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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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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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21 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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1answer
18 views

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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410 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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1answer
95 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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10 views

Running a linear model on zero-inflated data — which type of error?

When I have a response variable made up of count data with lots of zeroes, I often run a negative binomial GLM to test hypotheses. An example: if I counted butterfly eggs on 100 plants, most plants ...
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20 views

How can we predict reliability for type 1 censored data?

I am working on a somewhat challenging problem. I have data for a large set of equipment. My main research question is: How many units will fail in each future month in the coming decade? So far I ...
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14 views

How to Control the Type-1 Error Rate for T-Tests Used to Understand Sig. Interaction Effects

Basically, I ran a repeated measures ANOVA between groups R and D with one within-subjects factor with 2 levels. A significant interaction was found. To understand what was driving the interaction I ...
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1answer
36 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
34 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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15 views

Familywise error rate for multiple comparisons across multiple independent variables?

Is the familywise error rate of 1-(1-alpha)^k, where k is the number of tests performed still valid if not all comparisons are made using the same independent variable? Say, I have 3 categorical ...
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2answers
970 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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23 views

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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1answer
903 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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1answer
38 views

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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0answers
28 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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46 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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1answer
34 views

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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1answer
24 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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21 views

How to Work out Type 1 Error in Probability Distribution?

For (a), my answer is 'accept H0 if the sample mean = 0, otherwise reject'. Can anyone help me understand how to answer question (b)? I know that the P(Type 1 Error) = the significance level, but I'm ...
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1answer
43 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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12 views

Error correction within factorial GLMMs

Below is toy-data and analysis for a bog-standard factorial longitudinal GLMM ...
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0answers
77 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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75 views

Type I error rate simulations and p-value

In the simulation below with two random Poisson numbers with lambda = 42, the simulated type I error rate is around 4%, but the experimenter has chosen alpha = 0.05 as the true expected value. Does it ...
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4answers
202 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
2k 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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2answers
436 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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55 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
85 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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27 views

Is t-test the right test to use in this case?

I have two batches of 10 samples each of nominally the same component, each batch made via a different manufacturing technique ("old technique" and "new technique", where the new technique is cheaper ...
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0answers
25 views

How do I compare models with different scope?

I'm looking for any research papers in the Statistics literature or any information, in general, about comparing the performance of two different models when one of them imposes more severe ...
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1answer
337 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
344 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
262 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 ...
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27 views

Working on the topic of significance testing

I have a question as follows: Assuming the null hypothesis is true for all cases. If we perform multiple pairwise comparisons at the $\alpha = 0.05$ level, what is the probability of making type I ...
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1answer
19 views

Lower chance of type I error for A>B>C than for A>B?

Say I want to test the effect of two levels of my independent variable (IV) on some dependent variable (DV). For instance, administering a drug in a small vs large dosage, and then measuring reaction ...
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4k views

Why does collecting data until obtaining a significant result increase the Type I error rate?

I was wondering exactly why collecting data until a significant result (e.g., $p \lt .05$) is obtained (i.e., p-hacking) increases the Type I error rate? I would also highly appreciate an ...
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2answers
40 views

Type I/II error

In my analyses I had a clear hypothesis about a relationship Y ~ X1. In order to show that this is specific, I ran a control analyses with Y ~ X2. I showed that the relationship with X1 was ...
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331 views

“Inflated” type I error rate for correlation test when a variable has repeated values

For a given variable Y, if we independently generate a random variable X and test the correlation between Y and X, we know that the histogram of the p-values of the correlation test should show a ...
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37 views

Finding β for binomial experiment

$X\sim \text{Binomial}(5,P)$ Rejection region $X ≤1$ $H_\text{null}: P=0.6$ $H_\text{alt}: P<0.6$ Find $β$ at $P= 0.3$ I understand that ($β$ = not in the rejection region/H alt....
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0answers
51 views

How to determine the optimal ratio of a type I and type II error in a given business context? [closed]

Let us assume I have developed two designs (A, B) of a product and I want to see which one performs better in terms of sales. So I run an experiment where some customers can buy A whilst others can ...
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1answer
36 views

Using Benjamini and Hochberg's false discovery rate with one independent factor and multiple outcome variables

In a study where I compare the male vs. female university students (independent variable = gender) on 20 different outcomes (each referring to a wellbeing measure), can I apply a false discovery rate (...
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1answer
78 views

Calculate power of t test?

I was wondering how you would calculate the power of a one sided and two sided t test and whether it differed from the z test. I know for a z test it is $p(z < z_{alpha} - abs(u_{a} - u_0)/(s/sqrt(...
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0answers
44 views

Bayes Factor for model and variable selection and type I & II error rate

I am trying to implement Bayes Factor for model and variable selection in Bayesian Linear Regression and finding out corresponding type I and type II error. I need your help regarding this. I will be ...
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62 views

Can type 1 error give lower bound on power of test, if null-hypothesis is false

So basically I have the following scenario: I have developed a new way for conditional independence testing, and am bench-marking is against other methods. To do this, I test the power in scenarios, ...
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0answers
41 views

How to explain the difference in significance level and type I error in permutation test of Pearson correlation on non-normal bivariate data

Let $x,y$ be sampled from a bivariate distribution $\mathcal{D}$ with zero covariance / no correlation. Let $r(x,y)$ be the Pearson correlation between $x$ and $y$. Let $H_0$ be that there is no ...
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1answer
85 views

How to report findings to show lack of correlation?

I am looking at the relationship between two variables. Contrary to custom my given h0 is "there is a significant correlation" and my h1 is "there is no significant correlation". I calculated a ...
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1answer
67 views

Testing when the Null Hypothesis is that the distributions do differ. Application in the case of Kolmogorov-Smirnov test

My area of interest is Classification (Machine Learning). A Classifier will typically output a conditional probability distribution (P(Y=1|X) ) and the question may arise whether this predicted PDF ...
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1answer
163 views

Are type I error & FWER both conditional probabilities?

According to my textbook, type I error is defined as the conditional probability of rejecting $H_0$ given $H_0$ is correct. On the other hand, when I study the FWER (although the definition is related ...