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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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Power of a Poisson hypothesis test

A textbook of mine has online worked solutions, and the answer in the back of the book does not match the answer in the online solutions - they're not even close. My book says that the power of a ...
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23 views

Does a more powerful test mechanically lead to more type III errors then?

"Type III error occurs when you correctly conclude that the two groups are statistically different, but you are wrong about the direction of the difference. Say that a treatment increases some ...
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Uncertainty in Fit Parameters from R^2 and/or Independent Variable Uncertainties

Suppose that I am using a least-squares method to fit experimental data $(x,y)$ to the equation $$y = m x + b.$$ In order to determine $\sigma_m$ and $\sigma_b$, the uncertainty in the parameters $m$ ...
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27 views

Calculating type two error without std dev

I have this problem I’m working through that requires me to calculate the type two error but doesn’t supply the std Dev or any way to calculate it. A preschool teacher wants to test to see if more ...
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8 views

Tukey Kramer and the reduction of type one error

I hope everyone is doing well. I understand that the Tukey Kramer reduces the chance of getting a type 1 error by using a pooled variance. That pooled variance then gives you a lower standard error ...
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38 views

Is a Type III statistical error just a subset of Type I or II error?

I have recently come across the idea of a type III error through discussion with colleagues. The definition they gave me was something along these lines: "Type III error occurs when you correctly ...
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increasing accuracy of binary logistic regression by reducing type II error?

I am to use binary logistic regression predict a deadly disease from 109 cases out of 385 patients. If during the preliminary diagnosis all patients were sent to the expert doctor for secondary ...
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Multiple Testing - FWER

I am confused about Family Wise Error Rate(FWER) when dealing with multiple testing. What would change about the FWER in the case of positively correlated p-values. For example if I perform ...
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77 views

proof for the hypothesis testing $\alpha-\beta$ tradeoff

All the statistic's courses state that there is a tradeoff between the significance level ($\alpha$) and the probability of the Type II error ($\beta$). Specifically, for a fixed sample size, one ...
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64 views

Type 1 Error correction for multiple comparisons: ANOVA vs multiple regression

After looking into Type 1 error correction protocols for multiple comparisons in ANOVA vs. MR, I found two (conflicting?) messages. The same Type 1 Error corrections that apply to comparisons in ...
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21 views

Is it possible to experimentally reproduce the probability of type 1 errors in significance tests?

In some fields, a lot of sample studies feature statistical tests. Oftentimes, box plots of sample distributions are shown. I was wondering whether i could read distributional parameters from these ...
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24 views

Sample size formulae

In order to calculate sample size for hypothesis testing, we consider level of significance and power. For level of significance, two sided values ($Z_{\alpha/2}$) are taken into account, but for ...
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49 views

Can Bayes factors be an alternative to multiple comparisons corrections?

I am currently using p-values and Bayes factors to interpret my results. I have multiple comparisons so was going to perform a Bonferroni correction, however I am hesistant due to its highly ...
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Sensitivity and Specificity of gaussian and negative binomial glm family

I am dealing with count data that is over-dispersed and hence I consider using the negative binomial family (with glm()) instead of the gaussian family, as the link function. To find out the ...
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1answer
35 views

Type I error question

I have this question from a previous exam, since it didn't worth much points I suspect it should be something tricky. How to achieve a statistical test where the Type I error risk is $0$? Is it ...
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23 views

type 1 error for mean

I was trying to do an exercise that says to calculate the Type 1 error for the test function $\delta$ given by $$\delta(X_1,...,X_n) = 1 ~~~~~~~if~~~~~ |\overline{X}|\geq Q,~~~~~~~~\delta(X_1,...,X_n) ...
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36 views

How to measure risk of a Type 2 error in A/B tests

I'm conducting A/B tests where outcomes are binary (success or failure in control and experiment populations). The assessment of the risk of a Type 1 error is relatively straightforward: given an ...
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28 views

Finding the probability of a type II error for a poisson distribution

A poisson distribution is being tested with the hypothesis H0: λ = 1.7 and H1: λ ≠ 1.7 The true value of the mean is 2.3. For the significant level 10% calculate: a )The critical region b) The ...
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76 views

Finding the probability of a type II error for a binomial distribution

For a binomial distribution, the hypothesis $H_0: p = 0.2$ and $H_1: p\ne0.2$ are tested at the $10%$ level. $20$ trials are performed and the critical region is $X = 0$ or $X > 7$. Calculate the ...
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Replicating Dickey Fuller? How did they know something was wrong? [cross posted on QF] [closed]

I am interested in testing if there is size distortion through simulations. I have recently been interested in replicating Dickey and Fuller (1979) and this source from another post helped a lot, here ...
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64 views

Sample size calculation for Kendall's Tau in reproducibility study

Can anyone help with justifying (or rubbishing) a couple of aspects of a sample size calculation for a grant proposal. A pilot study gave significant results for the correlation of a continuous (non-...
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Type II error for share price event study - what is the difference between one and several securities?

I have a question regarding the type II error for a specific event study. It is a case study (i.e. one observation) with daily share prices. I want to test whether event day abnormal returns are ...
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1answer
37 views

Type-I and Type-II errors example explanation

In the following example, can someone help understand how the value for $k$ (highlighted in yellow) is derived below? How is $z_\alpha$ introduced in there?
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31 views

Find type II error for event study share returns

I need help with calculating the type II error for a specific event study. It is a case study (i.e. one observation) and I want to test whether event day abnormal returns are different from zero. I ...
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1answer
60 views

Type I and Type II errors in Hypothesis Testing

I am confused about the last highlighted sentence regarding finding a subset S, for which BOTH Type I and Type II error probabilities are 0. For $P_\theta S$, which is the probability with which we ...
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62 views

Empirical Type I error from simulation different from $\alpha$ and changes based on sample size $n$

I am simulating LRT based on Chi-squared random variables. I know that the asymptotic distribution of LRT statistic follows chi-squared distribution with $df=$difference of the degrees of freedom ...
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Probability of Type II error for simple hypothesis

I'm working through Intro to Probability and Statistics... and I'm a little confused about how to calculate the probability of a type II error, particularly as it relates to a simple hypothesis test, ...
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737 views

Is there a constraint on the sum of the type-I & type II error probabilities?

