Resilience, a ratio and a mindset

You've probably met all three of these ideas: that resilience is a rare quality some people have and others can train; that you need about three positive emotions for every negative one; and that believing stress is bad for you is what makes it bad for you. Each has a real paper behind it, in a real journal. This lesson follows each one back to its source and asks what the source said, what the evidence looks like now, and what changed on the way. The skill you're after is finding the step where a popular claim about wellbeing stopped matching its evidence, without sneering at the people who made it or the people who believed it.

Three shapes, borrowed from Sleep

Sleep lesson 7 organised its cases, as a frame of its own and not a finding, by three ways a claim changes shape on its way into a popular paragraph.⁹ The attribution moves, so a statement lands on a more authoritative name than the one that made it. An association hardens, so "linked with" becomes "causes", and a specific scope becomes a general one. And a small group that runs against a trend drops out. This lesson widens the third a little, to any inconvenient part that drops out, and that widening is this course's.⁹

Lesson 5 of this course met the second: a paper's hedged comparison, "comparable to or slightly greater than", became a press release's "1.5 times more effective". Here you'll meet the second again, the third, and one case the frame doesn't fit, because the problem was in the original paper.

Keep lesson 2's question running alongside: what did the comparison group get? It matters most in the resilience and stress sections.

How common resilience is

Start with a question you can answer before reading any evidence.

The review's abstract names the four trajectories without defining them, so these glosses are this course's, from the names.¹⁹ Resilience is staying roughly steady. Recovery is a real drop in how well someone is doing, then a climb back. Chronic is a drop that stays. Delayed onset is doing fairly well at first and worse later.

This course's drawing of the four trajectories in the 2018 review's abstract, on one scale.¹⁹ Each bar is an average share and each thin line its 95% interval. They add to more than 100 percent, and the abstract doesn't say why. This course's reading is that each figure averages over a different set of cases, since not every case found all four: the abstract reports resilience in 63 of its 67 cases, drawn from 54 studies, and delayed onset in 22.

Two things keep this from being a cheerful statistic you can apply to yourself. The review reports that "Sources of heterogeneity in estimates primarily resulted from substantive population differences rather than bias, which was observed when prospective data is lacking."¹ So the share varies mainly with who went through what, and the estimates looked biased where studies lacked data gathered over time. And an average of two thirds leaves about one person in three on another course. On average, across studies, recovery is the second most common, which means doing badly for a while and then better. Anyone having a hard time, on any of these courses, can use lesson 1's routes to help, and nobody can tell which course they're on from a chart. This course would add, and it's the sentence to keep if you're reading this after a hard year, that being on one of them says nothing about anyone's character.⁹

Why it looked rare

Bonanno's 2004 paper, which this course read at abstract level like the review, says why the common view ran the other way: "Many people are exposed to loss or potentially traumatic events at some point in their lives, and yet they continue to have positive emotional experiences and show only minor and transient disruptions in their ability to function." Then the reason for the older view: "because much of psychology's knowledge about how adults cope with loss or trauma has come from individuals who sought treatment or exhibited great distress, loss and trauma theorists have often viewed this type of resilience as either rare or pathological."¹

That is a sampling story. If you learn about grief from the people who come to a clinic, you learn about the people for whom it went hardest, and the ones who carried on never walk through the door. Memory and Note-Taking both asked what a finding was measured on. Here, on Bonanno's account, the answer explains why theorists saw resilience as rare.

Whether it can be trained

The second half of the popular idea is that resilience is a skill a programme can build. The best review this course found is a Cochrane review by Kunzler and colleagues of training for healthcare professionals, which this course read at abstract level.² It defines its subject this way: "Resilience can be defined as the maintenance or quick recovery of mental health during or after periods of stressor exposure". Notice that "quick recovery" is folded in. Bonanno treats resilience as "a distinct trajectory from the process of recovery", so the base rate above and the training results below don't use the word in quite the same way.¹²

