New tutorial on computing Bayes factors in R

I just published a practical guide on computing Bayes factors using various packages in R. Head over to RPubs and check out How to compute Bayes factors using lm, lmer, BayesFactor, brms, and JAGS/stan/pymc3.

My first goal is to present solutions to things that I found difficult in the respective packages and which are relatively undocumented. A second goal was to show a side-by-side comparison on whether the packages converge on the same Bayes factor estimates.

I hope to keep the document updated. In particular, I’m keeping an eye on the development of, BASand I need to learn how to specify a full JZS prior in brms.

Personally, this is a lot of firsts for me and took way too much time: my first R notebook (including Markdown), first tutorial in many years, and first use of brms and  BAS.

Software for graphical models

I’m currently writing a paper on a new Bayesian method for scoring Complex Span tasks. I needed some software to represent it using plate notation of a directed acyclic graph (DAG). Many people have pointed to the Tikz/pgf drawing library for latex, but I did not want to install latex for this simple task. Here I briefly review yEd, Daft, and Libreoffice Draw.


I ended up using yEd and produced this graph which contains plates, estimated nodes, deterministic nodes (double-lined), observed nodes (shaded), and categorical nodes (rectangles).yEd is purely graphical editing which is fast to work with and great for tweaking small details. A very handy yEd feature is its intelligent snapping to alignments and equal distances when positioning objects. Actually, I don’t understand why yEd almost never makes it to the “top 10 diagram/flowchart programs” lists.

A few things I learned: To make subscripts, you have to use HTML code. For example, the \(R_{trial_{i,j}}\) node is

However, it is not possible to do double-subscripts. Also, the double-edges node is made completely manually by placing an empty ellipse above another. I did not manage to align the \(WMC_i\) label a bit lower in the node. A final limitation is that arrowhead sizes cannot be changed. You can, however, zoom. Therefore, your very first decision has to be the arrowhead size. Zoom so that it is appropriate and make your graphical model. I didn’t think about this so the arrows are too large for me in the graph above.

I’m pretty pleased with the result. For the final paper I may try and redo this in Libreoffice Draw to see if I can fix the final details.

Libreoffice Draw

In retrospect, I think that Draw could have done better than yEd. First, you can scale arrowheads to your liking! Furthermore, you can write math in LibreOffice Math, so double-subscripting is no problem. However, you have to group a math object with an ellipse rather than entering it as “content”, which is a bit convoluted. Speaking of math, LibreOffice Math was great for entering the model specifications for the graphical model:

One small annoyance is that you have to choose between left-aligning everything including the denominators in fractions (which of course should be centered), or center-align everything. I would have liked a center-aligned denominator while left-aligning everything lines.

The above was created using the following code. The matrix was used to align the terms.

I have to say that there’s something to the lacking snap-to-alignment and the general interface in Draw that makes it feel less nice than yEd, even though it is probably more versatile for the present purpose. I may update this blog post with a Draw model when I get around doing it.


Daft is a python module for rendering graphical models. The syntax is quite nice, but I quickly learned that you have to choose between shaded or double-edged nodes as indicators of observed variables. You cannot have both. You can draw an empty smaller node on top to make it double-edged, but using the \(scale\) argument makes it non-aligned with the outer line. I raised this as a GitHub issue [UPDATE: Check the GitHub issue – it has been fixed now! I haven’t updated this post], but Daft has not been maintained for years, so I don’t expect this to be fixed. Also, you have to install an old fork to draw rectangular nodes. This is as far as I got:

Here’s the code to do it, very much inspired (/ripped off) by this example.

Some notes

Five divided by forty-nine

At a family dinner, my brother told me that he had stumbled upon a curious number. Divide five by forty-nine and take a look at the digits:

$$5 / 49 = 0.10204081632653061…$$

Do you see a pattern in the digits? Yes! It’s powers of two: (0.)1, 02, 04, 08, 16, 32, 65, … Huh, 65? Yes! The next number, 128, is a three-digit number and so the first digit “overlaps” the last digit of 64, making it 65. And this continues for the first digits of 256 (28 + 2 = 30), 512, the first two digits of 1024, etc. Then floating point errors kicked in, and we stopped there.

I immediately googled it, but no one seems to have noticed this pattern in the digits before. It began to dawn on us that we may just be looking at a hitherto undiscovered “interesting number” such as pi, e, the golden ratio, etc. But the social norms of family meetings do not allow for simulations and mathematical derivations, so we put it aside.


The number kept lingering in the back of my head. A few weeks later, I had several pressing deadlines, and as usual, procrastination kicked in full force. I needed to see how far this sequence continued. I fired up Python and wrote a small script which generates the power sequence first, then calculates the number 5/49, and finally identifies at what decimal place the two diverge:

The print-function in the first for-loop visualizes the adding of the power sequence:

and the other print functions compare the “ideal” number to the fraction:

Ok, wow, so it goes on for quite a while. Setting max_power = 10.000 and…

Now I’m convinced that this is an infinite pattern. But it gets even better: the sequence starts over every 42 digits. I repeat: Every. 42!!! Digits. Here are the first 168 decimals:

Is the key to the universe hidden in there somewhere!!?? I was exploding with excitement when I ran and presented this to my wife late in the evening.

The math

My wife is a mathematician. She was not impressed. “Jonas, do you know how to divide five by forty-nine by hand?”. No, I must admit that I never properly learned to do long division (even though I later enjoyed doing long polynomial division). And sure enough: the remainder of the first operation is 50-49 = 1. The remainder of the second operation is two decimal places further to the right where 1 is 100, and the equation becomes 100 – 98 = 2. Then two further to the right and doubling again: 200 – 196 = 4. Then 400 – 392 = 8, etc.

Every 21 such operations the division again hits the operation 50/49, and it repeats. This is extremely common for integer fractions in general. In fact, all rational numbers either have repeating decimals (like 5/49) or terminate (like 1/4 = 0.250000…), so one should not be surprised. Also, this particular 42-decimal period is shared by the division of 42 different integers by 49, albeit starting at different locations in the sequence, e.g., 1/49=0.02040816… and 3/49=0.06122448….

My wife went to bed. For a few seconds, I felt bad. My intellectual love affair crashed hard upon realizing that 5/49 was in many respects just a normal number. But as with human relationships, so with numbers: I’ve learned a great deal about rational numbers through this journey and that’s a comfort.


I do still think that 5/49 stands out. A 42-decimal period with powers of two is an intriguing property only shared by x/49 fractions. Furthermore, 5/49 is the only one of these fractions to start at 20=1 – the true beginning of the power sequence.

