[home](./index.md) ------------------ *author: niplav, created: 2019-08-03, modified: 2021-01-01, language: english, status: in progress, importance: 2, confidence: unlikely* > __Members of the NoFap movement often claim that abstinence from > masturbation increases male attractiveness. Experimental evidence is > collected and shows that \_.__ Abstinence from Masturbation and Success from Cold Approach =========================================================== > interesting things happen along borders–transitions–not in the middle where everything is the same *– [Neal Stephenson](https://en.wikipedia.org/wiki/Neal_Stephenson), [“Snow Crash”](https://en.wikipedia.org/wiki/Snow_Crash), 1992* Abstract -------- Members of the [NoFap community](https://en.wikipedia.org/wiki/NoFap) frequently claim that male physical attractiveness is causally influenced by the frequency and duration since the last occurence of masturbation. I present a method to test this claim (albeit imperfectly) by approaching 200 people in the street after 90 days of abstinence from masturbation and asking them for a date, and 200 again after a week of daily masturbation. The results are analyzed using a two-sample [Student's t-test](https://en.wikipedia.org/wiki/Student%27s_t-test) and various [descriptive statistical methods](https://en.wikipedia.org/wiki/Descriptive_statistics) and find that \_. Examples for the Claim ----------------------- To prevent the accusation of [straw-manning](https://en.wikipedia.org/wiki/Straw_man) the views of the NoFap community, I hereby present comments that broadly make the claim that "male abstinence from masturbation results in higher attractiveness, even with fixed behavior." The comments below were found by searching the [/r/NoFap](https://old.reddit.com/r/NoFap/) subreddit on reddit (one of the biggest NoFap communities on the internet) for the keywords "attractiveness" and "attractive" and collecting comments and posts from NoFap members that claim the practice had a positive influence on their attractiveness. Because the comments were hand-picked (with regard to the number upvotes), I tried including critical views or negative reports when they arose in the comment threads to present an even-handed picture of the views of the community. Of course, a survey would have been more informative. > Yesterday i was at a party and im currently on 12 days nofap. Normally this really never happens but a girl wanted to Kiss me. I think it was because of nofap. *– [marijn420_gotu](https://old.reddit.com/user/marijn420_gotu), [“Nofap really makes you more attractive”](https://old.reddit.com/r/NoFap/comments/bluepi/nofap_really_makes_you_more_attractive/) on [/r/NoFap](https://old.reddit.com/r/NoFap) (27 upvotes), 2019* Another user recounts a similar story: > I’m minding my own business in the laundromat, keeping to myself, this girl walks up to me and asks me if I can drop her off to her house, that she lives 2 minutes away. I look at her and ask her what made her come up to a complete stranger and ask such a thing, she says she doesn’t know, we have a little laugh. I drop her off, help her unload her laundry, and as I’m almost driving off she asks me if I need to head back, which I did, my laundry had 10 minutes left in the wash. I realized as I driving away that this stranger was literally inviting me in her house to get smashed, but I was genuinely trying to her [sic], I had no ulterior motives, and I wasn’t even that attracted to her. They literally smell it on you. I’m also 119 days hard mode. This shit is crazy. *– [TheMasterKey20](https://old.reddit.com/user/TheMasterKey20), [“They smell it on you.”](https://old.reddit.com/r/NoFap/comments/bzj8ra/they_smell_it_on_you/) [/r/NoFap](https://old.reddit.com/r/NoFap) (237 upvotes), 2019* Note that the poster does not mention any specific action on his side. A [commenter](https://old.reddit.com/user/AustinReckless) [suspects](https://old.reddit.com/r/NoFap/comments/bzj8ra/they_smell_it_on_you/eqt5bsv/): "Must be able to smell the pheromones." (23 upvotes). Another user [makes a similar claim](https://old.reddit.com/r/NoFap/comments/bzj8ra/they_smell_it_on_you/eqti6xg/). There are also strong claims on a direct relation between masturbation and attractiveness: > I was on a 10 day streak before I took a week off from work. When returning people were saying "I look tired" (I Fapped 5 times in the 2 days before returning to work). And the chick