Questions tagged [type-i-and-ii-errors]

Type I: rejecting the null hypothesis when it is true. Type II: not rejecting the null hypothesis when the alternative is true.

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50 views

Can you actually prove if the null hypothesis is true or a type II error has occurred?

Can you actually prove if the null hypothesis is true or a type II error has occurred? I'm new to statistics (sorry in advance!)
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0answers
54 views

Find the probability of an omitted alarm if the process shifts by δ (delta) = 2.0

I have an allegedly simple task: Based on the OC curve: Find the probability of an omitted alarm if the process shifts by $\delta = 2.0$ Unfortunately I have nothing to show (what I have tried or so, ...
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1answer
25 views

How do I correct for type I error in a mediation when using Hayes' PROCESS in SPSS?

I have performed three mediation analyses using PROCESS in SPSS, each with a different outcome/dependent variable. To prevent a type I error, I would like to perform a correction for this, but seeing ...
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1answer
44 views

Two sample t test with equal variances hypothesis

Given a trial to test a new drug. There are 20 volunteers with some disease. The volunteers are split into two groups (10 volunteers in each) randomly: the treatment group and the control group. ...
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0answers
57 views

When does a proxy/substitute variable distinguish between groups as well as the original variable?

I’m trying to determine when a proxy variable can be substituted for a real variable for the purposes of distinguishing two groups. To make this more concrete, suppose I want to determine, generally, ...
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1answer
30 views

Why reversing a continuous measure leads to a non-significant correlation coefficient

Background: I'm analyzing correlation between two behavioural types (boldness and aggression). Boldness values are continuous (range: 2 to 1195) and it's unit of measurement is in seconds (latencies). ...
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1answer
29 views

Hypothesis testing, type I and II error

A sample $X_1, X_2, X_3, X_4$ comes from a normal distribution $N(m, 2^2)$. To verify $H_0: m=4$ against $H_1: m = 1$ one uses a test with a critical region: $K = \{4X_1 − 2X_2 − 2X_3 + X_4 < −2\}$....
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30 views

Type I error level vs. sample size

From Jay and Devore's Modern Mathematical Statistics, Chapter 9, problem 61 c In most situations, would it be reasonable to use a level .01 test in conjunction with a sample size of 40,000? Why or ...
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2answers
48 views

Estimating minimal sample size for two sample test (comparing means)

If I want to perform a hypothesis test to compare the means of 2 equally big samples from normal distributions with equal variances, how would I compute the minimum required sample size for each ...
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0answers
18 views

Power or type II error for Hotelling's T^2 test

I am trying to estimate the performance of the hotelling's T^2 test. I simulate various test from assumptions of normality and also equal covariance matrix. I succeed in computing the level of the ...
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0answers
29 views

Why is the probability of a type 1 error, $\alpha$, the significance level?

I've seen this stated Why are p-values uniformly distributed under the null hypothesis? and https://support.minitab.com/en-us/minitab-express/1/help-and-how-to/basic-statistics/inference/supporting-...
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32 views

Why a false positive is called type I error and a flase negative a type II error? [duplicate]

I am trying to understand what are the historical reasons behind the choice of the term Type I and Type II error. I think is much more intuitive to use false positive and false negative. These two ...
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1answer
55 views

linear mixed effects models: should I aggregate repeated trials?

A colleague of mine asked me to analyse some data from a movement experiment. Participants were asked to turn their head three times to the left (toL), three times to the right (toR), with both the ...
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1answer
13 views

Correction for multiple comparisons in a linear mixed effects model with dummy coded categorical predictor

I'm analysing the data from a multi-group randomised controlled trial. Participants were assigned to one of five intervention groups, or a control group. They were tested twice, pre (T1) and post-...
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0answers
9 views

What to report regarding FPR/Type I errors in addition to p-values to avoid misinterpretation?

I would like to report some indication/estimation of the (minimum) false discovery (i.e., type 1 error rate) of my results because that is how p-values are often misinterpreted but I am unsure how to ...
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0answers
115 views

Cross validation and type I, type II error

In the context of building a predictive model, I understand that cross validation (such as K-Fold) is a technique to find the optimal hyper-parameters in reducing bias and variance somewhat. Recently, ...
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1answer
25 views

What would be the most appropriate test to compare two groups in the three parts of the data?