The long-division property can be exploited to generate numbers with custom power-sequences in the decimals. So without further ado, I give you:


… where x ∈ R≥0 is the root of the exponential and n ∈ N≥2 is the number of decimal places between each number. Let’s try this for a few numbers:

For two decimal places between powers of two, we get

$$10/(10^2 – 2) = 10/98 = 5/49$$

I hope that this number will henceforth be known as Lindeløv’s number. At least it’s on Google now.

I do not recommend hypnosis for brain injury (yet)

Jan 2019 update: Given the latest articles on this and a more extensive literature search, I am now convinced about the effectiveness of hypnosis after brain injury than I was when writing this initially. Still, much of this is lower-quality research than I’d like. So the below is still accurate.

I have been overwhelmed with requests following our article about the effect of hypnotic suggestion on working memory performance following acquired brain injury. I present frequent questions and very short answers below. My answers to the questions all originate in the same point: there is insufficient evidence right now to establish whether to use or not to use hypnosis for the treatment of cognitive problems following acquired brain injury. I predict that we should be able to give a recommendation (or refusal) regarding hypnosis following acquired brain injury in 2020.

Frequent questions from patients and relatives:

Question: I have a brain injury. Where can I get hypnosis?
Answer: I won’t give any recommendations. I am a researcher and there is not a firm research-based basis for such a recommendation. If you choose to find a hypnotist, make sure to avoid hypnotists who offer regression to past lives, healing of aura, contact with dead relatives, etc. They have demonstrated an inability to learn from science.

Question: Can I be a test subject in an experiment?
Answer: Unfortunately, not by asking me. If we had experiments with open recruitment, we would recruit through other sources to avoid the strong selection bias.

Question: My daughter is diagnosed with ADHD/Schizophrenia/chronic pain/other – can hypnosis help her?
Answer: The results from our experiment should not be uncritically transferred to other conditions. I do not know enough about the effectiveness of hypnosis for the condition you mentioned here.

Frequent questions from rehabilitation professionals and hypnotists:

Question: Can you send me the manuscript?
Answer: No, the manuscripts will be made freely available if (and only if) there is sufficient evidence to decide if it can be recommended as a generalized treatment. We expect to have that evidence in 2020. Here is a list of all public information about the our experiment, which is more than for most scientific articles. This includes some excerpts from the manuscript in the supplementary materials.

Question: Can you help us get started using this intervention for our clients?
Answer: I’m eager to work with you to set up a research project if you are an institution working professionally with brain-injured patients. That means that you can offer the treatment but you will have less control over to whom and how the treatment is administered while the research is ongoing. These projects are needed to accumulate the evidence to decide if hypnosis can be recommended as a treatment for cognitive problems following acquired brain injury.

Background to the answers

Although our study is very convincing in and of itself, it is just one study and one should remember to factor in prior skepticism and that skepticism should be quite high in this case. The results are surprising exactly because they seem unlikely given prior evidence. One also should consider the fact that the results from scientific studies on humans and animals often fail to replicate. I know of several widely used “treatments” in neurorehabilitation that was introduced because of positive early studies but they are still lingering on even though the collective evidence points to small or no effects. If our results should fail to replicate, its better that hypnosis was never brought to use in neurorehabilitation than spending everybody’s precious time on something ineffective.

I am personally optimistic because I have more (less scientific) sources of evidence than what has been published, but I am also a strong believer in science as the right way to make clinical recommendations. With the ongoing and planned studies, I expect that we have sufficient evidence to make a recommendation (whether for or against) in 2020. We keep the final details about the intervention to research projects until then.

I may come across as dismissive. I really am both personally moved by individual stories and intellectually baffled by the scale of the problem on a world scale. I believe that the solution above will, on average, be the best. One potential advantage of it is that it increases the probability that the treatment, if effective, will be implemented in standard treatment instead of on the all-too-grey market of private hypnotists.

See also my post on what our experiment did not show.

Jeg anbefaler ikke hypnose efter erhvervet hjerneskade (endnu)

Jeg får mange henvendelser omkring vores artikel om effekten af hypnotiske suggestioner på arbejdshukommelsen efter erhvervet hjerneskade. Nedenfor giver jeg korte svar på ofte stillede spørgsmål. Alle svarene bunder i den samme pointe: der er endnu ikke tilstrækkelig evidens til at afgøre, om hypnose kan- eller ikke kan anbefales som behandling af kognitive problemer efter erhvervet hjerneskade. Jeg forventer, at vi kan anbefale (eller afvise) hypnose efter erhvervet hjerneskade omkring år 2020.

Ofte stillede spørgsmål af patienter og pårørende:

Spørgsmål: Kan du anbefale en hypnotisør?
Svar: Jeg vil ikke anbefale nogen. Jeg arbejder med forskning og der er ikke et stærkt nok forskningsbaseret grundlag for at give en anbefaling. Hvis du vælger at opsøge en hypnotisør, så undgå alle der tilbyder regression til tidligere liv, healing af aura, kontakt med døde pårørende osv. De har dermed vist, at de ikke arbejder videnskabeligt.

Spørgsmål: Can jeg være med i et eksperiment?
Svar: Desværre ikke ved at spørge mig. Hvis vi havde eksperimenter der manglede deltagere ville vi rekruttere igennem andre kilder (fx hjerneskadeforeningen og hjernesagen) for at mindske selektionsbias.

Spørgsmål: Kan hypnose hjælpe mod ADHD/Skizofreni/kronisk smerte/andet?
Svar: Resultaterne fra vores eksperiment kan næppe overføres så direkte til andre patientgrupper. Jeg kender ikke nok til hvor effektiv hypnose er på den problematik du nævner til at give et svar.

Ofte stillede spørgsmål af professionelle indenfor rehabilitering og hypnose:

Spørgsmål: Kan du sende mig manuskriptet?
Svar: Nej, manuskripterne gøres frit tilgængelige, hvis (og kun hvis) der er tilstrækkelig med forskning der viser, at det kan anbefales som en generel behandling. Her er en oversigt over al offentlig information omkring vores eksperiment, hvilket er mere end for det meste forskning. Dette inkluderer nogle uddrag fra manuskriptet, som du finder i supplementary materials.

Spørgsmål: kan du hjælpe os i gang med at bruge denne intervention til vores klienter?
Svar: Jeg vil meget gerne samarbejde med jer om at starte et forskningsprojekt hvis I er en institution som arbejder professionelt med borgere med erhvervet hjerneskade. Det betyder, at I får muligheden for at tilbyde det til borgerne, men også at I får mindre kontrol over hvordan det udbydes, mens forskningen pågår. Denne slags forskningsprojekter er nødvendige for at afgøre, om hypnose kan abefales som en behandoling af kognitive problematikker efter erhvervet hjerneskade.

