Posts Tagged With: reformers

WHIPPING BOYS AND WITCH HUNTERS

This, from 2 years ago, “fits” at least as well today…HAPPY HALLOWEEN! Memory Lane

In an earlier post I alleged that frequentist hypotheses tests often serve as whipping boys, by which I meant “scapegoats”, for the well-known misuses, abuses, and flagrant misinterpretations of tests (both simple Fisherian significance tests and Neyman-Pearson tests, although in different ways).  Checking the history of this term however, there is a certain disanalogy with at least the original meaning of a of “whipping boy,” namely, an innocent boy who was punished when a medieval prince misbehaved and was in need of discipline.   It was thought that seeing an innocent companion, often a friend, beaten for his own transgressions would supply an effective way to ensure the prince would not repeat the same mistake. But significance tests floggings, rather than a tool for a humbled self-improvement and commitment to avoiding flagrant rule violations, has tended instead to yield declarations that it is the rules that are invalid! The violators are excused as not being able to help it! The situation is more akin to that of witch hunting, that in some places became an occupation in its own right.

Now some early literature, e.g., Morrison and Henkel’s Significance Test Controversy (1962), performed an important service over fifty years ago.  They alerted social scientists to the fallacies of significance tests: misidentifying a statistically significant difference with one of substantive importance, interpreting insignificant results as evidence for the null hypothesis–especially problematic with insensitive tests, and the like. Chastising social scientists for applying significance tests in slavish and unthinking ways, contributors call attention to a cluster of pitfalls and fallacies of testing. Continue reading

Categories: significance tests, Statistics | Tags: , , | 3 Comments

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

Having reblogged the 5/17/12 post on “reforming the reformers” yesterday, I thought I should reblog its follow-up: 6/2/12.

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 (the sample mean) 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 < 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):

This may be captured in :

FEV(ii): A moderate p-value is evidence of the absence of a discrepancy d from Ho only if there is a high probability the test would have given a worse fit with H0 (i.e., a smaller p value) were a discrepancy d to exist. (Mayo and Cox 2005, 2010, 256).

This is equivalently captured in the Rule of Acceptance (Mayo (EGEK) 1996, and in the severity interpretation for acceptance, SIA, Mayo and Spanos (2006, p. 337):

SIA: (a): If there is a very high probability that [the observed difference] would have been larger than it is, were μ > μ1, then μ < μ1 passes the test with high severity,…

But even taking tests and CIs just as we find them, we see that CIs do not avoid the fallacy of acceptance: they do not block erroneous construals of negative results adequately. Continue reading

Categories: CIs and tests, Error Statistics, reformers, Statistics | Tags: , , , , , , , | Leave a comment

Do CIs Avoid Fallacies of Tests? Reforming the Reformers (Reblog 5/17/12)

The one method that enjoys the approbation of the New Reformers is that of confidence intervals. The general recommended interpretation is essentially this:

For a reasonably high choice of confidence level, say .95 or .99, values of µ within the observed interval are plausible, those outside implausible.

Geoff Cumming, a leading statistical reformer in psychology, has long been pressing for ousting significance tests (or NHST[1]) in favor of CIs. The level of confidence “specifies how confident we can be that our CI includes the population parameter m (Cumming 2012, p.69). He recommends prespecified confidence levels .9, .95 or .99:

“We can say we’re 95% confident our one-sided interval includes the true value. We can say the lower limit (LL) of the one-sided CI…is a likely lower bound for the true value, meaning that for 5% of replications the LL will exceed the true value. “ (Cumming 2012, p. 112)[2]

For simplicity, I will use the 2-standard deviation cut-off corresponding to the one-sided confidence level of ~.98.

However, there is a duality between tests and intervals (the intervals containing the parameter values not rejected at the corresponding level with the given data).[3]

“One-sided CIs are analogous to one-tailed tests but, as usual, the estimation approach is better.”

Is it?   Consider a one-sided test of the mean of a Normal distribution with n iid samples, and known standard deviation σ, call it test T+.

H0: µ ≤  0 against H1: µ >  0 , and let σ= 1.

Test T+ at significance level .02 is analogous to forming the one-sided (lower) 98% confidence interval:

µ > M – 2(1/ √n ).

where M, following Cumming, is the sample mean (thereby avoiding those x-bars). M – 2(1/ √n ) is the lower limit (LL) of a 98% CI.

Central problems with significance tests (whether of the N-P or Fisherian variety) include:

(1) results are too dichotomous (e.g., significant at a pre-set level or not);

(2) two equally statistically significant results but from tests with different sample sizes are reported in the same way  (whereas the larger the sample size the smaller the discrepancy the test is able to detect);

(3) significance levels (even observed p-values) fail to indicate the extent of the effect or discrepancy (in the case of test T+ , in the positive direction).