I have a response dataset for twenty-five questions, which measures three grammar topics. The participants are two different English proficiency groups of intermediate and advanced. So, I want to ...
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1answer
66 views

Definition of a confidence interval

In one exercise of a mathematical statistics lecture, the teaching assistant wrote the following : A confidence interval for a given parameter $\theta$ is an interval [A,B] at level $\alpha$ such ...
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Convergence rate of type I error of test for difference in means with Brownian noise

Consider a stochastic process of the form $$dX_t = \mu(a_t)dt +\sigma dZ_t$$ where $\mu(a_t)$ is the deterministic drift of the process that depends on $a_t$, $Z_t$ is a standard Brownian motion, and $...
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Can the null hypothesis be **more** true than the alternative hypothesis or vice versa? [duplicate]

As the title says, my question is can the null hypothesis ($H_0$) be more true than the alternative hypothesis ($H_1$) or vice versa? For example, if the statistical power is really high (extremely ...
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0answers
43 views

Choice of critical/rejection region and relation of power function and type I/II error

A hypothesis test is, fundamentally, defined by a rejection region $R$(a set of the sample $\mathbf{X}$); not by statics such as LRT and MLE etc, but by a range (Must be so, see the following comment.)...
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43 views

Type I Type II error with power function as y-axis and mu(alternative) as x-axis

I stuck in the following graph for 2 days. I am confused because I ask myself the following two questions but did not get solved by myself. Q1: If Null (H0) is larger or equal to 5, then why when mu(...
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1answer
53 views

Orthogonal contrasts and the family-wise error rate

I recently read about contrasts and how to code them. Contrasts can be orthogonal which means that they are independent and the statistical tests for them are not correlated. Normally, when doing ...
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0answers
24 views

Type II error relevant limitation when Kaplan-Meier curves are identical?

Let's suppose that we have a made-up data including two diseases, and one of them is very rare (impossible to get a large sample size). Kaplan-Meier curves of the two diseases are almost identical, ...
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0answers
20 views

Permuting outcome variable to estimate null likelihood ratio distribution for Poisson GLM

I fit a Poisson GLM using a set of candidate explanatory variables ($\lambda = e^{\beta_{0} + \beta_{1}x_{1}+\beta_{2}x_{2}+...}$), tested against the global null hypothesis ($\lambda = e^{\beta_{0}}$)...
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2answers
302 views

The probability of type-II error for this test is_______?

Suppose X is a random variable on {0, 1, 2, . . .} with unknown p.m.f. p(x). To test the hypothesis $H_{0}$ : X ∼ $Poisson(1/2)$ against $H_{1}$ : p(x) = $2^{−(x+1)}$ for all x ∈ {0, 1, 2, . . .}, we ...
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1answer
46 views

Confusion about Type I Error and Sample Size

A candy company claims that its lollipops have an average weight of 23 grams. A statistician is suspicious of this claim (believing the average weight to be lower than 23 grams) and decides to conduct ...
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0answers
50 views

What statistical metrics / tools can be used to quantify underestimation of uncertainties in distances to astronomical objects?

Amazingly low uncertainties are frequently reported in distances to astronomical objects. However, the uncertain region of the measurements frequently fail to overlap. Is there a statistical measure / ...
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1answer
150 views

Ranked t-test or Mann-Whitney U test for commerical A/B testing

Please help me understand how this blog post relates to this experiment. Here I try to reproduce quite old paper from Zimmerman about Mann-Whitney U test and ranked t-test (and also plain t-test) ...
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1answer
77 views

How to Properly Interpret the Hypotheses/Results of a Permutation Test Based on the Test Statistic?

I asked a question recently: Is This an Appropriate Application of a Permutation Test?. All information about my data, the permutation test and the results can be found there, but here is a quick ...
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1answer
38 views

When will the type 1 and type 2 error be the same i.e. $\alpha = \beta$? [closed]

Suppose $x_{1}, x_{2},........,x_{n}$ be a random sample form normal distribution with mean $\theta$ and variance $1$. Under the following hypothesis: $H_{0}:\theta=\theta_{0}$ vs $H_{1}:\theta=\...
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1answer
33 views

Can I investigate the simple main effects of a factor with multiple one-way ANOVAs if the main effects (from two-way ANOVA) were insignificant?