Baggrund for svarene

Selvom vores resultater i ovenstående artikel er meget overbevisende isoleret set, er det stadig kun et enkelt eksperiment. Man skal huske at medregne den skepsis man ville have overfor resultaterne, da de bryder med en del veletableret forskning. Man skal også huske, at resultaterne fra videnskabelige studier på dyr og mennesker ofte ikke kan gentages. Jeg er bekendt med flere udbredte “behandlinger” i neurorehabilitering, som netop blev taget på grund af nogle positive resultater, og som stadig er i brug selvom den samlede evidens nu viser at effekten er meget lille eller helt fraværende. Hvis vores resultater ikke kan gentages, er det bedre at hypnose aldrig blev taget i brug i neurorehabilitering, end at alle bruger deres kostbare tid på noget ineffektivt.

Personligt er jeg optimistisk fordi jeg kender til flere (mindre videnskabelige) resultater end det der er blevet publiceret. Men jeg står også fast på, at videnskab må være det rigtige grundlag for kliniske anbefalinger. Med de igangværende og planlagte studier forventer jeg at vi har nok resultater til at give en egentlig anbefalinger (hvad end den er for eller imod) i år 2020. Indtil da holder vi visse detaljer om metoden lukket til forskningsprojekter.

Jeg kan måske give indtryk af at være afvisende. Jeg er personligt rørt over historierne fra alle de personer med hjerneskade jeg har mødt. Jeg er også intellektuelt oprørt over størrelsen af problemet på verdensplan. Jeg tror at ovenstående strategi vil give det bedste udfald i gennemsnit. En mulig fordel er fx at det øger sandsynligheden for, at behandlingen (hvis den er effektiv) bliver implementeret som en del af den offentlige behandling i stedet for at blive overladt til det grå marked af privatpraktiserende hypnotisører.

Se også min post om hvad vores eksperimnet ikke viser.

Decimals of PI with consistent colors

I was invited to do a fun task by my office colleague, Hazel Anderson. She researches synesthesia, and she wanted to induce grapheme-color synesthesia by having participants learn pi using digit-color mapping as one available strategy. So she needed something that could a Word document with pi with an arbitrary number of decimal places. Approximately 40 minutes of the pure joy of structured procrastination and:



Here’s the python script to generate this beauty:


Scientific papers on hypnosis and brain injury

This is an attempt to make a complete up-to-date list of all literature pertaining to hypnosis and brain injury. I now consider the literature so big and dispersed that I feel quite confident that my list won’t be complete, but hopefully, it can get close. In each section, the most informative paper(s) are highlighted in green font.

This list contains many case-studies so there is likely a strong positive bias. I would advise reading the cases purely for methodological inspiration and look to the more systematic and comprehensive studies for an actual assessment of treatment effects.

I recommend reading the review by Appel (2003) as a start. It is a review on hypnosis for rehabilitation in general (not only brain injury) and is by far the most comprehensive review available so far, citing around half of the papers below.

As a side note, I was completely unaware of the scale of the literature when I undertook this search. The first version of this post contained around 10 papers and I considered it complete. One notable surprise is that the list of researchers now includes Milton Erickson and Aaron T. Beck in addition to John Kihlstrom.


Status (April 2018): Completed.

Summary of the literature: There are (large) positive effects of hypnosis on cognition following acquired brain injury.

  • Cui-ping, L. I. (2011). Influence of hypnosis therapy on recovery of hemorrhagic stroke. Journal of Taishan Medical College, 1, 025. (see my English translation and comments)
    An RCT showing large effects (SMD = 1.0 to 1.7) on Barthel, anxiety, and depression in stroke patients given ten sessions of hypnosis between one and twelve weeks after the injury onset. The study is relatively large with 120 treatment-as-usual patients of which 49 had additional adjunctive hypnosis. It was published in Chinese in a Chinese journal with impact factor 0.1, and it is unclear whether it was peer-reviewed. In general, there are many reasons to be skeptical of the quality of this paper. Nonetheless, everything else being equal, it does increase the probability that hypnosis can improve cognition following acquired brain injury. With the help of Chinese friends, I got hold of the paper and helped reading it. I’ve added a link to my translation in the reference above, containing comments to clarify particular unclear sections and dubious statistics
  • Lindeløv, J. K., Overgaard, R., & Overgaard, M. (2017). Improving working memory performance in brain-injured patients using hypnotic suggestion. Brain, 140(4), 1100–1106.
    Our study, showing a large specific effect on working memory performance of hypnotic suggestions involving the return to pre-injury (or normal) functioning. It’s an RCT with a total of 68 patients stratified to targeted hypnosis, an active control, and a passive control. The effect of four and eight treatment sessions is assessed with long-term follow-up.
  • Milos, R. (1975). Hypnotic exploration of amnesia after cerebral injuries. International Journal of Clinical and Experimental Hypnosis23(2), 103–110.
    This paper is not really on cognitive rehabilitation but it does manage to (temporarily) get retrospective reports of experiences that were otherwise inaccessible due to retrograde or anterograde amnesia during hypnosis in 7 out of 20 cases of severe injury. It was not checked whether these reports were accurate, so this is prone to confabulations or changes in response criterions rather than a true cancellation of amnesia.
  • Sullivan, D. S., Johnson, A., & Bratkovitch, J. (1974). Reduction of behavioral deficit in organic brain damage by use of hypnosis. Journal of Clinical Psychology, 30(1), 96–98.<96::AID-JCLP2270300133>3.0.CO;2-A.
    Later we discovered this similar study had been carried out by Sullivan et al. (1974). The Sullivan study, however, had an intervention consisting of just seven sentences repeated twice – probably less than two minutes! They obtained a small positive effect on the Picture Completion task from the WAIS battery but not on the Binder-Gestalt test. They had a quite small sample, and the two-page article leaves many details unreported.
  • Vanhaudenhuyse, A., Laureys, S., & Faymonville, M.-E. (2015). The use of hypnosis in severe brain injury rehabilitation: a case report. Acta Neurologica Belgica115(4), 771–772.
    A brief report on a 50-year case with cerebral hemorrhage, who underwent hypnosis when he was deemed chronic with severe symptoms. Hypnosis sparked further improvement. As a side note, the authors write that “To the best of our knowledge, this is the first study reporting on the integration of hypnosis as part of rehabilitation treatment of severe brain injury patients.” Well… 🙂

Motor disorders

Status (April, 2018): Approximately 70% completed. Needs a search for post-2000 literature, references, and citations

With the notable exception of Spankus & Freeman (1962) and Irawan et al. (2018), this literature consists largely of single-case studies, making it very vulnerable to publication bias. Confirming this, most studies report positive findings while Spankus & Freeman (1962) only report positive outcomes for four out of nineteen patients with cerebral palsy. Although somewhat disconcerting, this observation may not generalize to all of the literature given the large variability in the patient characteristics and treatment protocols between papers.

