# Scratch Work for a SEV Homework Problem

Someone wrote to me asking to see the scratch work for the SEV calculations.  (See June 14 post, also LSE problem set.)  I’ll just do the second one:

What is the Severity with which (μ<3.29) passes the test T+ in the case where  σx = 2?  We have that the observed sample mean M is 1.4, so

SEV (μ < 3.29) = P( test T+ yields a result that fits the 0 null less well than the one you got (in the direction of the alternative); computed assuming μ as large as 3.29)

SEV(μ < 3.29) = P(M >1.4; μ >3.29) > P(Z > (1.4 -3.29)/2)) * = P(Z > -1.89/2) = P(Z > -.945 ) ~ .83

*We calculate this at the point μ = 3.29, since the SEV would be larger for greater values of μ.

That’s quite a difference from the power calculation of .5, calculated in the usual way of a discrepancy detect size (DDS) analysis.

QUESTIONS?

NEW PROBLEM: You want to make an inference that passes with high SEV, say you want  SEV(μ < μ’) = .99, with the same (statistically insignificant) outcome you got from the second case of test T+ as before (σx = 2).  What value for μ’ can you infer μ < μ’ with a SEV of .99?

Categories: Statistics |

### 5 thoughts on “Scratch Work for a SEV Homework Problem”

1. john byrd

I get that for M=1.4, and STD=2, you will have SEV=>0.99 obtained with an outcome of 6.06.

• Yes! You add 2.33 standard deviations to the outcome, 1.4. I’m glad someone is doing it. Thanks.

2. Corey

6

• Corey

Oh, someone already got it.

• Thanks Corey, and thanks for being the only one to offer the answer to my query about non-professional activities people engage in. Traveling back to the US today. Maybe you’d look at the Severity Evaluation Program on the right hand column. It’s limited, but I need to write the instructions for its use.