I want to analyze the results of an experiment that was conducted as a 3 X 3 balanced, repeated measures study. There are two factors in my design--let's call them Factor A and Factor B. Both factors ...
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0answers
10 views

Discriminant Analysis (LDA/QDA) error types associated with normality deviation

Are there any good resources for evaluating what happens with LDA/QDA binary classification when the data deviates from normality? I see a lot of questions on how to deal with deviation from normality,...
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2answers
102 views

Interpretation of power calculations

We got the following comment from an associate editor who asked for ex-post power calculations. We used the treatment difference and sample size from our study and reported the power of detecting the ...
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0answers
43 views

type 1 error, type 2 error

alpha=p(type 1 error), beta = p(type 2 error), and total error =alphap(H0) + betap(H1) where beta is a function of alpha. One metric of the effectiveness of a hypothesis test is the integral of the ...
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183 views

Type 1 and Type 2 error

What is/are the statistical term/s for the region/s where the type1 and type2 errors occur/intersect (in the diagram Red + Blue regions or in part)? THANK YOU!
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0answers
16 views

Control of type I error rate in functional ANOVA F-test

I am following how to compare curves via functional data analysis, specifically functional ANOVA. This video makes sense in describing it as being a lot like vanilla ANOVA...up to a point. When we do ...
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0answers
35 views

Finding $\beta$ as a function of $\alpha$ and $\mu$ in hypothesis testing

Question: Let $X_1,X_2,X_3,X_4 \stackrel{iid}\sim \mathrm N(\mu,1), \mu$ unknown. We want to decide between $H_0:\mu = 2 $ and $ H_1: \mu \ne 2$. If we require significance level $\alpha$, find $\beta$...
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1answer
34 views

Correctly apply linear model for categorical independent variable

This question is about the way to go with a very common statistical model: Continuos dependent and categorical independent variable. In my stats class I learned to use the ANOVA: check assumptions, ...
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0answers
47 views

How to adjust p-value with Bonferroni correction?

I think this is a simple question, but for which I've found conflicting answers around. Let's say, I measured a biomarker in a group of patients with 5 different methods and I want to perform ...
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1answer
330 views

Calculation of beta error in case of two-tailed test of mean

I came across this example of calculating a type 2 error. I understand it up to the following point: Therefore, so long as the sample mean is between 14.541 and 16.259 in a hypothesis test, the ...
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1answer
118 views

Adjust p-value for multiple ANOVAs

There are similar questions to mine but either with no response or the setting is different. In short: I have conducted a study with 1 independent categorical variable, 5 dependent variables and 4 ...
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0answers
33 views

power analysis for difference of means — without examining distribution of difference of means

I am interested in calculating the power of studies to detect differences of means with a z- or a t-test -- and in doing so without directly examining the sampling distribution of the difference of ...
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1answer
51 views

standard name for area under type 1 vs type 2 error curve?

we already have precision-recall, and roc curves, why aren't type 1-type 2 error curves more popular? Is there a standard name for the area under such plots?
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1answer
309 views

Should bootstrapping and collecting sample means from a series of binomial distributions result in standard normal?

I’m trying to better understand several statistical concepts (bootstrapping, central limit theorem, and confidence intervals) by applying them to a binomial distribution (you can think of it as a coin ...
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2answers
134 views

Is it possible to simultaneously call multiple regression coefficients significant?

Okay, this is a thought experiment: Suppose you have a dataset with 40 covariates. Suppose the data has every nice theoretical property you could want: randomly sampled, variables not correlated, etc....
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1answer
93 views

“Optional stopping” to *reduce* type-I-error

I ran an experiment to test for some effects (which I indeed see evidence for), but in the analysis, also found a surprising effect that I could find no theoretical justification for. Specifically, ...
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2answers
218 views

Is it possible to find out the probability of a type 2 error in 2 sample t test?

I was wondering if it's possible to see what is the probability of getting a type 2 error in my investigation into whether there is a difference in length of time between cells in anaphase and ...
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0answers
126 views

Multilevel models and correcting for multiple comparisons

I am conducting a study where there are three different DVs. For each DV I will be conducting a multilevel model with 2 predictors and will be interested in both main effects and interactions between ...
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0answers
32 views

Interim analysis and alpha spending in group sequence design of clinical trials

In group sequential design, does the type of interim analysis affect the alpha spending for each look? I tested in ADDPLAN, with two interim analyses, specifying "stopping for futility" or not does ...

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