  • Alexander, L. (1966). Hypnosis in primarily organic illness. American Journal of Clinical Hypnosis8(4), 250-253.
  • Appel, P. R. (1990). Clinical Applications of Hypnosis in the Physical Medicine and Rehabilitation Setting: Three Case Reports. American Journal of Clinical Hypnosis, 33(2), 85–93.
    See case number two.
  • Chappell, D. T. (1961a). A Psychological Approach to Traumatic Paraplegia: Use of Hypnosis. The Journal of Nervous and Mental Disease, 132(5), 432.
  • Chappell, D. T. (1961b). The Reduction of Spasticity in Paraplegia with Hypnosis. American Journal of Clinical Hypnosis, 3(4), 213–225.
  • Chappell, D. T. (1964). Hypnosis and Spasticity in Paraplegia. American Journal of Clinical Hypnosis, 7(1), 33–36.
  • Crasilneck, H. B., & Hall, J. A. (1970). The use of hypnosis in the rehabilitation of complicate vascular and post-traumatic neurological patients. International Journal of Clinical and Experimental Hypnosis, 18(3), 145–159.
  • Diamond, S. G., Davis, O. C., Schaechter, J. D., & Howe, R. D. (2006). Hypnosis for rehabilitation after stroke: six case studies. Contemporary Hypnosis, 23(4), 173–180.
  • Holroyd, J., & Hill, A. (1989). Pushing the limits of recovery: Hypnotherapy with a stroke patient. International Journal of Clinical and Experimental Hypnosis, 37(2), 120–128.
    This is an RCT on 2 x 16 stroke patients. Although the descriptive statistics seem convincing, there are some red flags. For example, the journal seems a bit dubious, there are spelling/grammatical mistakes, and half of the citations are non-English. More content-related, the statistics are relatively poor, lacking the test of the crucial 2 (pre/post) x 2 (treatment/control) interaction term, which would be identical to the independent t-test on the change scores in each group. It does look like such a test would come out significant with a test would come out positive given the large improvement in the treatment group (d = 1) as compared to the control group (d = 0.1).
  • Manganiello, A. J. (1986). Hypnotherapy in the rehabilitation of a stroke victim: a case study. The American Journal of Clinical Hypnosis, 29(1), 64–68.
  • Mauersberger, K., Artz, K., Duncan, B., & Gurgevich, S. (2000). Can children with spastic cerebral palsy use self-hypnosis to reduce muscle tone? a preliminary study. Integrative Medicine, 2(2), 93–96.
  • Martin, J. (1983). Hypnosis also useful in rehabilitation therapy. JAMA, 249(12), 1536–1536.
  • Radil, T., Snýdrová, I., Háĉik, L., Pfeiffer, J., & Votava, J. (1988). Attempts to influence movement disorders in hemipareticsScandinavian journal of rehabilitation medicine. Supplement17, 157-161.
  • Safitri, K. H., Irawaty, D., & Masfuri, M. (2018). Effect Hypnotherapy for Increasing Muscle Strength in Stroke Patient with Hemiparesis. International Journal of Nursing, Health and Medicine, 1(1), 7–13. All alarms go off with this paper. An unknown journal, major grammatical errors (bordering on not being comprehensible), and major omissions in the reporting. Still, it’s a controlled study with 44 hemmorrhagic stroke patients, so it has larger weight than many other studies on this list. Says that “No publication of research like this before” which is obviously false, as is apparent from this list.
  • Seder, I. I., & Gelberd, M. B. (1964). Hypnosis as a Relaxant for the Cerebral Palsied Patient. American Journal of Clinical Hypnosis, 6(4), 364–365.
  • Slater, R. C., & Flores, L. S. (1963). Hypnosis in organic symptom removal: A temporary removal of an organic paralysis by hypnosis. American Journal of Clinical Hypnosis5(4), 248-255.
  • Spankus, W. H., & Freeman, L. G. (1962). Hypnosis in cerebral palsy. International Journal of Clinical and Experimental Hypnosis, 10(3), 135–139.
  • Vodovnik, L., Roskar, E., Pajntar, M., & Gros, N. (1979). Modeling the voluntary hypnosis-induced motor performance of hemiparetic patients. IEEE Trans. on Systems, Man, and Cybernetics, SMC-9 (12).
  • Yensen, R. (1963). Hypnosis and Movement Re-Education in Partially Paralysed Subjects. Perceptual and Motor Skills17(1), 211–222.

Citations without available abstract or full text below. Notice that the list includes papers on neuromuscular illnesses, even though these typically relate to the peripheral nerve system. But due to my inability to scan these papers, I keep them on the list in case they include cases of brain injury.

  • Baer, R. F. (1962). Hypnosis in the treatment of neuromuscular sequelae of injuries. Industrial medicine & surgery, 31, 315.
  • Kroger, W.S. (1970) Hypnosis therapy in neuromuscular disorders. Osteopathic Physician (1970), pp. 69-70, September.
  • Martin (1983, see above) cites a paper by Korn which I cannot find, saying: “At least Errol R. Korn, MD, can point to definite rehabilitative gains made by “dozens of patients” with stroke and spinal cord injuries in relearning the swallowing reflex, regaining muscle and balance control, and healing decubitus ulcers.”
  • Ortega DF (1978). Relaxation exercise with cerebral palsied adults showing spasticity. J Appl Behav Anal 11(4):447-451
  • E. Roskar, M. Pajntar, L. Vodovnik, and N. Gros (1977) Improvements of motor response in hemiplegic patients by means of hypnosis, in Proc. I st. Mediterranean Conf. on Med. and Biol. Engng., Sorrento, Italy, pp. 1-85-I-88.
  • E. Roskar, M. Pajntar, L. Vodovnik, and N. Gros (1978.) Improved neuromuscular activity of hemiparetic extremity due to hypnosis, Advances in External Control of Human Extremities, Yugoslav Committee for Electronics and Automation, Belgrade, pp. 257-268
  • Secter IL, Gilberd MB (1964). Hypnosis as a relaxant for the cerebral palsied patient. Am J Clin Hypn 6:363-364.
  • Shires EB, Peters JJ, Krout RM (1954) Hypnosis in neuromuscular re-education. U.S. Armed Forces Medical Journal 5: 1519–23.


