

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What is the formula to compute the height of significance line on autocorrelation plot?

Autocorrelation of a time series can be plotted in R with use of acf function. For example: acf(ldeaths) # built-in series I ...
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Engle-Granger cointegration test critical values

I am conducting the Engle-Granger cointegration test on a system of three time series: logged spot exchange rates, logged domestic price index, and logged foreign price index. I would like to use ...
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Very narrow confidence interval in ACF and PACF graphs

I am trying to forecast electricity consumption using hourly consumption data over a span of 4 years. However, when I plot the ACF and PACF graphs, the confidence interval turns out to be very narrow, ...
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Determining and interpreting the critical region of a distribution

Suppose that you have a null hypothesis $H_0$ that you want to test. Let $\alpha$ be a given confidence level, for example $\alpha = 0.05$. Suppose that the test statistic $T$ follows (under $H_0$) a $...
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Doubt in calculation of critical region in two-tailed test

Consider the following question:- A tetrahedral die is manufactured with numbers 1, 2, 3 and 4 on its faces. The manufacturer claims that the die is fair. All dice are tested by rolling 30 times and ...
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Chi-Square Test vs Distribution confusion

Disclaimer: I'm new to stats so please bear with me Everywhere I look, the Chi-Square Distribution is explained with a (Z-Score)^2 i.e $$ ((X-\mu )/\sigma )^2 $$ and based on a random variable from a ...
mandem's user avatar
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Two-sided critical regions and two-sided P-value for discrete (integer-valued) negative binomial distribution

Let $X$ be a Negative Binomial random variable, $X \sim \mbox{NB}(n, p)$, with $P(X=x) = {n+x-1 \choose x} p^n (1-p)^x, x = 0, 1, 2, \cdots$. Suppose I do this experiment where I toss a coin until I ...
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Difference in the results of qbinom() and sensR::findcr() in R

I try to understand the difference of +/-1 in the result of two functions using the binomial distribution. I need to know the critical value of a situation where I have n=9 tests, the probability of ...
Indy's user avatar
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Finding critical value for F statistic

I am performing a hypothesis test and therefore intersted in finding the F critical value for my F statistic. Below is the anova output when I compare two models. ...
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Q-value for FDR correction in R stats package

I used FDR correction (i.e., Benjamin-Hochberg tests) from the R 'Stats' package, but I'm confused of the q value used in the package. The notations in the 'p.adjust' function does not include the ...
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Simulation about ADF test

I want to get ADF table critical values. However, the critical values I get are between -8 and -10. Where am I doing wrong? ...
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Efficient calculation of critical values for Mann-Whitney-Wilcoxon

Most tables of critical values for the Mann-Whitney-Wilcoxon rank sum test statistic, usually known as U, are only calculated for very small samples. Presumably, this is because the test is most ...
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Why do DW test have dL and dU, different from other tests? [duplicate]

I wonder why the Durbin-Watson test table has the critical values of dL and dU. This is different from other tests, Z, t, chi-squire, F. It has confused me. A test statistic has the sampling ...
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Define critical value c to find the number of rejects in strength of T-test calculation

I need to calculate the power of a t-test for set.seed(1) N=1000 mu=5 number.of.rejects=0 sd=1.2 first I want to calculate my number of rejects ...
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calculating confidence interval for critical value multiplying by negative 1

I am trying to understand how $$ \mathbb{P}\left(-z_{\alpha / 2} \leqslant \frac{\bar{X}-\mu}{\sigma / \sqrt{n}} \leqslant z_{\alpha / 2}\right) \approx 1-\alpha $$ can be converted to $$ \mathbb{P}\...
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Find Critical region for exponential distribution

The lifetime in hours of each bulb manufactured by a particular company follows an independent exponential distribution with mean $ \theta $ . To test the hypothesis $ \ H_0 : 2000 $ versus $ \ ...
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Finding a critical region for a mixture

Let $\ X_1 , X_2 $ be two iid random variables with normal N ( $\theta,1 $) distribution. Further , consider bernoulli random variable V with P(V=1) = $ \frac{1}{4} $ and which is independent of $\ ...
simran's user avatar
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Simulating critical values using standard Brownian motion

Using R, I am replicating the Table 1 results of this paper https://www.tandfonline.com/doi/abs/10.1080/03610926.2014.985841. I wrote the following ...
score324's user avatar
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Two ways of writing the critical region for Hypothesis Testing

I have one confusion in writing critical region. Let us suppose that we have a test condition that rejects the the null hypothesis if $T(X) > \chi_{2n,\alpha}$. Can we also write this same test as ...
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Testing for Cointegration with Dummy Variable (for outlier) in Cointegrating Equation

I have two time series $y_t, x_t$ which are both $I(1)$. I am following the 2-step Engle-Granger approach for testing cointegration between the two series. However, for known reasons, I also want to ...
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Testing a nonstandard hypothesis: constructing test statistic, finding rejection region and obtaining $p$-value

I have a sample of size $n=1$ (a single observation $x_1$) from a random variable $X\sim N(\mu,\sigma^2)$. The variance $\sigma^2$ is known, but the expectation $\mu$ is unknown. I would like to test ...
Richard Hardy's user avatar
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Is $z_{0.025}$ equal to -1.96, or 1.96?

I'm unsure about the interpretation of $z_{\alpha}$. I've seen some source claim that $z_{\alpha}$ is equal to the z value with $\alpha$ of the area to the right of it. Under this view, $z_{0.025}$ is ...
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What if the P-Value is less than 0.05, but the test statistic is also less than the critical value?

Let's say you let the Null Hypothesis $H_0$ be that the mean volume of water in a bottle is some $\mu$, and the alternate hypothesis $H_1$ be that the mean volume is not $\mu$. Let's assume you pick a ...
explodingfilms101's user avatar