that I work with that is normally all walkative and flirty with me was not so much and seemed to act like I wasn't even there LOL. […] On a 20 day streak one time I had one after another woman looking at me. I recall one was a receptionist at an office building and when I went in and walked up to her coworker she was just gazing at me almost that bite your lip look, and honestly looked like she was getting wet. […] It's almost comical how woman treat me when on a streak, and when off one. It's night and day different. […] off a streak or over ejaculation several times in a day, it seems woman look past me and don't ever look at me. I know it has something to do with the pheromones you emit when not spilling your seed needlessly all the time […]. *– [cee9](https://old.reddit.com/user/cee9), [“Fapping ruins your attractiveness.”](https://old.reddit.com/r/NoFap/comments/3mt0nu/fapping_ruins_your_attractiveness/) (95 upvotes), 2015* Note that all typos and grammatical mistakes could be affixed with "[sic]" (the comment was copy-pasted). This user claims there is a noticeable difference between the behavior of women in regard to abstinence from masturbation, and attributes this difference to "pheromones". Another user claims this ["difference in how people (both men and women) respond"](https://old.reddit.com/r/NoFap/comments/3mt0nu/fapping_ruins_your_attractiveness/cvhvbdc/) is visible in both genders. Another commenter [agrees](https://old.reddit.com/r/NoFap/comments/3mt0nu/fapping_ruins_your_attractiveness/cvhyqwb/), but a response is critical: > I lost my nearly 28 day streak last night. Didn't notice a difference apart from thinking more aggressive at times and thinking average women were hot\wanting to bang them. >Nobody ever approached me or started convos. >Will try longer this time. *– [enrodude](https://old.reddit.com/user/enrodude), [comment](https://old.reddit.com/r/NoFap/comments/3mt0nu/fapping_ruins_your_attractiveness/cvhzmd1/) on [“Fapping ruins your attractiveness.”](https://old.reddit.com/r/NoFap/comments/3mt0nu/fapping_ruins_your_attractiveness/) on [/r/NoFap](https://old.reddit.com/r/NoFap/) (6 upvotes), 2015* Other users try to condone him. Since the claims are quite repetitve, I will now just list them and write down important key words from the claim (especially the time it takes for the effect to take place, the effect itself and the given explanation). > Sorry to all the doubters or people that it hasn't worked for. But this is my fourth time getting to 40+ days. And EVERY DAMN TIME I get to this point girls start hitting on me. > Some people say it's placebo. But to that I say (even if that is the case) well then it still works. > Whether it's psychological or physiological is irrelevant. *– [topdizzel](https://old.reddit.com/user/topdizzel), [“I'm sorry, but no fap just fucking works”](https://old.reddit.com/r/NoFap/comments/9treo6/im_sorry_but_no_fap_just_fucking_works/) on [/r/NoFap](https://old.reddit.com/r/NoFap) (606 upvotes), 2018* Effect takes place after 40 days, women started hitting on him, reason: possibly placebo. A commenter agrees: > I will vouch for this. I'm on 84 days (nearly 90!) And I keep getting hit on. *– [a_jedi_in_bed](https://old.reddit.com/user/a_jedi_in_bed), [comment](https://old.reddit.com/r/NoFap/comments/9treo6/im_sorry_but_no_fap_just_fucking_works/e8yos6k/) on [“I'm sorry, but no fap just fucking works”](https://old.reddit.com/r/NoFap/comments/9treo6/im_sorry_but_no_fap_just_fucking_works/) on [/r/NoFap](https://old.reddit.com/r/NoFap) (123 upvotes), 2018* Effect takes place after at least 84 days, women start hitting on him. > Haha I'd wish that'd happen to me. I've never been able to attract women, but that's just how it is. […] *– [meditate03](https://old.reddit.com/user/meditate03), [comment](https://old.reddit.com/r/NoFap/comments/9treo6/im_sorry_but_no_fap_just_fucking_works/e8yo7xd/) on [“I'm sorry, but no fap just fucking works”](https://old.reddit.com/r/NoFap/comments/9treo6/im_sorry_but_no_fap_just_fucking_works/) on [/r/NoFap](https://old.reddit.com/r/NoFap) (126 upvotes), 2018* This commenter disagrees. > I like to say they can 'smell the no fap' when really you're just being your true self, they can see you carry yourself in high regard and that shit is like crack for them. *– [NZbakedbanana](https://old.reddit.com/user/NZbakedbanana), [comment](https://old.reddit.com/r/NoFap/comments/9treo6/im_sorry_but_no_fap_just_fucking_works/e8yr8p0/) on [“I'm sorry, but no fap just fucking works”](https://old.reddit.com/r/NoFap/comments/9treo6/im_sorry_but_no_fap_just_fucking_works/) on [/r/NoFap](https://old.reddit.com/r/NoFap) (126 upvotes), 2018* This commenter attributes the higher attractiveness to higher self-confidence. > All men are trying to find ways to make themselves more attractive to the females around them. It’s a constant battle to outmaneuver the other guys around you. Luckily, most guys don’t know how NoFap can cause extreme levels of attraction. Here’s how this works; while you were doing PMO, you were masking your inner beauty. You were hiding your personality from all the girls around you. Once you stop doing PMO, talking and bonding with other people becomes much easier. Your outer look is only a reflection of your inner thoughts. Girls have a sixth-sense about knowing how powerful a guy is. Power is the thing that attracts girls the most. The more in control you are, the more girls are going to be able to sense this. […] To sum up – NoFap is going to make you more attractive to the opposite sex […] *– [debasish_patro0007](https://old.reddit.com/user/debasish_patro0007), [“Can NoFap Really Make You More Attractive?”](https://old.reddit.com/r/NoFap/comments/bl2ioe/can_nofap_really_make_you_more_attractive/) on [/r/NoFap](https://old.reddit.com/r/NoFap) (107 upvotes), 2019* It seems like this redditor claims that micro-expressions are the cause of higher attractiveness, though the "sixth sense" could refer to more "spiritual" way of transmitting information. A commenter specifically refers to micro-expressions: > It doesn't make you "more attractive" in the physical sense, although it might support that as a side effect but not directly.[…] > Here's the rundown on how it "makes men more attractive"; You constantly transmit micro expressions. You are a walking transmitter whether you like it or not. Women, they have a sharper decoder that men have, and they are much better, subconsciously, decoding the codes you transmit.[…] > Fapping, essentially, other than a huge surge of dopamine that makes you lazy and self destructive, is also a simulator for the mind that you are getting laid. […] As long as you see naked women, hear them do the thing, and have your peepee touched, your mind perceives it as sex. […] So, when your mind is extremely satisfied (sex every day would be a fucking luxury for a caveman), your mind stops "supporting" your sexuality and the need to attract females. Your thoughts and desires become mundane, you stop focusing on yourself, you care less about your physique and looks, and you tend to communicate with females with a much softer sexual aggression […]. […] when you are in a long Nofap period, your mind is being rewired to suddenly care about your reproduction and gene survival, so your communication becomes more aggressive, therefore attractive. […] your body language improves.[…] > This works with nofap too. When you're deprived of sex, your mind will help you make yourself attractive and will push you to desire sex. *– [NorsemanLewis](https://old.reddit.com/user/NorsemanLewis), [comment](https://old.reddit.com/r/NoFap/comments/bl2ioe/can_nofap_really_make_you_more_attractive/emlb1zu/) on [“Can NoFap Really Make You More Attractive?”](https://old.reddit.com/r/NoFap/comments/bl2ioe/can_nofap_really_make_you_more_attractive/) on [/r/NoFap](https://old.reddit.com/r/NoFap) (145 upvotes), 2019* They also talk about increased amounts of flirting in conversations, higher sexual aggressiveness and higher motivation to find a partner, which should at least partially be testable during cold approach. They don't seem to consider the possibility that masturbation is not a feature of modern civilisation, but rather a biological instinct. Widespread pornography, on the other hand, is a feature of modern civilisation. Another commenter refers to this baseless speculation as "science": > A healthy dose of actual science on here. This post should be stickied IMO. Everyone on here would benefit so much if they understood the underlying mechanics of our natural biology and neuro chemistry. The NoFap movement would never have kicked off like it did if there wasn't actual science to back it up. *– [cheezeebreed](https://old.reddit.com/user/cheezeebred), [comment](https://old.reddit.com/r/NoFap/comments/bl2ioe/can_nofap_really_make_you_more_attractive/emm4x5r/) on [“Can NoFap Really