It included 44 randomised trials. The headline results, at the end of training: "very-low certainty evidence indicated that, compared to controls, healthcare professionals receiving resilience training may report higher levels of resilience (standardised mean difference (SMD) 0.45, 95% confidence interval (CI) 0.25 to 0.65; 12 studies, 690 participants), lower levels of depression (SMD -0.29, 95% CI -0.50 to -0.09; 14 studies, 788 participants), and lower levels of stress or stress perception (SMD -0.61, 95% CI -1.07 to -0.15; 17 studies, 997 participants)." And on the rest: "There was little or no evidence of any effect of resilience training on anxiety (SMD -0.06, 95% CI -0.35 to 0.23; 5 studies, 231 participants; very-low certainty evidence) or well-being or quality of life (SMD 0.14, 95% CI -0.01 to 0.30; 13 studies, 1494 participants; very-low certainty evidence). Effect sizes were small except for resilience and stress reduction (moderate)."²

Then the limits, in the authors' words: "The paucity of medium- or long-term data, heterogeneous interventions and restricted geographical distribution limit the generalisability of our results." And their conclusion: "The findings suggest positive effects of resilience training for healthcare professionals, but the evidence is very uncertain."²

Read that fairly in both directions. It isn't evidence that resilience training fails. On resilience, depression and stress the effects point the right way at the end of training, in nurses, doctors and hospital staff, and the authors call them positive; on anxiety and well-being the review found little or no evidence of any effect. Nor is it evidence that a programme will build something lasting in you, because the review cannot say what happened months later, or what happens outside a hospital.² Two further Cochrane reviews exist, on healthcare students and on military and emergency staff, and this course didn't open them.

So the claim "resilience is rare, and you can train it" goes wrong in two ways, in this course's sorting.⁹ The first inverts a base rate. The second turns a very uncertain, short-term finding in one occupational group into a promise to everyone, which is Sleep's second shape in its scope form.

Three to one

In 2005, Fredrickson and Losada published a paper in American Psychologist, whose abstract is what this course read. They built on Fredrickson's broaden-and-build theory of positive emotion and on Losada's mathematical model of team performance, and "the authors predict that a ratio of positive to negative affect at or above 2.9 will characterize individuals in flourishing mental health. Participants (N=188) completed an initial survey to identify flourishing mental health and then provided daily reports of experienced positive and negative emotions over 28 days."³

The result and the claim built on it: "Results showed that the mean ratio of positive to negative affect was above 2.9 for individuals classified as flourishing and below that threshold for those not flourishing. Together with other evidence, these findings suggest that a set of general mathematical principles may describe the relations between positive affect and human flourishing."³ The critics who later examined the paper give the two group averages as 3.2 and 2.3, in a sample of college students.⁴

The examination

In 2013, American Psychologist published a critique by Brown, Sokal and Friedman. This course read its abstract and, in the authors' own preprint, the introduction's opening, the end of the section on how the number was derived, the sections on the empirical study and on an upper ratio, and the conclusion and concluding remarks. The preprint's wording may differ from the published version's.⁴

Their abstract: "We find no theoretical or empirical justification for the use of differential equations drawn from fluid dynamics, a subfield of physics, to describe changes in human emotions over time; furthermore, we demonstrate that the purported application of these equations contains numerous fundamental conceptual and mathematical errors." And the conclusion that matters here: "Fredrickson and Losada's claim to have demonstrated the existence of a critical minimum positivity ratio of 2.9013 is entirely unfounded."⁴

The part you can follow without the mathematics is where the number came from. The formula rested on three settings, and the preprint's point is that they could have been anything within wide limits: "Choose different values of the parameters σ, b, i and one gets a completely different prediction". Of the first setting it says: "Recall that Saltzman (1962) chose σ = 10 for illustrative purposes and purely for convenience; then Lorenz (1963) and Losada (1999) followed him." Change only σ, from 10 to 16, and leave the other two where they were, and the preprint reports that the same formula gives 4.1655405 instead of 2.9013.⁴ So the precise-looking figure rested on choices nobody had made for reasons to do with emotions.