We would like to know for what values of δ it is warranted to infer  µ > µ0 + δ. Continue reading

Categories: confidence intervals and tests, reformers, Statistics | Tags: , , , | 7 Comments

Saturday Night Brainstorming and Task Forces: (2013) TFSI on NHST

img_0737Saturday Night Brainstorming: The TFSI on NHST–reblogging with a 2013 update

Each year leaders of the movement to reform statistical methodology in psychology, social science and other areas of applied statistics get together around this time for a brainstorming session. They review the latest from the Task Force on Statistical Inference (TFSI), propose new regulations they would like the APA publication manual to adopt, and strategize about how to institutionalize improvements to statistical methodology. 

While frustrated that the TFSI has still not banned null hypothesis significance testing (NHST), since attempts going back to at least 1996, the reformers have created, and very successfully published in, new meta-level research paradigms designed expressly to study (statistically!) a central question: have the carrots and sticks of reward and punishment been successful in decreasing the use of NHST, and promoting instead use of confidence intervals, power calculations, and meta-analysis of effect sizes? Or not?  

This year there are a couple of new members who are pitching in to contribute what they hope are novel ideas for reforming statistical practice. Since it’s Saturday night, let’s listen in on part of an (imaginary) brainstorming session of the New Reformers. This is a 2013 update of an earlier blogpost. Continue reading

Categories: Comedy, reformers, statistical tests, Statistics | Tags: , , , , , , | 8 Comments

G. Cumming Response: The New Statistics

Prof. Geoff Cumming [i] has taken up my invite to respond to “Do CIs Avoid Fallacies of Tests? Reforming the Reformers” (May 17th), reposted today as well. (I extend the same invite to anyone I comment on, whether it be in the form of a comment or full post).   He reviews some of the complaints against p-values and significance tests, but he has not here responded to the particular challenge I raise: to show how his appeals to CIs avoid the fallacies and weakness of significance tests. The May 17 post focuses on the fallacy of rejection; the one from June 2, on the fallacy of acceptance. In each case, one needs to supplement his CIs with something along the lines of the testing scrutiny offered by SEV. At the same time, a SEV assessment avoids the much-lampooned uses of p-values–or so I have argued. He does allude to a subsequent post, so perhaps he will address these issues there.

The New Statistics

PROFESSOR GEOFF CUMMING [ii] (submitted June 13, 2012)

I’m new to this blog—what a trove of riches! I’m prompted to respond by Deborah Mayo’s typically insightful post of 17 May 2012, in which she discussed one-sided tests and referred to my discussion of one-sided CIs (Cumming, 2012, pp 109-113). A central issue is:

Cumming (quoted by Mayo): as usual, the estimation approach is better

Mayo: Is it?

Lots to discuss there. In this first post I’ll outline the big picture as I see it.

‘The New Statistics’ refers to effect sizes, confidence intervals, and meta-analysis, which, of course, are not themselves new. But using them, and relying on them as the basis for interpretation, would be new for most researchers in a wide range of disciplines—that for decades have relied on null hypothesis significance testing (NHST). My basic argument for the new statistics rather than NHST is summarised in a brief magazine article (http://tiny.cc/GeoffConversation) and radio talk (http://tiny.cc/geofftalk). The website www.thenewstatistics.com has information about the book (Cumming, 2012) and ESCI software, which is a free download.

Continue reading

Categories: Statistics | Tags: , , , , , , , | 5 Comments

Repost (5/17/12): Do CIs Avoid Fallacies of Tests? Reforming the Reformers

The one method that enjoys the approbation of the New Reformers is that of confidence intervals (See May 12, 2012, and links). The general recommended interpretation is essentially this:

For a reasonably high choice of confidence level, say .95 or .99, values of µ within the observed interval are plausible, those outside implausible.

Geoff Cumming, a leading statistical reformer in psychology, has long been pressing for ousting significance tests (or NHST[1]) in favor of CIs. The level of confidence “specifies how confident we can be that our CI includes the population parameter m (Cumming 2012, p.69). He recommends prespecified confidence levels .9, .95 or .99:

“We can say we’re 95% confident our one-sided interval includes the true value. We can say the lower limit (LL) of the one-sided CI…is a likely lower bound for the true value, meaning that for 5% of replications the LL will exceed the true value. “ (Cumming 2012, p. 112)[2]

For simplicity, I will use the 2-standard deviation cut-off corresponding to the one-sided confidence level of ~.98.

