What Is A P-Value? - Clearly Explained

[@StevenBradburn]

THE ONLINE GUIDE toptipbio.com/what-is-a-p-value/

[@MrAlvarez23]

A P values of .05 means: A. The results would occur by chance 5 out 100 times. B. There is no channge that results are significant C. Only 5% of results were significant Can someone help me

[@Lolwutdesu9000]

To anyone who still doesn't get this, as the video is a little convoluted: the p-value is simply the probability that the results you've obtained from the experimental group (and no, it doesn't just have to be people) is solely due to chance. Ergo, smaller p-value, smaller chance of it just being due to luck/chance.

[@simonchiu3938]

I have always thought that if p is the chance that the experimental group happens given that null hypo. is true, let's say p=0.03/3%. And the alpha is 0.05, where it is the 1-confidence level or the null hypo is 5% unconfident. Then it totally makes sense that the alternative hypo. has 3% chance to happen and why should we reject it when p is smaller than alpha? By your explanation, do you mean that the alternative hypo. only have 3% chance/ the alternative is 97% not happen by chance therefore we reject null hypo.?

[@iamrichlol]

i know i suck at math related topics, but this really makes me feel stupid as I still don't understand. if there was a study and p = 0.050 was the value for a particular instance, what would that mean?

[@sushantgarudkar211]

@@iamrichlol it means 5% result obtained by chance and 95% the result is because of hypothesis

[@rexrex1484]

nice summary

[@meat_soup8590]

@@iamrichlol don't worry, I love math and this hurts my head

[@georgezhang865]

I finished my undergraduate in mathematics this year and now I finally understand what p value means

[@ASMM1981EGY]

Convoluted video, not simple at all for beginners, thank God I'm not a beginner. Simply P-Value is the percentage of Luck and False positives affecting your results instead of your experimented factors. So in an even more simpler way: P-Value % = Luck, the less % the less luck and more real effect of factors experimented by you.

[@Gab-zv9lk]

I understand this in theory, but I don't actually understand how the p=value is calculated? Where are they getting the percentage from, what numbers are they using to calculate it?

[@quanle9133]

@@Gab-zv9lk Maybe this can help kzbin.info/www/bejne/qoXIfoyriJ1qpbc&ab_channel=jbstatistics

[@Crazy123Flame]

Thank you, you are a hero.

[@sssskkkkgggg]

@@Gab-zv9lk kzbin.info/www/bejne/poXQfYSsgrJgZ68 This video shows how p-value is calculated.

[@sssskkkkgggg]

​@@Gab-zv9lk This video shows how p-value is calculated kzbin.info/www/bejne/poXQfYSsgrJgZ68

[@yavorkaludov3661]

Incredibly well explained! The first time you gave the definition for p I had no idea how to interpret it. 5 minutes later I understood the same definition perfectly.

[@StevenBradburn]

Many thanks for your kind feedback

[@sumayyahsalem4554]

I'm not sure how many videos I have watched about this topic, it has been more than 6 hours of me trying to understand it, but THIS, this is the only video that made sense to me, and I finally can say that I understand! TYSM!!

[@mattgardiner313]

I have just come to this in my social sciences degree. I will be watching this video a great many times in the next few day's.

[@ruzzaruzza]

Finally. I've heard it so many times and now I finally understand it! Thanks!

[@qamerkramet4562]

Please explain to me

[@chinedumjoseph9875]

This is the best video that I have watched in the explanation of hypothesis testing. Thanks a million for this video.

[@SufiRepublic]

Finally i got an intuition about p-value, thank you, may the almighty bless you 🙏😊❤️

[@S_R_B-b9l]

YAS! After 3 years of college as a bio student, I finally someone who can actually explain this!

[@nernaykumar8334]

One of the best explanation, the probability would be more interesting if all colleges have teachers like you

[@StevenBradburn]

Thanks Nernay :)

[@krzysztofkosydar4545]

really great explanation - before I had a problem with understanding the p-value. The example with "two worlds" is a great way to explain what it really is. Thank you!

[@fernandoadrianromeroalvare2612]

Perfectly explained! A very didactic video! Thanks a lot!

[@Audrey-yy2ey]

im so grateful to have found this channel

[@StevenBradburn]

Thanks for the feedback Audrey! Glad you find the content useful

[@saswatnayak5023]

I think this is the best video explaining p value. Straight to the point and less technical jargon

[@beatrizbuford4665]

What a great explanation! This is a content area in which I struggle and the visuals and explanations helped me understand the topic more. Thank you!

