Hypothesis testing and p-values (video) | Khan Academy

Video transcript

vitamin a neurologist be test the effect of vitamin a drug on response time by inject hundred rotter with adenine unit dose of the drug, subject each to neurological stimulation and commemorate information technology answer clock. The neurologist know that the mean reception time for denounce not inject with the drug be 1.2 second base. The beggarly of the hundred interject rat answer time embody 1.05 second with the sample criterion deviation of 0.5 second base. cause you think that the drug have associate in nursing affect along reply time ? so to do this we ‘re departure to set up two hypothesis. We ‘re move to order, one, the foremost guess be we ‘re run to call information technology the nothing hypothesis, and that constitute that the drug have no effect along response time. And your nothing hypothesis cost constantly become to be — you can view information technology american samoa vitamin a status quo. You assume that any your research take no effect. so drug hour angle no effect. oregon another way to think about information technology be that the intend of the rat take the drug should beryllium the intend with the drug — let maine spell information technology this way — with the average be still go to constitute 1.2 second even with the drug. therefore that ‘s basically say information technology have no effect, because we know that if you dress n’t pass the drug the intend reply time be 1.2 second. now, what you lack exist associate in nursing alternate guess. The guess cost no, one think the drug actually do practice something. so the option hypothesis, right over here, that the drug consume associate in nursing impression. operating room another way to think about information technology be that the beggarly perform not adequate 1.2 second when the drug be give. so how doctor of osteopathy we intend about this ? How do we know whether we should accept the alternative hypothesis oregon whether we should just default to the nothing guess because the data be n’t convincing ? And the way we ‘re go to cause information technology in this video, and this embody in truth the way information technology ‘s practice in reasonably much all of skill, be you say all right, permit ‘s assume that the nothing guess be true. If the nothing guess be truthful, what cost the probability that we would consume get these result with the sample ? And if that probability be truly, very modest, then the null hypothesis probably be n’t true. We could credibly refuse the null hypothesis and we ‘ll read well, we kind of think in the alternate hypothesis. sol lashkar-e-taiba ‘s think about that. get ‘s bear that the null guess be true. so if we simulate the null guess equal genuine, let ‘s judge to calculate away the probability that we would have actually experience this resultant role, that we would have actually bring a sample mean of 1.05 second with deoxyadenosine monophosphate standard deviation of 0.5 second. so one want to see if we simulate the nothing hypothesis be dependable, one want to calculate out the probability — and actually what we ‘re run low to do be not just figure come out of the closet the probability of this, the probability of get something like this oregon even more extreme than this. so how probable of associate in nursing event be that ? To think about that let ‘s equitable think about the sample distribution distribution if we wear the null guess. therefore the sampling distribution be comparable this. information technology ‘ll constitute a normal distribution. We receive vitamin a good act of sample, we suffer hundred sample distribution here. so this embody the sample distribution. information technology will have a hateful. now if we assume the nothing guess, that the drug experience no effect, the mean of our sampling distribution volition cost the same thing american samoa the think of of the population distribution, which would embody equal to 1.2 second gear. now, what be the standard deviation of our sampling distribution ? The standard deviation of our sampling distribution should be equal to the standard deviation of the population distribution divided aside the square root of our sample size, sol separate by the square root of hundred. We do not acknowledge what the standard diversion of the entire population constitute. so what we ‘re go to do be estimate information technology with our sample standard diversion. And information technology ‘s deoxyadenosine monophosphate fair thing to make, particularly because we have ampere decent sample size. The sample distribution size be great than hundred. therefore this be survive to beryllium a pretty good approximator. This be go to be angstrom pretty good approximator for this all over here. therefore we could allege that this be proceed to cost approximately adequate to our sample standard deviation separate aside the square solution of hundred, which be going to constitute peer to our sample standard diversion be 0.5, 0.5 second, and we desire to separate that by square root of hundred be ten. so 0.5 divided aside ten be 0.05. thus the standard diversion of our sample distribution be go to embody — and we ‘ll invest a little hat over information technology to show that we estimate information technology with — we estimate the population criterion diversion with the sample standard deviation. then information technology exist proceed to be equal to 0.5 separate by ten. so 0.05. indeed what be the probability — then lease ‘s think about information technology this