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/)
Questions tagged [critical-value]
16 questions
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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}\left(\bar{X}-\frac{z_{\alpha / 2}}{\sqrt{n}} \cdot…
Kirsten
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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 95% confidence interval, so $\alpha = 0.05$.…
explodingfilms101
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3
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2 answers
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 $\ X_1 , X_2 $ .
Define $ \ X_3 $ as =
$\ X_1 $, if…
simran
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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 commonly recommended for non-normally distributed…
Westcroft_to_Apse
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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 r function However, my output deviates significantly. Please see the equation below. I considered…
score324
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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 reject $H_0$ if
$T(X) < \chi_{2n,1-\alpha}$.
If…
userNoOne
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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 the null hypothesis
$$H_0\colon \quad \mu=0 \quad…
Richard Hardy
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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 equal to the 97.5th percentile, and therefore…
Guillaume F.
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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 $ \ H_1 : 1000 $ an experimenter sets up an …
simran
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vote
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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 include a dummy variable for additive type outlier…
Dayne
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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?
set.seed(4)
n<- 100
M<- 50000
rho<-numeric(M)
std<-numeric(M)
for (i in 1:M){
b0 <- 1.5
b1 <- 2
U<-rnorm(n, mean=0,…
blh
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Why do DW test have dL and dU, different from other tests?
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 distribution and then I can get the definite critical…
Coadak
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Is it proper use of Karlin-Rubin theorem? Different approaches
I know version of Karlin-Rubin theorem* which makes assumption that if $f_\theta(x)$ is joint density of variables $X_1, ... X_n$ (our sample), then $l(x) = \frac{f_{\theta_1}(x)}{f_{\theta_0}(x)}$ (called likelihood ratio) is non-decreasing…
Brzoskwinia
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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 with:
for(i in 1:N){
x=rnorm(n=16,mean = mu,sd=1.2)
#calculate test size
…
firmo23
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How to find the Chisq values for a two tailed test in R?
How do we find the chisq value for a two tailed test?
For left tail we use qchisq(x,df,lower.tail="True")
For right tail we use qchisq(x,df,lower.tail="False")
What about two tailed?