Status (April 2018): Completed.

  • Kirkner, F. J., Dorcus, R. M., & Seacat, G. (1953). Hypnotic motivation of vocalization in an organic motor aphasic case. Journal of Clinical and Experimental Hypnosis, 1(3), 47–49.
  • Laures, J. S., & Shisler, R. J. (2004). Complementary and alternative medical approaches to treating adult neurogenic communication disorders: a review. Disability and Rehabilitation, 26(6), 315–325.
    Contains a very short section (page 317-318) reviewing Thompson et al. (1986) and Manganielly (1986) (see this list). Finds the results promising but insufficient due to weaknesses from inconsistency in the former and lack of objective outcome measures in the latter.
  • Macfarlane, F. K., & Duckworth, M. (1990). The use of hypnosis in speech therapy: a questionnaire study. British Journal of Disorders of Communication25(2), 227-246.
    This is just a survey on usage frequencies without an assessment of effectiveness. Also covers non-neurological speech problems.
  • Mason, C. F. (1961). Hypnotic motivation of aphasics. International Journal of Clinical and Experimental Hypnosis, 9, 297–301.
  • McKeever, W. F., Larrabee, G. J., Sullivan, K. F., Johnson, H. J., Furguson, S., & Rayport, M. (1981). Unimanual tactile anomia consequent to corpus callosotomy: Reduction of anomic deficit under hypnosis. Neuropsychologia, 19(2), 179–190.
  • Moss, C. S. (1972). Recovery with aphasia: The aftermath of my stroke. Oxford, England: U. Illinois Press.
    This is a self-report (i.e., not a scientific paper) of a clinical neuropsychologist who suffered from aphasia following a cerebral vascular incident. Moss recovered well and reports, among other things, on hypnotherapy in the process.
  • Thompson, C. K., Hall, H. R., & Sison, C. E. (1986). Effects of hypnosis and imagery training on naming behavior in aphasia. Brain and Language, 28(1), 141–153.

   Citations without available abstract or full text:

  • Glazer, M. J. (1964). A comparison of performance of predominantly expressive aphasic patients before, during and after hypnosis: a thesis (Doctoral dissertation, Tulane University).


Status (April, 2018): Approximately 50% completed. Needs a systematic search, reference search, and citation search.

  • Eisenberg, M. G., & Jansen, M. A. (1983). Rehabilitation psychology: State of the art. Annual review of rehabilitation.This review contains a quite extensive section on hypnosis for dementias. Though this is superseded by Appel the (2003) review
  • Duff, S., & Nightingale, D. (2007). Alternative Approaches to Supporting Individuals With Dementia: Enhancing Quality of Life Through Hypnosis. Alzheimer’s Care Today, 8(4), 321. is an RCT with a treatment group, an active control group (discussion groups) and a treatment-as-usual group. The participants were recruited from care homes and had vascular dementia (acquired brain injury) or dementia (unspecified…), and a few Parkinson’s patients. The intervention was quite extensive with 36 weekly sessions of hypnosis or discussion and a 12-month follow-up after that. The outcome was a questionnaire-only assessment of Quality of Life with large effects on all aspects which were all maintained after 12 months, except for relaxation. The small sample size and the subjective nature of the report are reasons to be cautious, but otherwise, it’s some of the most informative data on hypnosis for dementias to date (2018).
  • Palmieri, A., Kleinbub, J. R., Calvo, V., Sorarù, G., Grasso, I., Messina, I., & Sambin, M. (2012). Efficacy of hypnosis-based treatment in amyotrophic lateral sclerosis: a pilot study. Frontiers in psychology3, 465. A small sample of 8 ALS patients was treated using Ericksonian hypnosis during four weekly 45-minute sessions. A CD with the hypnotic induction was offered for daily home use. The effect sizes on (self-reported) depression, anxiety, and quality-of-life was beyond-large (cliff’s delta around 0.75) in general with some larger and some smaller. There were similar effects on relative-reported caregiver burden. While this study is stronger than case studies (eight times stronger?), the lack of control likely means that these effects are likely overestimated.
  • Elkins, G., Sliwinski, J., Bowers, J., & Encarnacion, E. (2013). Feasibility of clinical hypnosis for the treatment of parkinson’s disease: a case study. International Journal of Clinical and Experimental Hypnosis61(2), 172-182. Almost complete removal of tremor in a parkinson patient following three weekly hypnosis sessions. It’s hard to know from this case how well this generalizes, or whether there was something special (read: unrepresentative) about this patient.
  • Stambaugh, E. E. (1977). Hypnotic treatment of depression in the Parkinsonian patient: A case study. American Journal of Clinical Hypnosis19(3), 185-186.

Not properly vetted for this list yet (copy-pasted from Appel (2003)):

  • H.J. Wain, D. Amen, B. Jabbari The effects of hypnosis on a Parkinsonian tremor: Case report with polygraph/EEG recordings.
    Am J Clin Hypn, 33 (1990), pp. 94-98
  • F.A. Buell, J.P. Biehl The influence of hypnosis on the tremor of Parkinson’s disease
    Journal of Disorders of the Nervous System, 10 (1949), pp. 20-23
  • H.W. Bird Varying hypnotizability in a case of Parkinsonism
    Bull Menninger Clin, 12 (1948), pp. 210-217
  • M. Witz, S. Kahn Hypnosis and the treatment of Huntington’s Disease
    Am J Clin Hypn, 34 (1991), pp. 79-90
  • R. Moldawsky Hypnosis as an adjunctive treatment in Huntington’s disease
    Am J Clin Hypn, 26 (1984), pp. 229-231
  • V. Stein Hypnotherapy of involuntary movements in an 82-year-old man
    Am J Clin Hypn, 23 (1980), pp. 128-131
  • D. Vann Successful hypnotherapy for anxiety neuroses in Huntingtonı́s chorea
    Med J Aust, 2 (1971), p. 166
  • G. Ambrose Multiple sclerosis and treatment by hypnotherapy
    Am J Clin Hypn, 3 (1955), pp. 203-209
  • R.F. Baer Hypnosis, An adjunct in the treatment of neuromuscular disease
    Arch Phys Med Rehabil, 41 (1960), pp. 514-515
  • J.T. Brunn Hypnosis and neurological disease: A case report
    Am J Clin Hypn, 8 (1966), pp. 312-313 (Link)
  • J.R. Dane Hypnosis for pain and neuromuscular rehabilitation with multiple sclerosis: Case summary, literature review, and analysis of outcomes
    Int J Clin Exp Hypn, 44 (1996), pp. 208-231
  • H. McCord Hypnotically hallucinated physical therapy with a multiple sclerosis patient
    Am J Clin Hypn, 5 (1963), p. 168
  • H. McCord Hypnosis and multiple sclerosis: A brief case report
    Am J Clin Hypn, 8 (1966), pp. 313-314
  • D.Y. Medd The use of hypnosis in multiple sclerosis: Four case studies
    Contemp Hypn, 9 (1) (1992), pp. 62-66
  • B. Strauss, S. Billie Hypnosis with cerebral palsy patients, and how may it be applied
    ASCH Newsletter, 26 (6) (1985), p. 2
  • R.F. Baer Hypnosis applied to bowel and bladder control in multiple sclerosis, syringomelia and traumatic transverse myelitis
    Am J Clin Hypn, 4 (1961), pp. 22-23
  • Also check out other papers by Duff. For example, is this a fulltext? Are they merely reporting the same results as Duff (2007) at earlier stages? 