On the empirical study: "there is nothing inherently implausible about the idea that people with a higher ratio of positive to negative emotions might experience better outcomes than those with a lower ratio. But the suggestion that people with a positivity ratio of 2.91 are in some discontinuous way significantly better off than those with a ratio of 2.90, simply because this number has crossed some magic line, is not supported by any evidence."⁴

They drew their own boundary, in the preprint's conclusion: "We do not here call into question the idea that positive emotions are more likely to build resilience than negative emotions, or that a higher positivity ratio is ordinarily more desirable than a lower one." They added: "We cannot, of course, prove that no such “tipping point” exists".⁴ Their concluding remarks are harsher than that boundary. They quote a sociologist's 1972 description of borrowing mathematics with no bearing on human behaviour, and say that "as applied to the articles of Losada (1999), Losada and Heaphy (2004), and Fredrickson and Losada (2005), Andreski’s portrayal is, alas, literally accurate." Only then do they say their concern was "with the objective properties of published texts, not the subjective states of mind of the authors".⁴

The reply

Fredrickson's response, in the same issue and read here at abstract level, describes the critique as one that "concluded that mathematical claims for a critical tipping point positivity ratio are unfounded".⁵ She sets out what she's arguing for: "In the present article, I draw recent empirical evidence together to support the continued value of computing and seeking to elevate positivity ratios. I also underscore the necessity of modeling nonlinear effects of positivity ratios and, more generally, the value of systems science approaches within affective science and positive psychology." And her position: "Even when scrubbed of Losada's now-questioned mathematical modeling, ample evidence continues to support the conclusion that, within bounds, higher positivity ratios are predictive of flourishing mental health and other beneficial outcomes."⁵

She calls the modelling "now-questioned" and no longer rests her case on it, while still arguing that nonlinear effects of positivity ratios need modelling. The claim she keeps is about direction, "higher positivity ratios", with a limit, "within bounds", and no tipping point in it.

The journal's correction

PubMed's entry for the 2005 paper lists an erratum, published in the 2013 issue, and no retraction.³ The notice itself is a correction. This course read it as Retraction Watch reprinted it in September 2013, because the journal's own page refused this course's request. It says that "the modeling element of this article is formally withdrawn as invalid and, along with it, the model-based predictions about the particular positivity ratios of 2.9 and 11.6." The 11.6 was an upper limit the paper also predicted. And it says: "Other elements of the article remain valid and are unaffected by this correction notice", naming among them "the finding that positivity ratios were significantly higher for individuals identified as flourishing relative to those identified as nonflourishing."³

This case does not fit Sleep's shapes, because the problem was in the paper, not a retelling. The shapes describe what can happen next. A version that still says "three to one" has dropped the examination and the correction, and one that says "positivity was debunked" has dropped the half both sides agree on. Both are the third shape in this lesson's wider sense, and in this course's reading both drops run toward a simpler story.⁹ And the ratio is one claim, not a field. This course hasn't read the wider research on positive emotion or on positive-psychology interventions, so nothing in this section is a verdict on either.

The belief that stress is bad for you

The stress case has a wrinkle. The experimental evidence is real, and small. The claim as it's usually repeated rests on something else.

Many people meet this idea through a TED talk and a book, The Upside of Stress, by McGonigal. This course hasn't read the book or watched the talk, so nothing in this section is a claim about them.¹⁰ What it has read is the study.

The survey

Keller and colleagues, in 2012, used a large American survey. This course read the abstract and, in the free full text, the results with Table 3, the sensitivity analysis and the discussion.⁶ The design: "Data from the 1998 National Health Interview Survey were linked to prospective National Death Index mortality data through 2006." People were asked how much stress they'd had in the past year and how much they thought it had affected their health, and deaths were counted over the following years. "33.7% of nearly 186 million (unweighted n = 28,753) U.S. adults perceived that stress affected their health a lot or to some extent."⁶

The headline result: "those who reported a lot of stress and that stress impacted their health a lot had a 43% increased risk of premature death (HR = 1.43, 95% CI [1.2, 1.7])."⁶ HR is a hazard ratio, which lesson 6 met. Here 1.43 means deaths ran at about 1.43 times the rate of people who reported almost no stress and hardly any effect of stress on their health, after the authors' adjustments, which their Table 3 lists and which include smoking, physical activity and a flag for chronic conditions.⁶

The full text gives the same result in absolute terms: "This represents an increase in the predicted cumulative hazard of death due to the stress interaction from 3.5% to 5.1% for those who reported a lot of stress in the past 12 months and the perception that stress affects health a lot compared to those who did not report either."⁶ At values this small, a cumulative hazard is roughly the predicted share who had died by the end of follow-up, so this is a rise of about 1.6 percentage points; the gloss and the subtraction are this course's.⁹ Lesson 2 showed why you want the absolute figure beside the relative one.