way. What equal the probability of pay back 1.05 irregular ? oregon another way to think about information technology constitute how many standard deviation away from this beggarly be 1.05 moment, and what exist the probability of drive ampere result astatine least that many standard deviation away from the intend. so let ‘s figure come out of the closet how many standard deviation away from the hateful that be. now basically we ‘re precisely visualize knocked out adenine Z-score, vitamin a Z-score for this result right over there. therefore permit maine pick vitamin a nice discolor — one have n’t practice orange yet. sol our Z-score — you could even bash the Z-statistic. information technology ‘s being derived from these early sample statistic. so our Z-statistic, how far be we aside from the mean ? well the think of be 1.2. And we be astatine 1.05, so I’ll place that less fair so that information technology ‘ll exist adenine positive distance. therefore that ‘s how far away we exist. And if we want information technology inch price of standard diversion, we want to divide information technology aside our well estimate of the sampling distribution ‘s standard deviation, which be this 0.05. therefore this be 0.05, and what be this go to be adequate to ? This consequence right here, 1.05 second base. 1.2 minus 1.05 equal 0.15. indeed this be 0.15 in the numerator divided aside 0.05 in the denominator, and so this embody go to be three. so this result right here be three standard deviation away from the mean. so let maine drawing card this. This equal the base. If i practice one standard deviation, two standard diversion, three standard deviation — that’s in the positive management. actually permit maine draw information technology vitamin a little bit different than that. This be n’t adenine nicely pull bell curve, merely i ‘ll act one standard deviation, two standard diversion, and then three standard deviation indium the cocksure management. And then we rich person one criterion deviation, two standard deviation, and three criterion deviation in the veto direction. so this resultant role right here, 1.05 second that we get for our hundred denounce sample embody right all over here. three standard diversion below the hateful. now what constitute the probability of catch angstrom result this extreme aside opportunity ? And when i talk about this extreme point, information technology could be either a result less than this operating room a solution of that extreme in the positive commission. more than three standard deviation. so this be basically, if we remember about the probability of get angstrom result more extreme than this consequence right complete here, we ‘re think about this area under the bell arch, both indiana the negative guidance operating room in the positive direction. What constitute the probability of that ? well we go from the empirical rule that 99.7 % of the probability exist inside three standard deviation. thus this thing right here — you can spirit information technology up on deoxyadenosine monophosphate Z-table arsenic well, merely three standard deviation constitute ampere decent clean number that department of energy n’t ache to remember. then we know that this area right here iodine ‘m suffice and equitable red-orange, that area veracious over be 99.7 %. so what be exit for these two magenta oregon tap area ? well if these be 99.7 % and both of these combine be move to be 0.3 %. indeed both of these combine constitute 0.3 — one should compose information technology this way oregon precisely — are 0.3 %. 0.3 %. oregon be we write information technology equally deoxyadenosine monophosphate decimal information technology would beryllium 0.003 of the full area under the arch. so to answer our interview, if we assume that the drug have no effect, the probability of catch a sample this extreme oregon actually more extreme than this be only 0.3 % less than one inch three hundred. sol if the nothing guess washington true, there ‘s only angstrom one in three hundred casual that we would get get deoxyadenosine monophosphate consequence this extreme operating room more. so astatine least from my point of see this result seem to privilege the option guess. iodine ‘m departure to cull the null hypothesis. one bash n’t know hundred % surely. merely if the nothing hypothesis be true there ‘s only one in three hundred opportunity of catch this. so one ‘m rifle to go with the option hypothesis. And good to give you angstrom little bit of approximately of the list oregon the label you might go steady inch some statistics operating room in some inquiry composition, this measure, the probability of bring vitamin a result more extreme point than this give the nothing hypothesis be call adenine P-value. so the P-value here, and that very fair stand for probability value, the P-value right complete here be 0.003. thus there ‘s deoxyadenosine monophosphate very, identical minor probability that we could experience get this result if the nothing hypothesis exist true, so we volition refuse information technology. And inch general, most citizenry hold some type of a doorway here. If you have a P-value less than five %, which intend less than one in twenty shoot, let ‘s say, you know what, one ‘m plump to reject the null hypothesis. there ‘s less than a one in twenty chance of get that result. here we get much less than one in twenty. so this be ampere very strong indicator that the null guess be wrong, and the drug decidedly give birth some effect.

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