However, there is a duality between tests and intervals (the intervals containing the parameter values not rejected at the corresponding level with the given data).[3]

“One-sided CIs are analogous to one-tailed tests but, as usual, the estimation approach is better.”

Is it?   Consider a one-sided test of the mean of a Normal distribution with n iid samples, and known standard deviation σ, call it test T+.

H0: µ ≤  0 against H1: µ >  0 , and let σ= 1.

Test T+ at significance level .02 is analogous to forming the one-sided (lower) 98% confidence interval:

µ > M – 2(1/ √n ).

where M, following Cumming, is the sample mean (thereby avoiding those x-bars). M – 2(1/ √n ) is the lower limit (LL) of a 98% CI.

Central problems with significance tests (whether of the N-P or Fisherian variety) include: Continue reading

Categories: Statistics | Tags: , , , | Leave a comment

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

Categories: Reformers: Prionvac, Statistics | Tags: , , , , , , , | 8 Comments

Do CIs Avoid Fallacies of Tests? Reforming the Reformers

The one method that enjoys the approbation of the New Reformers is that of confidence intervals (See May 12, 2012, and links). The general recommended interpretation is essentially this:

For a reasonably high choice of confidence level, say .95 or .99, values of µ within the observed interval are plausible, those outside implausible.

Geoff Cumming, a leading statistical reformer in psychology, has long been pressing for ousting significance tests (or NHST[1]) in favor of CIs. The level of confidence “specifies how confident we can be that our CI includes the population parameter m (Cumming 2012, p.69). He recommends prespecified confidence levels .9, .95 or .99:

“We can say we’re 95% confident our one-sided interval includes the true value. We can say the lower limit (LL) of the one-sided CI…is a likely lower bound for the true value, meaning that for 5% of replications the LL will exceed the true value. “ (Cumming 2012, p. 112)[2]

For simplicity, I will use the 2-standard deviation cut-off corresponding to the one-sided confidence level of ~.98.

However, there is a duality between tests and intervals (the intervals containing the parameter values not rejected at the corresponding level with the given data).[3]

“One-sided CIs are analogous to one-tailed tests but, as usual, the estimation approach is better.”

Is it?   Consider a one-sided test of the mean of a Normal distribution with n iid samples, and known standard deviation σ, call it test T+. Continue reading

Categories: Statistics | Tags: , , , , , , | 14 Comments

Saturday Night Brainstorming & Task Forces: The TFSI on NHST

Each year leaders of the movement to reform statistical methodology in psychology and related social sciences get together for a brainstorming session. They review the latest from the Task Force on Statistical Inference (TFSI), propose new regulations they would like the APA publication manual to adopt, and strategize about how to institutionalize improvements to statistical methodology. See my discussion of the New Reformers in the blogposts of Sept 26, Oct. 3 and 4, 2011[i]

While frustrated that the TFSI has still not banned null hypothesis significance testing (NHST), since attempts going back to at least 1996, the reformers have created, and very successfully published in, new meta-level research paradigms designed expressly to study (statistically!) a central question: have the carrots and sticks of reward and punishment been successful in decreasing the use of NHST, and promoting instead use of confidence intervals, power calculations, and meta-analysis of effect sizes? Or not?  

Since it’s Saturday night, let’s listen in on part of an (imaginary) brainstorming session of the New Reformers, somewhere near an airport in a major metropolitan area.[ii] Continue reading

Categories: Statistics | Tags: , , , , , , | 7 Comments

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

Categories: Reformers: Prionvac, Statistics | Tags: , , , | 3 Comments

WHIPPING BOYS AND WITCH HUNTERS

In an earlier post I alleged that frequentist hypotheses tests often serve as whipping boys, by which I meant “scapegoats”, for the well-known misuses, abuses, and flagrant misinterpretations of tests (both simple Fisherian significance tests and Neyman-Pearson tests, although in different ways).  Checking the history of this term however, there is a certain disanalogy with at least the original meaning of a of “whipping boy,” namely, an innocent boy who was punished when a medieval prince misbehaved and was in need of discipline.   It was thought that seeing an innocent companion, often a friend, beaten for his own transgressions would supply an effective way to ensure the prince would not repeat the same mistake. But significance tests floggings, rather than a tool for a humbled self-improvement and commitment to avoiding flagrant rule violations, has tended instead to yield declarations that it is the rules that are invalid! The violators are excused as not being able to help it! The situation is more akin to that of witch hunting, that in some places became an occupation in its own right. Continue reading

Categories: Statistics | Tags: , , | 8 Comments

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