Make You More Attractive?”](https://old.reddit.com/r/NoFap/comments/bl2ioe/can_nofap_really_make_you_more_attractive/) on [/r/NoFap](https://old.reddit.com/r/NoFap) (4 upvotes), 2019* A commenter claiming to be a scientist says: > Well essentially due to the addiction. It causes lowered sensitivity to neurotransmitters such as dopamine and serotonin this causes lowered motivation, dry skin, depression and anxiety. As a result of quitting porn ones sensitivity to neurotransmitters return and their neuropathways start functioning correctly (hence no brain fog) *– [ReAp_QS_Killzz](https://old.reddit.com/user/ReAp_QS_Killzz), [comment](https://old.reddit.com/r/NoFap/comments/bl2ioe/can_nofap_really_make_you_more_attractive/eml1sr9/) on [“Can NoFap Really Make You More Attractive?”](https://old.reddit.com/r/NoFap/comments/bl2ioe/can_nofap_really_make_you_more_attractive/) on [/r/NoFap](https://old.reddit.com/r/NoFap) (19 upvotes), 2019* If this is true, then abstinence from masturbation should lead to increased mental health, but except "clearer skin" there is no obvious way in which this would increase attractiveness. Another commenter [claims](https://old.reddit.com/r/NoFap/comments/bl2ioe/can_nofap_really_make_you_more_attractive/emli3ml/) that his "face has this droopy tired look" during periods of masturbation. > Increased sexual interest from others. Many rebooters claim they notice more signals of sexual attraction directed at them: more looks, more smiles, more flirting. Many believe this to be a side-effect of feeling more confident, while others theorize that rebooters simply notice more signals than they did when they were obsessed with porn. *– [NoFap.com](https://nofap.com/), [“Rebooting from Porn Addiction”](https://nofap.com/rebooting/), 2017* ### The Broad Picture A broad picture emerges: NoFap claims that long-term abstinence from masturbation has noticeable effects on male attractiveness for women, this effect emerges at around 40 days or more (and doesn't diminish with the time since the last masturbation increasing further), it also has an effect on other men, though this is not really elaborated further. The effects are noticeable. The reasons given for this increase in attractiveness are as follows: * [Microexpressions](https://en.wikipedia.org/wiki/Microexpression) * [Pheromones](https://en.wikipedia.org/wiki/Pheromone) * [Placebo effect](https://en.wikipedia.org/wiki/Placebo) * Higher effort in searching partners Two of these reasons are independent from the attitude of a person towards NoFap (pheromones and microexpressions), while the others are dependent on being a NoFap enthusiast. Given these claims, it should be possible to at least somewhat check the claims made by members of the NoFap community. ![Nice Hypothesis](img/masturbation_and_attractiveness/sagan_test_meme.png "(Zooming into face of Carl Sagan, looking smug) “Nice Hypothesis you have there. Would be a shame if someone were to test it”") (Taken from [Scott Alexander (2013)](https://slatestarcodex.com/2013/10/20/the-anti-reactionary-faq/ "The Anti-Reactionary FAQ")) Method ------ Relevant information about me: I am a male living in a european country, my age being in the early twenties. I seem to fall into the same demographic as most members of the NoFap community. To test the claims by the NoFap community, I performed a small self-experiment. Data was collected as follows: I abstained from masturbating and watching pornography from 2021-01-01T02:00 to \_, resulting in >90 days of abstinence from masturbation (which is also the period [recommended by the NoFap community](https://nofap.com/rebooting/): "NoFap’s gold standard of success is our 90-day reboot."). From \_ to \_, I went on the streets of a major european city and approached 100 people I read as men and 100 people I read as women alternatingly with the words > Hi, I know this is really spontaneous, but I just saw you and thought you looked really nice. What is your name? The other person answered with their name, and I replied with > Nice to meet you, . To make a long story short, I'd like to take you out on a date sometime. When are you free? In case of them agreeing to go on a date, a time and place were agreed upon, and I came to the date to check whether they had showed up. The people who were approached were chosen by their attractiveness to the author. In the week following the last approach, I masturbated once every day with the aid of