What the authors said it could not show

This is the part that matters most, and it's in the authors' own discussion. They estimated how many deaths a year the combination might account for, under a condition they stated: "If this were in fact a causal relationship, 20,231 deaths each year would be attributable to having a lot of stress and perceiving that stress affects health a lot."⁶ And straight after: "While this study is unable to establish a causal relationship, these results highlight the necessity for further research".

They named the most obvious alternative themselves: "In addition, reverse causality may partially explain the findings in this study. Adults who reported poor health may have been more likely to report that stress impacts their health simply due to their poor health status; moreover poor health status could also have influenced the amount of stress reported."⁶ The main model had already included a chronic-condition flag, "To account for the possibility that prior health status may have influenced individuals’ perceptions of how stress affected their health", and they add that "this measure may not have adequately captured prior health status."

Then, in a sensitivity analysis, they added how healthy people said they were. They describe it as having "mediated" the relationship: "the inclusion of self-reported health mediated the relationship between the stress interaction term and mortality such that the highest interaction category (reported experiencing a lot of stress and perceiving that stress impacts their health a lot) was attenuated from HR of 1.43 to HR of 1.18 and was of borderline significance (p=0.076)."⁶ Borderline means it no longer quite cleared the usual bar for being distinguishable from chance. In this course's reading, a drop like that fits reverse causality (poor health driving both the answers and the deaths) and mediation (stress acting through health) alike, and a survey of this design cannot tell them apart.⁹

To be fair to the headline writers, the abstract does say "impact" once, in its methods: the models were used "to determine the impact of perceiving that stress affects health on all-cause mortality." But its conclusion says the stress measures are "each associated with poor health and mental health", and the discussion says the study "is unable to establish a causal relationship".⁶

The experiments

The better test of whether a stress belief matters is to change the belief and see what happens. That has been done, and it's a different question with a different outcome.

Crum, Salovey and Achor, in 2013, read here at abstract level, showed first that the belief can be moved: "In Study 2, we demonstrate that stress mindsets can be altered by watching short, multimedia film clips presenting factual information biased toward defining the nature of stress in 1 of 2 ways". And then: "In Study 3, we demonstrate the effect of stress mindset on physiological and behavioral outcomes, showing that a stress-is-enhancing mindset is associated with moderate cortisol reactivity and high desire for feedback under stress."⁷ Cortisol is a stress hormone. Their conclusion: "Together, these 3 studies suggest that stress mindset is a distinct and meaningful variable in determining the stress response." The Study 3 sentence uses two verbs, "the effect of" and "is associated with", and the abstract does not say what was manipulated in that study, so this lesson does not rest a causal claim on it. That claim rests on the randomised trials next.

The fullest summary is a 2024 meta-analysis by Bosshard and Gomez of randomised trials, which this course read at the level of its abstract and its section on publication bias.⁷ It pooled two kinds of intervention, stress arousal reappraisal (SAR) and stress-is-enhancing (SIE) mindset training, the kind Crum tested. Both aim to change the stress response "by educating individuals about the functionality of stress". The outcome was performance on a task, either a public performance or a written cognitive one. Its effect size, d, is the same kind of number as lesson 2's g and lesson 3's SMD: a difference between group averages, in standard deviations.

"The results revealed an overall small significant improvement in task performance (d = 0.23, p < 0.001)." Then the authors checked for missing studies: "Smaller studies (i.e., higher SEs) had a disproportionate amount of effect sizes larger than the pooled effect size."⁷ SE is standard error, and a small study has a large one, meaning its estimate is less precise. If small studies with small effects went unpublished, the ones left would look like that.

The arms differed. The largest was reappraisal alone: "SAR-only interventions (k = 33, d = 0.22, p < 0.001)", where k is the number of effect sizes. The mindset idea alone was "SIE mindset-only interventions (k = 6, d = 0.18, p = 0.22)", which wasn't distinguishable from nothing, though this course's reading is that six effect sizes may simply be too few to tell a d of 0.18 from zero.⁷⁹ Interventions that added other content did best, at d = 0.45 on five.⁷

With lesson 2's table, and the bell-curve assumption it named, this course's arithmetic puts the average person who had the intervention ahead of about 59 percent of the comparison group at d = 0.23, and about 56 percent at d = 0.14, against 50 for no effect.⁹ The authors say plainly that these interventions aren't a cure-all, and then that they "offer a promising cost-effective low-threshold approach to improve performance across various domains."⁷ Cheap, easy to deliver, a small effect on performance.