Pain, vertigo, anxiety (in progress)

Status (April, 2018): Approximately 40% completed. Needs a systematic search, reference search, and citation search.

This is a catch-all category for directly unpleasant sequelae following acquired brain injury. Sullivan et al. (1974) hypothesized that they relieved anxiety. But they never directly assessed anxiety, so I presented it on the list for cognitive rehabilitation. Fromm (1964) and Gruenewald & Fromm (1967) tried to induce catastrophic anxiety in healthy subjects.

  • Cedercreutz, C., Lähteenmäki, R., & Tulikoura, J. (1976). Hypnotic treatment of headache and vertigo in skull injured patients. International Journal of Clinical and Experimental Hypnosis, 24(3–4), 195–201.
    This paper summarizes clinical results of 155 patients with pain and/or vertigo sequelae. So this is a large portion of evidence as compared to the rest of this list. As with the other case studies, it may be prone to experimenter bias. The reported effects are quite impressive in a median of three-to-four sessions to achieve complete symptom relief in more than half of the patients.
  • Laclave, L. J., & Blix, S. (1989). Hypnosis in the management of symptoms in a young girl with malignant astrocytoma: A challenge to the therapist. International journal of clinical and experimental hypnosis37(1), 6-14.
    A single-case study on a 6½-year old girl predominantly focused on nausea following chemotherapy. I still include it on this list because of the neurogenic nature of the disease.
  • Moss, D. (2018). I hurt so: hypnotic interventions and palliative care for traumatic brain injury. Annals of Palliative Medicine, 7(1), 151–158.
    Case study with a TBI patient. Hypnosis for pain and anxiety.
  • Sapp, M. (1992). Relaxation and hypnosis in reducing anxiety and stress. Australian Journal of Clinical Hypnotherapy and Hypnosis, 13(2), 39-55. Stuff
  • Bertoni, F., Bonardi, A., Magno, L., Mandracchia, S., Martinelli, L., Terraneo, F., & Tonoli, S. (1999). Hypnosis instead of general anaesthesia in paediatric radiotherapy: report of three cases. Radiotherapy and oncology52(2), 185-190.
    Two cases of child patients with resected cerebellar tumors undergoing hypnotically induced general anesthesia.
  • Nolan, M. (2008). Hypnosis to enhance time limited cognitive-behaviour therapy for anxiety. Australian Journal of Clinical and Experimental Hypnosis36(1), 30-40.
    I was in doubt whether to include this on the list. It is the case of hypnosis with a client who self-reports transient ischemic attacks and fears a full-blown stroke, but there no direct evidence is reported for either. She did have high blood pressure and was subjected to bypass and other treatments.


Status (April 2018): Completed.

Take-home: Brain injured patients are as suggestible/hypnotizable as the general population

  • Laidlaw, T. M. (1993). Hypnosis and Attention Deficits After Closed Head Injury. International Journal of Clinical and Experimental Hypnosis, 41(2), 97–111.
    No difference in suggestibility on the HGSHS:A for young concussion patients relative to healthy controls.
  • Lindeløv, J. K., Overgaard, R., & Overgaard, M. (2017). Improving working memory performance in brain-injured patients using hypnotic suggestion. Brain, 140(4), 1100–1106.
    Our study tested 49 brain-injured patients on SHSS:C but did not compare them directly to healthy controls. However, looking at SHSS:C norms from other countries, the suggestibility of the patients seemed normal.
  • Kihlstrom, J. F., Glisky, M. L., McGovern, S., Rapcsak, S. Z., & Mennemeier, M. S. (2013). Hypnosis in the right hemisphere. Cortex, 49(2), 393–399.
    No difference in suggestibility between middle-aged stroke patients relative to young controls on AMSH.

General reviews

Status (April 2018): Completed.

  • Appel, P. R. (2003). Clinical hypnosis in rehabilitation. Seminars in Integrative Medicine, 1(2), 90–105.
    This is an impressive review of the field. For brain injury and neurological conditions, pages 96-97 are particularly relevant.
  • Appel, P. R. (2003) Clinical Hypnosis. In S. Wainapel, & A. Fast (Eds.) Alternative Medicine and Rehabilitation: A guide for practitioners. NY: Demos
    This is basically a shortened version of the excellent other Appel (2003) review. Pages 224-227 are especially relevant for neurological cases.
  • Wainapel, S. E., & Fast, A. (2002). Alternative Medicine and Rehabilitation: A Guide for Practitioners (1 edition). New York: Demos Medical.
    There is a short review on hypnosis for rehabilitation of motor dysfunction, aphasia, etc. on page 225-227. Most, if not all, of the cited literature by Weinapel is on the present list.

Citations without available abstract or full texts:

  • Wright, M. E. (1960) Hypnosis and rehabilitation. Rehabilit. Lia, 21(1), 2-12.
  • LaScolla, R. (1975). Hypnosis in stroke rehabilitation. In Scientific Proceedings of the 22nd Annual Meeting of the Am Society of Clinical Hypnosis.
  • Feher, T.L. (1987) Hypnosis in clinical neurology. In W. Wester (Ed.), Clinical Hypnosis: A Case Management Approach, Behavioral Science Center Inc. Publications, Cincinnati, OH
  • Celinski, M.J. (1992) Hypnosis in neurological rehabilitation. In W. Bongartz (Ed.), Hypnosis: 175 years after Mesmer-Recent developments in theory and application, Universitaetsverlag, Konstanz, Germany, pp. 357-362
  • Halama, P. (1993). Hypnotherapy for stroke patients. Hypnos20(3), 154-162.
  • Spellacy, F. (1992). Hypnotherapy following traumatic brain injuries. Hypnos19(1), 34-39.

