The Stack Overflow podcast is back! Listen to an interview with our new CEO.

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.

Filter by
Sorted by
Tagged with
1
vote
0answers
8 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 ...
-1
votes
1answer
27 views

Alpha and Hypothesis Testing [closed]

(The type I error, alpha) Which one of the statements about the alpha level is correct? a) The alpha level is the predefined probability of making a mistake when the null hypothesis is false. b) The ...
-1
votes
1answer
25 views

What is the difference between type I error and type II error in default or non-default case?

What is the difference between type I error and type II error in forecasting default of a company? For example, I can set null hypothesis to be "The company will default next year", or I can set it to ...
2
votes
1answer
58 views

P-values in multiple comparison t-test

I'm a biologist trying to teach my college class about the issue of multiple comparisons with t-tests. I've explained that the alpha value must be "combined" so to speak from each of the related ...
0
votes
0answers
12 views

Deriving the experiment-wise error rate of testing all hypotheses at the same time

$\textbf{Q}$: Suppose that we are conducting the tests on the hypotheses $H_i , i = 1, \dots ,k$. For each hypothesis, a test statistic $T_i$ is formed, where each $T_i, i = 1, \dots , k$ are ...
0
votes
0answers
26 views

Nonlinear Wald Test

Say we have a bivariate distribution $~~~~~f(x,y|\theta=\{a,b,t,c\}).$ An event of interest is when ab=c, that is, $~~~~~H_0: g(\theta)=c-ab=0$ versus $H_1: g(\theta)=c-ab \neq 0.$ I attempt to ...
4
votes
1answer
79 views

In what sense does interim monitoring of clinical trials “cost” a Bayesian?

I have read (and will seek a specific reference on the subject) that unlike Frequentist trials, Bayesians can continually monitor data as it accrues. A Frequentist tries to control, and thus ...
5
votes
1answer
124 views

Family-wise Type I error OLS regression

Why is it advised to control the Type I error rate (e.g. Turkey's HSD) when conducting several pairwise comparisons, but not when assessing the significance of several coefficient estimates when ...
2
votes
1answer
43 views

What is allowable deviation from desired significance/coverage?

Consider performing a statistical hypothesis test and wants to achieve significance $\alpha$. What is a good rule of thumb for an allowable deviation from the desired confidence level? Say I want to ...
1
vote
2answers
99 views

Why must a null hypothesis contain equality?

Using the inference of mean as an example, the null and alternative hypothesis could be $$H_0: \mu \le 0 \Leftrightarrow H_1: \mu > 0$$ It is often argued that this makes the calculation of the $...
1
vote
1answer
51 views

Using the $Z$-test instead of the binomial test for small $n$ - effect on power and Type I error

Setup Let $M \sim \text{Bin}(p,n)$. Let us then state the following two hypotheses: $$\begin{align} H_0: p = 0.5 \text{ vs } H_1: p > 0.5 \end{align}$$ To test these hypotheses, I could use the ...
0
votes
0answers
8 views

RNA-seq: probabiliy of at least one type I error

I need to find a mathematical expression for the probability of finding at leat one type I error. I know that in general that probabilty is: P=1-(1-a)^m. With a being the probabily of making a type I ...
1
vote
1answer
58 views

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 ...
1
vote
1answer
26 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 ...
0
votes
0answers
18 views

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 $m$ ...
0
votes
1answer
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 ...
0
votes
1answer
10 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 ...
1
vote
1answer
40 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 ...
0
votes
0answers
34 views

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 ...
1
vote
0answers
21 views

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 ...
1
vote
2answers
94 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 ...
0
votes
0answers
100 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 ...
0
votes
0answers
25 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 ...
1
vote
0answers
25 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 ...
0
votes
0answers
72 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 ...
0
votes
0answers
38 views

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 ...
0
votes
1answer
36 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 ...
0
votes
0answers
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) ...
0
votes
1answer
39 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 ...
1
vote
0answers
34 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 ...
0
votes
1answer
192 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 ...
1
vote
0answers
54 views

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 ...
2
votes
1answer
115 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-...
0
votes
0answers
12 views

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 ...
0
votes
1answer
44 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?
0
votes
0answers
33 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 ...
0
votes
1answer
97 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 ...
0
votes
0answers
103 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 ...
0
votes
1answer
25 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, ...
3
votes
3answers
1k 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 ...
3
votes
3answers
376 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 ...
3
votes
1answer
69 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 ...
2
votes
1answer
94 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 ...
10
votes
2answers
2k 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?
0
votes
2answers
27 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 ...
21
votes
1answer
1k 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?
0
votes
1answer
62 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 ...
0
votes
0answers
81 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 ...
0
votes
0answers
89 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 ...
2
votes
1answer
45 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 ...