Two findings, two outcomes

Now set the two pieces side by side, because this is the wrinkle. The survey is about death, followed through 2006, and it cannot separate belief from illness. The experiments are about performance on a task, and they can separate cause from association, because people were randomly assigned to an intervention meant to change the belief. In this course's reading of the two designs, neither can stand in for the other.⁹ An experiment on task performance, public or written, says nothing about lifespan, and a survey about deaths says nothing about what changing your belief would do.

Writing it down

One more method sits close to these. Frattaroli's 2006 meta-analysis, read here at abstract level, defines it as "Disclosing information, thoughts, and feelings about personal and meaningful topics (experimental disclosure)". It's most often done in writing, and most people know it as expressive writing, though that description is this course's gloss, not the review's.⁸⁹ The review pooled "One hundred forty-six randomized studies of experimental disclosure" and found that "experimental disclosure is effective, with a positive and significant average r-effect size of .075."⁸

For small r, d is about 2r, so that's roughly d = 0.15 by this course's arithmetic: small, at the low end of the effects this course has met, and pooled across outcomes the abstract does not name.⁸⁹ What 146 trials buy is confidence that a very small effect is not zero, not a bigger effect.

Six things people get wrong

"Resilient people are rare, and resilience is a skill you can train." Across 54 studies, about two in three people followed the resilient course after a potentially traumatic event. Training has been tested in healthcare workers, with effects on resilience, depression and stress at the end of training, none shown on anxiety or well-being, all on very-low-certainty evidence and with little data on what lasts.

"You need three positive emotions for every negative one." The tipping point of 2.9013 was shown to be unfounded, the journal's correction withdrew it with the modelling, and its first author now rests her case on evidence without that mathematics.

"The positivity research was debunked, so positive emotion doesn't matter." This is the same mistake the other way. The critics said they weren't questioning that a higher ratio is ordinarily better, Fredrickson still holds that claim within bounds, and the correction says the paper's finding of higher ratios in the flourishing group stands.

"The ratio paper was retracted." It was corrected. The notice formally withdraws the modelling and the predicted ratios and says the other elements remain valid, and PubMed indexes it as an erratum.

"Believing stress is harmful is what kills you." The source is a survey. Its authors say it cannot establish cause and name reverse causality, and the belief alone didn't independently predict death. The experiments that did change the belief measured task performance.

"The stress-mindset research found nothing." Reappraisal and mindset interventions improved task performance, by d = 0.23 overall and 0.14 after correction, and reappraisal alone was significant. The mindset-only arm wasn't, on six effect sizes. The finding is small and about performance, which isn't the same as nothing.

Practice

Connections

Back. Sleep lesson 7's shapes, lesson 2's comparison question and Sleep lesson 3's line between association and cause all did work here: the question found the waiting lists inside the resilience trials, and the line is the one the stress-mindset claim crossed.

Forward. Lesson 8 is the loudest dispute in this subject, over antidepressants, and it has a different structure from the ones here. In the ratio dispute, one claim fell and a weaker one was left. In lesson 8, the two sides agree on the number and disagree about what it means.

Go deeper

• Brown, Sokal and Friedman's preprint, 2013, free on arXiv. This course read the abstract and, in the preprint, the introduction's opening, the end of the derivation section, the two sections on the empirical study and the upper ratio, and the conclusion and concluding remarks. The conclusion is readable without any mathematics, and it's where the critics mark the limits of their own case.
• Keller and colleagues, 2012, free at PubMed Central. This course read the abstract, the results with Table 3, the sensitivity analysis and the discussion. Read the discussion's reverse-causality paragraph and then compare it with any retelling you meet.
• Bosshard and Gomez, 2024, free in Scientific Reports. Read here at the level of its abstract and its publication-bias section. It prints a headline effect and its corrected figure a few lines apart.
• Kunzler and colleagues, 2020, the Cochrane review of resilience training. Abstract only here. Cochrane publishes a plain-language summary, which this course didn't open.

