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Results tagged with hypothesis-testing
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user 230329
This tag is for questions on hypothesis testing in statistics, including questions about constructing or setting up a test, selecting an appropriate test for a particular application, and computing test statistics.
0
votes
Any relationship between the bias in estimating regression coefficient and p-values?
It depends also on their (estimated) variance, i.e., if $|\beta_{1,1}| \le |\beta_{1,2}|$, and if their estimated variance is the same, thus $p_{1,2} \ge p_{1,1}$. However, without knowing anything on …
- 16.5k
1
vote
Accepted
Supposedly easy one-sided test
According "the corresponding estimated asymptotic standard error is..." I believe you can assume that $n \ge 6$, then you can use the $t$ table in order to verify the answer. Your t statistics is $t_{ …
- 16.5k
1
vote
For which $\alpha$-sizes is there a MP level-$\alpha$ test?
The test should be a function of the minimal sufficient statistic, namely $X_{(n)} = \max\{X_1,...,X_n\}$, such that if $X_{(n)} > \theta_1$ then you reject $H_0$ with $\alpha = 0$ and where $X_{(n)} …
- 16.5k
0
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What statistical test should I use?
You are comparing a dichotomous variable (win / loss) with the same two players (dependent) in two different settings (no variation / variation). It sounds like McNemar's test would be a good fit for …
- 16.5k
1
vote
The Difference between Significance Level and Type I Error?
If you say that your test has significance level of $\alpha$, it is by definition means that the probability of rejecting the null hypothesis under $H_0$ is $\alpha$. Namely, you said that your test i …
- 16.5k
2
votes
Accepted
Testing hypothesis using Extra Sum of Squares (F-Test)
$c$ should be the number of restrictions or equivalently the difference between the "degrees of freedom" between the unrestricted and restricted model. In your case, $c=4-0=4$ (you have "restrictions" …
- 16.5k
1
vote
Accepted
$0 \in $ CI, should we consider p-value? If so, how?
1) Interpretation: The probability of making a mistake in rejecting $H_0$ is $0.03596$.
2) Your hypothetical scenarios are impossible as for confidence level of $95\%$, p.value$<0.05$ iff $0 \notin C …
- 16.5k
0
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The highest level of significance at which the null will not be rejected (t-distribution)
The "p-value" can be viewed as an empirical highest level of significance, i.e., in your case is $0.001$.
- 16.5k
1
vote
Accepted
Difference between two statistical approaches to same question
Not identical. The first one based on approximation, i.e., the sample distribution of $\hat{p}$ is only approximately normal for any finite $n$, while $n\hat{p}$ is exactly Binomial.
- 16.5k
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MP test construction for shifted exponential distribution
If $X_{(1)} \in (\theta_0, \theta_1)$, then there is no uncertainty and you sure that $H_0$ right. If $X_{(1)} \ge \theta_1$, then the MP test of size $\alpha$ is: reject $H_0$ if
$$
c\le\frac
{\exp\ …
- 16.5k
2
votes
Accepted
Basic question about significance of statistical tests
Let $SW$ be the Shapiro-Wilk statistic, and $P = F(SW)$ be its p.value. As
$$
F(P \le p) = F(F(SW) \le p) = F( SW \le F^{-1}(p)) = F(F^{-1}(p)) = p,
$$
hence $F(SW) \sim U[0,1]$. Namely, under $H_0$ …
- 16.5k
1
vote
Accepted
Derivation of statistical test for equality of two regression slopes
Under $H_0$, $\alpha = \beta$ and given that $\epsilon_i$, $i=1,2$ follows a normal distribution you have
$$
\frac{ \hat{\alpha} - \hat{\beta} }{\sigma_{\hat{\alpha} - \hat{\beta} }}\sim N (0,1),
$$
w …
- 16.5k
0
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How to rigorously justify using a T-test rather than just $\bar{X}-\bar{Y}$?
Assume, for the sake of simplicity, that $n_Y = n_X = n$ and $\sigma^2_Y = \sigma^2_X = \sigma^2$ and $H_0: \mu_X = \mu_Y$ against two sided alternative, $H_1: \mu_X \neq \mu_Y$. As in real world case …
- 16.5k
2
votes
Accepted
What F-test is performed by $\texttt{lm()}$ function in R, at the end of the output?
By default it tests the full model against the null model which includes intercept only, i.e.,
$$
H_0: \beta_1 = \beta_2 =... = \beta_p=0.
$$
Let $SSreg(F)$ be the sum of squares of the full model, i …
- 16.5k
0
votes
Accepted
Linear Constraints in Regression Model (Self Study)
I hope that I understand your questions correctly..
The most frequently used estimator of variance if the unbiased estimator, i.e.,
$$
S^2_{\epsilon} = \frac{\sum_{i=1}^T(y_i - \hat{y}_i)^2}{T-k},
…
- 16.5k