Is it true that if $H_0$ and $H_a$ are complementary hypotheses of the Binomial trial, i.e., the negation of $H_0$ is $H_a$ then the type-I error $\alpha$ plus type-II error $\beta$ equals 1? Or is ...
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264 views

Does multicollinearity cause type I errors?

Citing Wikipedia on multicollinearity, One of the features of multicollinearity is that the standard errors of the affected coefficients tend to be large. In that case, the test of the hypothesis ...
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48 views

Can I perform a Chi Square test comparing the one year mortality of my 160 patients versus the 108000 patients of a cohort in the litterature?

I have exactly zero experience with statistics. I was interested in comparing 1 year mortality of patients $\ge$ 60 years old versus $<$ 60 in a cohort after a specific intervention. I performed ...
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1answer
70 views

Type I and Type II errors when varying the number of treatments

I have a hypothetical sample of n observations, and I want to test if there are significant differences across multiple treatments. I need to know how the number of treatments interfere in the type I ...
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1k views

“Liberal” p-values?

My question is rather semantic. When a method routinely produces high p-values it is called conservative. Would you call the opposite, i.e. a method with a high type-II-error rate liberal?
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Minimize Type II errors in black-box testing

Okay so I have a function in the shape of a black box that I'd like to test. It's characteristics are: It gives either 0, 1 or -1 as output. I can query it easily, producing tens of thousands of ...
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966 views

Why the names Type 1, 2 error?

What is the motivation of introducing an additional level of indirection from the descriptive 'false positive' to the integer '1'? Is 'false positive' really too long?
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Calculate type 2 error using one data file

I am a bit confused on how to calculate type 2 error to check whether the sample data I am using is sufficient. I have a data file that I have used to build a machine learning model. This data file ...
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60 views

How to get Type II error probability from G*Power

I realize that having standard error of the mean, critical value, sample mean values from a simple a priori power test in the G*Power free download, one could use NORM.DIST in Excel (Argh!) following ...
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65 views

What is the smallest value of r that gives a test of size not exceeding 0.05?

I've been given a question that I don't understand. Question: Consider a test which rejects $H_0$ if the number of observed successes is $≥ r$ , where $r$ is some number. What is the smallest value ...
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What if we use this kind of region of rejection?

I'm wondering how do we decide the "shape" of region of rejection in a hypothesis testing problem. Let's take a two-tailed z-test as an example. What if we choose the weird-looking region of rejection ...
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56 views

How to calculate % information in longitudinal group sequential design

I'm looking at using group sequential design for a study that will treat subjects with drug or placebo and then follow them for a year. The subjects get measured every 3 months for the year under ...
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65 views

why correct for multiple comparisons in a correlation table?

I often read that in a correlation matrix the p-values for all correlations in a NxN matrix should be adjusted for multiple comparisons (for example: Multiple comparisons for correlation matrix?). ...
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92 views

Bias-variance decomposition for a statistical test

A statistical estimator can be characterized – among others – by its bias and variance. These are different aspects, but if one is willing to accept a certain loss function (risk) than they can merged;...
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4answers
314 views

Known alpha and type I error rate simulation

I am not sure why running the following code in R does not result in a type I error rate of exactly 5% given alpha = 0.05 when set.seed is set to 1. Is there a reason why running the simulation below ...
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2answers
6k views

FPR (false positive rate) vs FDR (false discovery rate)

The following quote comes from the famous research paper Statistical significance for genome wide studies by Storey & Tibshirani (2003): For example, a false positive rate of 5% means that on ...
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In using backward elimination procedure how to control for type I error?

Use backward elimination procedure to decide which predictor variables can be dropped from the regression model. Control the type I error at = . 10 at each stage In using backward ...
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456 views

How to rigorously justify chosen false-positive/false-negative error rates and underlying cost ratio?

Context A group of social scientists and statisticians (Benjamin et al., 2017) have recently suggested that the typical false-positive rate ($\alpha$ = .05) used as a threshold for determining "...
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67 views

When can I use a permutation test to see if means of two distributions differ without Type I errors?

I am analyzing psych experiments which generally take the form of a list of outcome measures for the test and control groups, with roughly equal sample sizes, and I would like to compare their means ...
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1answer
113 views

Power function of a test,example

Consider a population with the pdf $N(\theta,1)$ where $\theta$ is unknown and hypothesis $H_0:\theta=5.5$ and $H_1:\theta=8$.Suppose that $\bar{X}=\frac{1}{9}\sum_{i=1}^9 X_i.$Reject $H_0$ iff $\bar{...
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438 views

Formulas to calculate power of a test. What am I doing wrong?

In Jay L. Devore 'Probability and Statistics for Engineering and the Sciences', he presents the following formula to retrieve β, when we consider a two-tailed test and the population mean is known. $\...
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2answers
508 views

Does Central Limit Theorem Apply to Bayesian inference?

In reading a Paper on Bayesian estimation, I came across a sentence that had me think: "Bayesian statistics is not based on large samples (i.e., the central limit theorem) and hence may produce ...
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3answers
386 views

Chi-squared test of independence: is a type II error by itself a bad thing?

Let us assume I sell a product that I have modified recently and I want to check if the old or the new version sells better. Therefore, I conduct an experiment in which a hundred people are offered ...