pornography. Afterwards, I repeated the procedure of approaching 100 men and 100 women with the same words from \_ to \_. Data that was logged included date and time of day (in [ISO-8601](https://en.wikipedia.org/wiki/ISO_8601)), whether the approach was after abstinence from masturbation or after the one-week period of masturbation (1 for the part after abstinence, and 0 for the part after masturbation), perceived gender of the person approached ("m", "f" or "o"), and how far the interaction went: * 1 (ignored): the person walked past and did not react * 2 (stopped): the person stopped, but didn't answer any question (started laughing or walking away) * 3 (name): person gave name, but then started walking away * 4 (rejection): person answered that they were in a relationship/had no interest * 5 (flake): person gave contact information, but did not reply * 6 (date): person showed up to the date Results were logged in a [CSV](https://en.wikipedia.org/wiki/Comma-separated_values). Results Analysis ----------------- The raw data is available [here](./data/masturbation_attractiveness.csv). ### Visualizing the Results Cold approach is a conversion funnel: there are a number of different stages an approachee goes through, and each one can fail. This way, one can visualize how far the interaction went by making a bar graph of the people dropping out at a certain stage (ignoring the approach, stopping but not giving a name, giving a name but not agreeing to come on a date, agreeing to come on a date but flaking, and showing up to a date). Showing up to the date was considered a condition of success, but one could imagine further steps like having sex, getting into a relationship with the person, getting married with the person and having children with the person, though these were deemed excessive and out of the scope of a simple self-experiment. The bargraph below shows how many people were lost at which stage of the funnel, ignoring gender. The white bars show the numbers during a period of abstinence from masturbation, after 90 days of abstinence, the black bars show the numbers after a period of weekly masturbation. Code: .l("nplot") .l("./load.kg") cgrid(["ignored" "stopped" "name" "rejection" "flake" "date"];[0 200 10]) text(20;400;"white: during abstinence, before masturbation, black: after masturbation") fillrgb(0;0;0) {bar(2*x;during.stag@x;12)}'!6 fillrgb(1;1;1) {bar(1+2*x;after.stag@x;12)}'!6 draw() ![Gender non-specific loss in different stages of the funnel](./img/masturbation_and_attractiveness/dur_after_bar.png "Gender non-specific loss in different stages of the funnel.") *Gender non-specific loss in different stages of cold approach* Very similar diagrams can be made for male and female data points: Male: .l("nplot") .l("./load.kg") cgrid(["ignored" "stopped" "name" "rejection" "flake" "date"];[0 100 10]) text(10;400;"light blue: during abstinence, before masturbation, dark blue: after masturbation") fillrgb(0.4;0.4;1) {bar(2*x;duringm.stag@x;12)}'!6 fillrgb(0;0;0.6) {bar(1+2*x;afterm.stag@x;12)}'!6 draw() ![Male loss in different stages of the funnel](./img/masturbation_and_attractiveness/dur_after_m_bar.png "Male loss in different stages of the funnel.") *Male loss in different stages of cold approach* Female: .l("nplot") .l("./load.kg") cgrid(["ignored" "stopped" "name" "rejection" "flake" "date"];[0 100 10]) text(20;400;"light red: during abstinence, before masturbation, dark red: after masturbation") fillrgb(1;0.4;0.4) {bar(2*x;duringf.stag@x;12)}'!6 fillrgb(0.6;0;0) {bar(1+2*x;afterf.stag@x;12)}'!6 draw() ![Female loss in different stages of the funnel](./img/masturbation_and_attractiveness/dur_after_f_bar.png "Female loss in different stages of the funnel.") *Female loss in different stages of cold approach* Another possible method could be to visualize cumulative survival rates for the different stages by percentage by showing a [Kaplan-Meier plot](https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator). The overall graph for this would look like this: .l("nplot") .l("./load.kg") cgrid(["ignored" "stopped" "name" "rejection" "flake" "date"];[0 1 0.1]) text(27;200;"light gray: during abstinence, before masturbation, black: after masturbation") setwidth(4) setrgb(0;0;0) plot({during.cumperc@(_x)-1}) setrgb(0.8;0.8;0.8) plot({after.cumperc@(_x)-1}) draw() ![Survival percentages for different stages, overall](./img/masturbation_and_attractiveness/survival.png "Survival percentages for different stages, overall") *Survival percentages for different stages, overall* .l("nplot") .l("./load.kg") cgrid(["ignored" "stopped" "name" "rejection" "flake" "date"];[0 1 0.1]) text(10;200;"light blue: during abstinence, before masturbation, dark blue: after masturbation") setwidth(4) setrgb(0.4;0.4;1) plot({duringm.cumperc@(_x)-1}) setrgb(0;0;0.6) plot({afterm.cumperc@(_x)-1}) draw() ![Survival percentages for different stages, men](./img/masturbation_and_attractiveness/survival_m.png "Survival percentages for different stages, men") *Survival percentages for different stages, men* .l("nplot") .l("./load.kg") cgrid(["ignored" "stopped" "name" "rejection" "flake" "date"];[0 1 0.1]) text(27;200;"light red: during abstinence, before masturbation, dark red: after masturbation") setwidth(4) setrgb(1;0.4;0.4) plot({duringf.cumperc@(_x)-1}) setrgb(0.6;0;0) plot({afterf.cumperc@(_x)-1}) draw() ![Survival percentages for different stages, women](./img/masturbation_and_attractiveness/survival_f.png "Survival percentages for different stages, women") *Survival percentages for different stages, women* ### Descriptive Results Before testing the hypotheses, one can compare the results using very simple descriptive methods. For this purpose, I used the mean and the standard deviation to compare the different parts of the dataset. Here the table for the different mean values and their variances in parentheses (the botttom right cell contains the overall mean value):
during after
f μ_duringf (var) μ_afterf (var) μ_f (var)
m μ_duringm (var) μ_afterm (var) μ_m (var)
μ_during (var) μ_after (var) μ (var)
As one can see, \_. The code for calculating these can be found [here](./code/masturbation_and_attractiveness/load.kg). ### Testing the Hypothesis The NoFap community claims that abstinence from masturbation increases male physical attractiveness for women. This means that cold approach should be more successful after a long period of abstinence from masturbation than after a period of sustained masturbation. This assumption generates three hypotheses: 1. H₀: `$\mu_{during} \le \mu_{after}$` 2. H₁: `$\mu_{during} = \mu_{after}$` 3. H₂: `$\mu_{during} \ge \mu_{after}$` The result implied by the views of the NoFap community would be that H₀ would definitely be rejected, and that it would be very likely that H₁ would also be rejected. Note that these hypothesis are not exclusive, and can all be accepted at the same time. It is merely the case that if a hypothesis gets rejected, the probability that it got rejected although it is true is lower than a given percentage (usually and also in this case 5%). I used a two-sample Student's t-test to test the hypotheses, under the assumption that the distribution of results from cold approach was roughly [normally distributed](https://en.wikipedia.org/wiki/Normal_distribution) and that the [variance](https://en.wikipedia.org/wiki/Variance) of the two sample sets was also roughly equal. As one can see from the figures, this assumption of normal distribution \_. To calculate Student's t-test, let `$\{X_{1}, \cdots, X_{m}\}=X_{i}\sim{\cal{N}}(\mu_{X}, \sigma_{X})$` be the first sample, and `$\{Y_{1}, \cdots, Y_{n}\}=Y_{i}\sim{\cal{N}}(\mu_{Y}, \sigma_{Y})$` the second sample. Let then `$T$` be
$$T:=\sqrt{\frac{n+m-2}{\frac{1}{m}+\frac{1}{n}}}*\frac{\overline{X}-\overline{Y}}{\sqrt{(m-1)*S_{X}^{2}+(n-1)*S_{Y}^{2}}}$$
where `$\overline{X}$` and `$\overline{Y}$` are the sample mean of the two sample sets, and `$S_{X}^{2}$` and `$S_{Y}^{2}$` are the sample variances of the two sample sets. Different hypotheses are then tested by comparing `$T$` to the [quantile function](https://en.wikipedia.org/wiki/Quantile_function) of [Student's t-distribution](https://en.wikipedia.org/wiki/Student%27s_t-distribution). In this case, our sample sizes are bigger than 30, and so the quantile function of Student's t-distribution can be approximated using the quantile function of the normal distribution. The two-sided Student's t-test can thus be implemented (the full code for different hypothesis testing can be found [here](./code/masturbation_and_attractiveness/hypo.kg): .l("nstat") .l("math") tstt::{t::sqr(((#y)+(#x)-2)%(%#x)+%#y)*(mu(x)-mu(y))%sqr((((#x)-1)*svar(x))+((#y)-1)*svar(y)); :[t>qf(1-z);.p("μ_X≤μ_Y rejected (p≤",($z),")");.p("μ_X≤μ_Y accepted (p≤",($z),")")]; :[(#t)>qf(1-z%2);.p("μ_X=μ_Y rejected (p≤",($z),")");.p("μ_X=μ_Y accepted (p≤",($z),")")]; :[t