Sources

1. I. R. Galatzer-Levy, S. H. Huang and G. A. Bonanno, "Trajectories of resilience and dysfunction following potential trauma", Clinical Psychology Review 63, 2018, doi 10.1016/j.cpr.2018.05.008; and G. A. Bonanno, "Loss, trauma, and human resilience", American Psychologist 59(1), 2004, doi 10.1037/0003-066X.59.1.20. Read: both abstracts. Supports: the four trajectories and their figures, the case counts, the population differences and the bias clause, Bonanno's account of the older view, and his distinction between resilience and recovery.
2. A. M. Kunzler and colleagues, "Psychological interventions to foster resilience in healthcare professionals", Cochrane Database of Systematic Reviews 2020, CD012527, doi 10.1002/14651858.CD012527.pub2. Read: the abstract. Supports: the definition, the trial count, the comparators, the risk of bias, every effect size, the size labels and the conclusions.
3. B. L. Fredrickson and M. F. Losada, "Positive affect and the complex dynamics of human flourishing", American Psychologist 60(7), 2005, doi 10.1037/0003-066X.60.7.678, PMC3126111. Read: the abstract; PubMed's record of the paper (PMID 16221001), which lists an erratum and no retraction; and the journal's correction notice as reprinted in full by Retraction Watch on 2013-09-19. The journal's own page for the notice was not opened.
4. N. J. L. Brown, A. D. Sokal and H. L. Friedman, "The complex dynamics of wishful thinking: the critical positivity ratio", American Psychologist 68(9), 2013, doi 10.1037/a0032850. Read: the published abstract; and in the authors' preprint, arXiv 1307.7006v1, the introduction's first two paragraphs, the closing paragraphs of the derivation section, the sections on the empirical study and on an upper ratio, and the conclusion and concluding remarks. The published text was not opened and may differ in wording from the preprint. Supports: the abstract's two quotations, the group averages of 3.2 and 2.3, the arbitrary settings and the alternative ratio, the passages on the empirical study, and the critics' statements of scope, of tone and of motive.
5. B. L. Fredrickson, "Updated thinking on positivity ratios", American Psychologist 68(9), 2013, doi 10.1037/a0033584. Read: the abstract. Supports: every quotation from her reply.
6. A. Keller and colleagues, "Does the perception that stress affects health matter? The association with health and mortality", Health Psychology 31(5), 2012, doi 10.1037/a0026743, PMC3374921. Read: the abstract, and in the full text the results with Table 3, the sensitivity analysis and the discussion including its limitations. Supports: the design, the sample, the hazard ratio with its reference group and adjustments, the interaction result, the cumulative hazards, the 20,231 figure with its condition, the reverse-causality paragraph, the chronic-condition flag, the mediation analysis, and the abstract's "impact" and "associated".
7. A. J. Crum, P. Salovey and S. Achor, "Rethinking stress: the role of mindsets in determining the stress response", Journal of Personality and Social Psychology 104(4), 2013, doi 10.1037/a0031201 (read: the abstract); and M. Bosshard and P. Gomez, "Effectiveness of stress arousal reappraisal and stress-is-enhancing mindset interventions on task performance outcomes", Scientific Reports 14, 2024, doi 10.1038/s41598-024-58408-w (read: the abstract and the publication-bias subsection of the results). Supports: Studies 2 and 3 and Crum's conclusion, and every figure from the meta-analysis.
8. J. Frattaroli, "Experimental disclosure and its moderators: a meta-analysis", Psychological Bulletin 132(6), 2006, doi 10.1037/0033-2909.132.6.823. Read: the abstract. Supports: the definition, the study count and the pooled r. No moderator result is used.
9. This course's own constructions, labelled where they appear. The three shapes are Sleep lesson 7's organising frame, not a finding, and this lesson's wider third shape is this course's. Also this course's: the glosses of the four trajectories; the chart and its reading of why the figures add to more than 100; the sentence on character; the reading of the "very-low certainty" label; the sorting of the resilience claim and of the ratio case into shapes; the gloss of cumulative hazard and the subtraction of 3.5 from 5.1; the reading that the mediation analysis cannot separate reverse causality from mediation; the reading that six effect sizes may be too few; the percentile conversions from lesson 2's table; the gloss "most often in writing" and the r-to-d conversion; and the reading that the survey and the experiments cannot stand in for each other.
10. McGonigal, The Upside of Stress, and her TED talk. Not read and not watched. Named only as the route by which many readers meet the Keller study; nothing in this lesson is attributed to either.