Reformers: Prionvac

Anything Tests Can do, CIs do Better; CIs Do Anything Better than Tests?* (reforming the reformers cont.)

*The title is to be sung to the tune of “Anything You Can Do I Can Do Better”  from one of my favorite plays, Annie Get Your Gun (‘you’ being replaced by ‘test’).

This post may be seen to continue the discussion in May 17 post on Reforming the Reformers.

Consider again our one-sided Normal test T+, with null H0: μ < μ0 vs μ >μ0  and  μ0 = 0,  α=.025, and σ = 1, but let n = 25. So M is statistically significant only if it exceeds .392. Suppose M just misses significance, say

Mo = .39.

The flip side of a fallacy of rejection (discussed before) is a fallacy of acceptance, or the fallacy of misinterpreting statistically insignificant results.  To avoid the age-old fallacy of taking a statistically insignificant result as evidence of zero (0) discrepancy from the null hypothesis μ =μ0, we wish to identify discrepancies that can and cannot be ruled out.  For our test T+, we reason from insignificant results to inferential claims of the form:

μ < μ0 + γ

Fisher continually emphasized that failure to reject was not evidence for the null.  Neyman, we saw, in chastising Carnap, argued for the following kind of power analysis:

Neymanian Power Analysis (Detectable Discrepancy Size DDS): If data x are not statistically significantly different from H0, and the power to detect discrepancy γ is high(low), then x constitutes good (poor) evidence that the actual effect is no greater than γ. (See 11/9/11 post)

By taking into account the actual x0, a more nuanced post-data reasoning may be obtained.

“In the Neyman-Pearson theory, sensitivity is assessed by means of the power—the probability of reaching a preset level of significance under the assumption that various alternative hypotheses are true. In the approach described here, sensitivity is assessed by means of the distribution of the random variable P, considered under the assumption of various alternatives. “ (Cox and Mayo 2010, p. 291):

Continue reading

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Part 3: Prionvac: How the Reformers Should Have done Their Job

Here’s how the Prionvac appraisal should have ended:

Prionvac: Our experiments yield a statistically significant increase in survival  among scrapie-infected mice who are given our new vaccine compared to infected mice who are treated with a placebo (p = .01). The data indicate H: an increased survival rate of 9 months, compared to untreated mice.

Reformer: You are exaggerating what your data show. In fact, there is a fairly high probability, more than .5, that your study would produce a p = .01 difference, even if the actual increased rate of survival were only 1 month! (That is, the power to reject the null and infer H: increase of 1 months, is more than .5.) Continue reading

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Part 2 Prionvac: The Will to Understand Power

As a Nietzschean, I am fond of the statistical notion of power; yet it is often misunderstood by critics of testing. Consider leaders of the reform movement in economics, Ziliac and McCloskey (Michigan, 2009).

In this post, I will adhere precisely to the text, and offer no new interpretation of tests. Type 1 and 2 errors and power are just formal notions with formal definitions.  But we need to get them right (especially if we are giving expert advice).  You can hate them; just define them correctly please.  They write: Continue reading

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Part 1: Imaginary scientist at an imaginary company, Prionvac, and an imaginary Reformer

Prionvac: Our experiments yield a statistically significant increase in survival among scrapie-infected mice who are given our new vaccine (p = .01) compared to infected mice who are treated with a placebo. The data indicate H: an increased survival time of 9 months, compared to untreated mice.* Continue reading

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KURU

I have been reading about a disorder that intrigues me, Kuru (which means “shaking”) widespread among the Fore people of New Guinea in the 1960s. In around 3-6 months, Kuru victims go from having difficulty walking, to outbursts of laughter, to inability to swallow and death. Kuru, and (what we now know to be) related diseases, e.g., Mad Cow, Crutzfield Jacobs, scrapie) are “spongiform” diseases, causing brains to appear spongy. (They are also called TSEs: transmissible spongiform encephalopathies). Kuru clustered in families, in particular among Fore women and their children, or elderly parents. Continue reading

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