Finding the beta risk from the alpha risk

  • Context: Graduate 
  • Thread starter Thread starter DivGradCurl
  • Start date Start date
  • Tags Tags
    Alpha Beta
Click For Summary

Discussion Overview

The discussion revolves around the procedure for calculating beta risk (Type II error) after conducting a hypothesis test with a known alpha risk (Type I error). The context includes statistical analysis using a t-test and considerations regarding the assumption of equal variances.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant seeks guidance on how to calculate beta risk after obtaining an alpha value and performing a t-test, noting the importance of understanding the implications of assuming equal variances.
  • Another participant suggests that knowing the critical value and distribution parameters (mean and variance) should allow for the calculation of both alpha and beta risks, asking for clarification on the specifics of the situation.
  • A participant clarifies that the inquiry is not related to homework but rather a practical application using a computer program, emphasizing the need for a mathematical explanation for the beta calculation.
  • One response indicates that knowing the critical value (zc) allows for determining the tail probability of the alternative distribution to find beta risk.
  • Another participant elaborates that the alternative distribution's parameters can be derived from the known means and variances, reinforcing the assumption of equal variances for both distributions.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the calculation of beta risk, with some providing methods while others seek clarification. No consensus is reached on a definitive procedure for calculating beta risk in this context.

Contextual Notes

The discussion highlights the dependence on the assumptions of equal variances and the specific parameters of the distributions involved, which remain unresolved in terms of their implications for the calculations.

DivGradCurl
Messages
364
Reaction score
0
Hello,
I would like to know the procedure in order to find the beta risk once the hypothesis test has been made.

I am aware of the fact that it is efficient to set both alpha and beta prior to data collection, but, in this case, I was given the observations and an alpha value. I used the t-test to compare the means, and one of the requirements is to test the hypothesis that the variances are the same. From the information that I have, the p-values and F-values do not allow the rejection of the null, which makes it possible to pool the variances and calculate the t-statistic for the first hypothesis. I understand how the alpha and beta risks are pictorially represented and what they mean, but unfortunately I don't see how to get this.

The answer to this question would be useful; it would be possible to state the risk of having assumed equal variances.

Any help is highly appreciated.
 
Physics news on Phys.org
If you have a critical value and a distribution (i.e. a mean and a variance) then you should be able to calculate both the "alpha" and the "beta" -- by which I am assuming you mean Type I and Type II errors. Can you explain a little?

Is this homework?
 
No. This is not homework. I'm using a computer program to analyze data. Just an alpha value (5%) was provided along with it. I am trying to find the procedure used to calculate the correspondent beta. Yes, alpha and beta stand for Type I and II errors, respectively. I can't just pick a value and say it is true. There must be some mathematical explanation (since the value was not predetermined).

Does this answer your question?
 
Since you know alpha, you know the critical value: given the location (mean) and the spread (variance) of the distribution, the "z" value that equates the tail probability to your alpha value is the critical value zc.
 
Since you know zc, all you have to do is to look at the other (alternative) distribution and calculate its tail probability, which would be the beta.

The other distribution is determined by the other (alternative) mean and the variance (since variances tested identical, you can assume the same variance for both distributions).
 

Similar threads

High School Statistical Errors, Type I and Type II
  • · Replies 43 ·
2
Replies
43
Views
6K
Undergrad Desirable estimator properties...
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad How far and how close to p=0.05 for statistical significance?
  • · Replies 24 ·
Replies
24
Views
7K
High School How Can We Compare Two Means to Test the Effectiveness of Diet A on Weight Loss?
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad Proper understanding of p-value
  • · Replies 5 ·
Replies
5
Views
2K
MHB Confidence Interval for Child's Weight Based on Television Watching
  • · Replies 26 ·
Replies
26
Views
3K
Graduate Beta Decay, why did they have to resort to Neutrinos?
  • · Replies 32 ·
2
Replies
32
Views
5K
MHB Performance of students - Hypothesis testing
  • · Replies 20 ·
Replies
20
Views
4K
Undergrad Type 1 Error Increases with Sample Size?
  • · Replies 9 ·
Replies
9
Views
4K
High School Rejection region of hypothesis testing
  • · Replies 6 ·
Replies
6
Views
2K