# 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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2answers
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### 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!)
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, ...
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 ...
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. ...
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, ...
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). ...
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: $K = \{4X_1 − 2X_2 − 2X_3 + X_4 < −2\}$....
0answers
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 ...
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 ...
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 ...
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-...
0answers
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 ...
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 ...
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-...
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 ...
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, ...
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 ...
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 ...
0answers
6 views

1answer
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### 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 ...
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,...
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 ...
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 ...
0answers
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!
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 ...
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 $\beta$...
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, ...
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 ...
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 ...
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 ...
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 ...
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?
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 ...
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....
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, ...
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 ...
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 ...
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 ...