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Questions tagged [hypothesis-testing]

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.

In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold probability, the significance level. A statistical hypothesis test is a method of inference using data from a study which is used to determine if a measured result differs from a predicted result in a statistically significant way.

The phrase "test of significance" was coined by statistician Ronald Fisher. These tests are used in determining what outcomes of a study would lead to a rejection of a null hypothesis for a pre-specified level of significance. This can help to decide whether results contain enough information to cast doubt on conventional wisdom, given that conventional wisdom has been used to establish the null hypothesis. The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis.

Statistical hypothesis testing is sometimes called confirmatory data analysis, in contrast to exploratory data analysis, which may not have pre-specified hypotheses.

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When to use which multiple testing correction?

There are a large number multiple testing p-value correction methods. e.g.: bonferroni : one-step correction sidak : one-step correction holm-sidak : step down method using Sidak adjustments holm : step-down method using Bonferroni…
lordy
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One way ANOVA or chi-squared testing?

I face problem in the following exercise: "In the professional football championship, it was said that during the last eight years, there was a discriminatory treatment of the team1, in relation to the other two equivalent team2 and team3. You argue…
Magda
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Hypothesis Testing for Poisson rvs

Let $x_1,\dots,x_m$ be iid Poisson$(\lambda_1)$ and $y_1,\dots,y_m$ be iid Poisson$(\lambda_2)$ and independent of $x_1,\dots,x_m$. $S_1=\displaystyle\sum_{i=1}^mx_i$ and $S_2=\displaystyle\sum_{i=1}^ny_i$ are independent Poissons with parameters…
Andrea
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Wilcoxon test for hypothesis testing in case the null hypothesis uses median as a parameter not mean ( in program R).

I want to test whether I could reject a null hypothesis that the data has a median of 600. I need to use the wilcox test or maybe construct it in R, but I am not sure if the builded in test supports for parameter - median? Because I think it may…
user
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Can we use t-test to liner combination of random variables?

Suppose X and Y are two random variables. And I have some samples of them: [9, 10, 11, 9, 10, 8, 10] and [100, 99, 101, 110, 120]. I want to test if Y is statistically larger than 10*X, Question: Can I use t-test and assume H0: 10*X ≤ Y with…
Tim He
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Derivation of hypothesis testing -- intuition?

Let's say I have data points $0.1$, $0.2$, $0.3$ coming from a normal distribution with mean $\mu$ and standard deviation $1$. If I want to test the hypotheses $H_0: \mu = 0.15$ vs. $H_1: \mu > 0.15$, then the test statistic is $$T =…
OneGapLater
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Hypothesis testing alpha-beta curve has to be convex?

In any hypothesis test, we have a false positive rate (a.k.a. $\alpha$; a.k.a. type 1 error rate) and false negative rate (a.k.a. $\beta$; a.k.a. type 2 error rate). It's clear that we can set the $\alpha$ to whatever we like. But the smaller the…
Rohit Pandey
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One sample t test cases

So I want to know when do we accept the null hypothesis and when we don't in t test. Case 1: t cal>t tab and p value >0.05,we accept null hypothesis Case 2: t cal>t tab and p value <0.05 we don't accept null hypothesis. Case 3: t cal < t tab and p…
prishila
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Hypothesis experiment

[Im am told to carry out a suitable hypothesis test to determine whether the removal of the red cedar trees has reduced the mean number of leaves with rust spots. I have stated the null hypothesis which is the mean number of leaves with rusts…
jon doe
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two types of errors can occur during hypothesis testing

The painkiller drug needs to have a time of effect of at most 200 seconds to be considered as having done a satisfactory job. Given the same sample data (size, mean, and standard deviation) of the previous question, test the claim that the newer…
Mohammed Habeeb Rehaman
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How to calculate test statistic when $H_0$ is not equal

So I'm trying to perform a $t$ test with sample mean $\bar{x}$ and sample variance $s^2$. I know how to do this with $H_0 = a$ and $H_a \ne a$. But now I'm given $H_0 < a$ and $H_a \ge a$. How do I modify the $t$ test formula?
PTN
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hypothesis testing, P-value calculation, standard deviation unknown

i have following problem, "The null hypothesis says that a sprinter's reaction time follows a normal distribution with mean at most 0.150 seconds. Six measurements of a sprinter's reaction time show 0.152, 0.154, 0.166, 0.147, 0.161, and 0.159…
Nour
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Paired T Test Hypothesis Interpretation

With a paired T test I understand the first part of the hypothesis: $H0: \mu_d = 0$ The alternative hypothesis I get a little mixed up and I am trying to figure out when to appropriately use the alternatives. If the alternative hypothesis is: $H1:…
AxGryndr
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If two tailed or one tailed should be used to test Hypothesis

The production rate of a Company has been normally distributed over a period of time. The mean production rate is 100 pieces per day and standard deviation is 9.Recently the board of management introduced new production methods to improve the…
Shehan Tearz
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GLRT Inconclusive for Gaussian Detection

When constructing a detection test between two Gaussian vectors, I have $H_0: \mathcal{N}(0, \sigma_n^2)$ and $H_1: \mathcal{N}(0,\sigma_n^2 + \sigma_s^2)$, and $\sigma_n^2$ is unknown under finite samples collected, while $\sigma_s^2$ in known.…
King008
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