# Posts Tagged With: Geoff Cumming

## 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. Read more »

Categories: confidence intervals and tests, reformers, Statistics | | 7 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.

## 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: Read more »

## 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+. Read more »

Categories: Statistics | | 14 Comments