Papers not fitting into the above categories

  • Gravitz, M. A. (1981). Non-verbal hypnotic techniques in a centrally deaf brain-damaged patient. International Journal of Clinical and Experimental Hypnosis29(2), 110-116.
  • Erickson, M. H. (1963). Hypnotically Oriented Psychotherapy in Organic Brain Damage. American Journal of Clinical Hypnosis, 6(2), 92–112.
    A case of hemiparesis, aphasia, and hyperalgesia following some vascular anomalities. This is Milton Erickson! After 11-months of no progress, Erickson takes on therapy in (at least) five months. There was great progress in this time, though it is not self-evident that this can be attributed to the intervention given the extensive duration of the intervention. His strategy relies heavily on frustrating the patient including lying, overruling, deceiving, etc. in front of others. I personally find his approach appalling. There is very little formal hypnosis in this paper.
  • Beck, A. T., & Guthrie, T. (1956). Psychological Significance of Visual Auras: Study of Three Cases with Brain Damage and Seizures. Psychosomatic Medicine, 18(2), 133–142. (link to PDF)
    Epilepsy following acquired brain injury. Hypnosis was employed in two cases to reveal painful emotional memories connected to the aura. Yes, Aaron T. Beck, the father of cognitive behavioral therapy (CBT) did a study on hypnosis and acquired brain injury!
  • Mittenberg, W., & Burton, D. B. (1994). A survey of treatments for post-concussion syndrome. Brain Injury, 8(5), 429–437.
    Simply shows the result of a survey, that 5.1 % (around 7 out of 165) of therapists use hypnotherapy for post-concussion patients. This is the only mention of hypnosis in the article.

Brain injury “models” in non-injured humans

Status (April 2018): Probably completed. But needs systematic search, reference search, citation search.

Take-home: healthy subjects can be hypnotized to play the role of brain-injured patients, but they are probably not realistic brain-injury models.

  • Fromm, E., Sawyer, J., & Rosenthal, V. (1964). Hypnotic simulation of organic brain damage. The Journal of Abnormal and Social Psychology, 69(5), 482.
    Hypnotized subjects (n=9) to believed that they had sustained an organic brain injury. After “hypnotic brain injury,” the subjects who experienced being in deep hypnosis were judged to be more “organic” by blinded neuropsychologists than under “hysterical” and no-hypnosis conditions, in which they were judged to be non-injured. The results from this study failed to replicate in a methodologically superior follow-up in Gruenwald & Fromm (1967).
  • Gruenewald, D., & Fromm, E. (1967). Hypnosis, simulation, and brain damage. Journal of Abnormal Psychology, 72(2), 191–192. 
    Replication of Fromm et al. (1964) with an improved method, controlling for more potential confounders. There were no difference between the hypnosis and control group judgment, actual score, or subjective experience.
  • Wagstaff, M., Parkes, M., & Hanley, J. R. (2001). A comparison of posthypnotic amnesia and the simulation of amnesia through brain injury. International Journal of Psychology and Psychological Therapy, 1(1), 67–78.
    Like Fromm (1964), but adds malingering-detection tests to the test battery, showing that “hypnotically brain injured” healthy subjects indeed do act as malingerers, not as real brain-injured patients.

Search strategy and current status of this list

Google Scholar was searched using the term “hypnosis OR “hypnotic suggestion” brain-injury OR brain-damage OR stroke OR hemiplegia OR paraplegia OR “traumatic brain” OR “diffuse axonal” OR hemorrhage”. The reference list of all hits for which I had access to full texts were scanned. For some papers, the list of papers citing that paper were scanned too, using Google Scholar.

Next steps (my to do):

  • Read Appel (2003) thoroughly again for more keywords to search on.
  • Make a histogram of publication years relative to general science publication volume.
  • Do searches on post-concussion syndrome?
  • Dementias? start with this Duff search.

Identified papers that I need to screen/comment:

  • Look into Apparently contains something on hypnosis and brain injury
  • Appel PR: Performance enhancement in physical medicine and rehabilitation. Am J Clin Hypn 35:11-19, 1992

Highlight these as best-quality (not necessarily “very good”!) publications in their field:

  • Lindeløv
  • Irawan
  • Duff
  • Cedercreutz
  • Laidlaw
  • Appel (2003)
  • Wagstaff

Hypnosis and brain injury: where to find stuff

This post is a continually updated list of important communications on research following our paper in Brain entitled “Improving working memory performance in brain-injured patients using hypnotic suggestion.”

Scientific reports

All my/our articles have associated free data and analysis. I encourage everyone to scrutinize this, e.g., with alternative analyses, and let me know what you conclude. Please notice that a pre-print is the author’s manuscript before peer-review. So it may have weaknesses that will be corrected through peer-review. Sometimes, peer review also obscures it a bit, so there are pros and cons.

My blogs with further info

  • A list of published scientific literature on hypnosis and brain injury. Three papers support the positive effect of hypnosis on cognitive sequelae following acquired brain injury. Many more have been published on motor rehabilitation, aphasia, pain, dementia, etc.
  • An anti-hype blog post: Anticipates some potential overinterpretations by the general public (particularly journalists, therapists, and patients) and counter them.
  • Answers to frequently answered questions by patients, relatives and rehabilitation professions: English and Danish.

Press and public dissemination

  • Spot on Danish national television, including a case with a 19-year old man who had sustained a traumatic brain injury in a high-speed car crash two years before enrollment in the experiment. The spot is accompanied by two articles and a radio spot (also Danish). Our impression is that this case is in the top 30% on real-life improvement, i.e. not too unrepresentative.
  • Oxford University Blog: A summary for the general public. It includes a back-of-the-envelope estimation of how much you should update your belief based on this study alone.
  • This study has been featured in multiple Danish papers, but this contains no new information that isn’t contained in the above. See my press appearances here.

Can I get the manuscript / are new studies ongoing?

We plan to make the hypnosis scripts available to everybody eventually. On the other hand, we want to avoid putting it “out in the wild” if it somehow turns out to be a fluke. So for now, we pursue a strategy where we only make non-published details about the intervention and the hypnosis scripts available to institutions/companies who can and will evaluate the effectiveness of the scripts systematically.

If you’re such an institution, we’d be eager to set up a collaboration. For example, Tryg Foundation just funded an RCT at Jobkompagniet Silkeborg which will include 90 patients. The first results are expected to be published around January 2021 with an additional report in the summer of 2022. The design and outcome measures simultaneously satisfy research purposes and Jobkompagniet’s core mission.

We expect to stick to this institution-and-evaluation-only strategy for 2-4 years until enough evidence has accumulated that we feel confident about the clinical effectiveness of hypnosis following acquired brain injury. If you’re a private therapist, if you have suffered an acquired brain injury, or if you’re a relative, we will ask you to wait until we have this evidence. Also, see FAQ and answers in the previous section.

What our paper on hypnosis following brain injury does not show

We just published a paper in Brain entitled “Improving working memory performance in brain-injured patients using hypnotic suggestion.” We argue that for patients with acquired brain injury, hypnotic suggestion which asks the patient to recover an ability to concentrate and remember improves working memory performance. I also reported the study and the results at the Oxford University Press blog, including an estimate of how skeptical you should be. We expect quite some publicity – and perhaps even hype – around the results of this paper.

Hype and overinterpretation work for advertising but not for science. In this post, I will try to counter some potential misunderstandings. We are incredibly excited about our findings. We just want to make sure that the public is excited for the right reasons and at the right level. As I argued on the OUP blog post, the appropriate state of belief is probably that of a “pessimist turned hopeful” who awaits further data to decide whether to leave the pessimistic stance or keep it. Given that brain injury constitutes the second- and third-largest health-related cost in the world, even a small hope is quite substantial.

Before I continue, I want to highlight that this research was a joint effort by Professor Morten Overgaard, hypnotist Rikke Overgaard, and me. The project was funded by the European Research Council and the Karen Elise Jensen Foundation and organized under Cognitive Neuroscience Research Unit at Center for Functionally Integrative Neuroscience and Aalborg University. The following reflect the views of all authors.

This study does not show that subjects were “cured”

The participants in our study improved to the population average in measures of working memory, which is an important but not all-encompassing cognitive function. We did not assess other domains such as psychological trauma, physical impairment, etc. because we did not target the hypnosis at these domains and therefore it was not part of the research question. Therefore, we cannot make any data-based claims about the effect of hypnosis on those domains.

Hypnosis does not involve anything “mystic” or otherwise “out of this world”

On the gray market of hypnotists, it is all too common to see the same persons offering regression to previous lives, contact with the dead, healing auras, etc. As a scientist, I reject this. In our experiment, the hypnotist sat in a chair and read aloud from a piece of paper. The patient sat in another chair and listened. There’s only a vibrating vocal chord, sound moving through the air, hitting the eardrums of the patient, and then sensory transduction to action potentials in the brain. From there, we strongly expect that the mechanism underlying the effect will eventually be identified among the on-shelf phenomena in psychology and neuroscience, e.g. neural plasticity working bottom-up, unlearning learned non-use, using a different strategy/realization of the same surface behavior, etc. The only novelness of our findings, if they replicate, would then be that these mechanisms apply to brain injury with a large effect size. There’s a long and serious research history on hypnosis in the top neuroscience journals by top researchers. See e.g. this 2013-paper in Nature Reviews Neuroscience by Oakley & Halligan. This is the line of research we are continuing, and it is very different from the current public perception of what hypnosis is.

The cognitive consequences following acquired brain injury are not unreal or hypocrisy

Some may say “if it’s that easy to recover, then it wasn’t a real problem” and perhaps even put the patient at fault. I hope you would agree with me that such a claim would be straight up ridiculous. First, such a claim would entail a psychology-only understanding of brain injury, and since we do now know the mechanism of why hypnotic suggestion works, this remains an open question. Second, even if it turns out that the cognitive impairment following acquired brain injury somehow can be described in purely psychological terms, this does not change the seriousness of the condition. PTSD is not less severe or hypocrisy because it has a psychogenic origin.

No direct evidence of clinical effectiveness (yet)

Neuropsychological test have surprisingly low predictive value for the ability to participate in society, e.g. returning to work, living independently, etc. which is often the primary criterion of clinical success in rehabilitation (sorry, psychologists!) We did not assess the latter directly, but we plan to this in an in-progress follow-up experiment. However, we do have anecdotal evidence that targeted hypnotic suggestion could be effective for participation. Many of the patients returned to us with reports of getting jobs, beginning or finishing education, not getting exhausted from grocery shopping and family parties, etc. This effect was immediate for some and slower for others. I recall one case where the patient only realized that there had been an improvement when the spouse pointed to very tangible evidence such as no more bruises from inattentively walking into stuff. Similarly, an independent psychologist was inspired by our findings and used hypnosis on two brain injured clients with excellent clinical results. But these reports are prone to selection bias (only the positive cases report back) and neglecting base-rate improvements (some would have improved anyway). We need direct evidence on clinical effectiveness, and we don’t have that now.

No direct evidence that hypnosis drives the effect (yet)

In casual talk, it’ll be easy to say that “hypnosis improved working memory.” We even do this ourselves. However, it does not follow directly from our design since both the targeted suggestion procedure and our non-targeted (intended as placebo) suggestion procedure was administered under hypnosis. We did not deliver the same treatment in a non-hypnotic setting (the so-called London-Fuhrer design). So it remains possible that hypnosis is not necessary. From the empirical literature, however, it is generally found that hypnosis boosts the effect of suggestion (though it’s disputed why; some of it is just that the Gandhi-Oakley finding that the word “hypnosis” increases suggestibility in and of itself). My best guess is that hypnosis adds considerably to the effect given that, if not, the effect of suggestion on working memory performance would have been discovered a long time ago in studies of psychotherapeutic treatment following acquired brain injury.


$$\sqrt{2}$$ is superior to Bessel’s correction

… for the estimation of the population standard deviation. That is, if you substitute $$n – 1$$ with $$n – \sqrt{2}$$, you get a much less biased estimate of the population SD. I just stumbled upon this when I desperately (!) looked to frequentist methods because of convergence problems with my bayesian model. The details can be seen in my post on Cross Validated about this curious finding as well as some excellent answers/elaborations.

I’m re-posting the simulation results here, just because they’re pretty and I want some content on this blog.

TL: no correction. TR: Bessel’s correction. BL: $$\sqrt{2}$$ correction (superior). BR: 1.5. Red: real population sd. Blue: estimated sd (corrected). Gray lines indicate different sample size with 3000 simulations per sample size. Click on the image to view the script.

Naturally, $$\sqrt{2}$$ doesn’t outperform the analytically correct solution but it is a surprisingly good approximation. For larger sample sizes (n > 10), $$n – 1.5$$ becomes superior. In any case, it’s a nice reminder that Bessel’s correction does NOT magically make the sample SD into a population SD as is currently taught in many statistics classes.

I’m considering adding this fun-fact to the Wikipedia page on unbiased estimation of the standard deviation, where you can read more about the issue of bias in frequentist estimation.