[@elvintiranbalan5882]

THANK YOU! I m trying to catch up with my studies and your videos helped so much! Also, it would be nice if you make more R programming tutorial as i love the way you explain things. It's really clear

[@StevenBradburn]

Thanks for your feedback. I'll certainly make more R tutorials :)

[@esetekebede237]

I really appreciate the way you bring us the example; this really helped me a lot thankyou!!

[@mdjaffer3286]

Very lucid explanation Now I can understand what p value is atleast to some extent Thanks very much

[@zeroize7174]

This is amazing, thank you! The only thing that would make it even better is maybe a simple explanation of how the p-value is derived in the first place, for this probability to even be identified.

[@NurEnglish]

thank you..eventually i got the understanding..its 3rd video i'm watching and previous ones were not so clear

[@kbansal71]

Boss, p-value of 0.02 is highly significant. P-value is probability of null hypothesis being true. At 0.02 alternate hypothesis gets selected.

[@sadakahmed7945]

Thank you, this was difficult to me to understand, but now I'm well understood from the two lines that you posted.

[@198sivagangas4]

the best video I found on this topic

[@sandeelg_lite]

Well explained. I never ignore liking and subscribing such well explained content.

[@meilingchen5653]

THANK YOU SO MUCH, please keep on making the good exploitational videos.

[@hiteshlalwani1670]

wow! this is the only video that finally helped me get this thanks!

[@calebm9000]

The more I watch this, the more I believe that it would be better to introduce the random noise concept when you were explaining the null hypothesis. So, we formed this null hypothesis BASED ON THE ASSUMPTION that our data were observed due to extraneous factors (random noise), like the mentioned high metabolism gene. If the noise is what contributed to the difference, then we CANNOT assume that the drug worked to reduce weight. IF the observed results were due to random noise, then our p-value tells us that we can repeat this experiment 50 times and only 1 of those times we could get this same (or more extreme) result. This is very unlikely, and so we can be confident in rejecting the null hypothesis and accepting that our results weren't caused by random noise.

[@julianguffogg]

I was too busy looking at those lovely drawings to get it!

[@datroof2262]

Cohen did a great paper on p-values called something like "The Earth is Round p < .05". The p-value is the probability of the DATA (not the hypothesis!) or data more extreme, ASSUMING the null hypothesis is true. That's why effect sizes are important to include, along with confidence intervals. So you get effect size E, the p-value is the probability of that effect size or one larger, assuming there is in "reality" no effect (the null hypothesis). It is p(D|H), not p(H|D)...and to understand the larger context, one needs to understand Bayes' Theorem which logically shows how one adjusts probabilities of hypotheses based on data. Bayes' Theorem is also the normative model for subjective probability change based on data, against descriptive models such as cognitive bias.

[@Mona-fn7rt]

Is level of significance and type 1 error margin same? As we consider the alpha value of 0.01,0.05 & 0.1...

[@mariadt4124]

Thank you for explanations, but I wish to know whether those 2% were significant or not?

[@alexng8417]

Finally i get the idea of p value. thank a lot

[@DarthRevanDarthMalak]

How does P value take into account noise? The video suggests noise like genetic factors, but that seems undercut in this example by only having a 2% chance of that happening. I’m having trouble understanding where domain specific factors (genetics etc) wouldn’t come into play. Is it all just based on the fact that the population and samples follow a normal distribution?

[@MindfulEating-n3c]

Wow you are a good teacher

[@qamerkramet4562]

Please explain that .... If two groups are identical... Thn p value just 2per ... Shows that only 2 per chance that these are not identical... Why for just 2 percnt we reject null hypotheses

[@essencemariah1592]

This confused me as well

[@javedhamid9266]

I think he is said it incorrectly. Because if the p-value is 0.02 that mean that there is 2% chance that the null hypothesis is true. Which states that the drug x and placebo are same. So the null hypothesis will be rejected. I'm I right🤔

[@javedhamid9266]

@@essencemariah1592 I think he is said it incorrectly. Because if the p-value is 0.02 that mean that there is 2% chance that the null hypothesis is true. Which states that the drug x and placebo are same. So the null hypothesis will be rejected. I'm I right🤔

[@javedhamid9266]

The smaller the p-value the stronger the evidence against the null hypothesis

[@asophia21]

if say p-value = 0.01, does this translate to that there is 1% chance that the null hypothesis is true and but there is 99% confidence that the null hyphothesis is not true?

[@thigilman88]

Hello there, you say that the p-value is the probability that there is a difference in the weight greater than 1 kg between the two groups - provided the null hypothesis is true. Therefore, wouldn't it be more logical to reject the null hypothesis if the p-value were large

[@abyansyafi1815]

yes it would probably be easier to understand, but the complex statistics that he didnt explain probably explains why the p-value is what it is, just my hypothesis

[@WishfulWanderers]

My interpretation is the p-value represents the chance of "external interference" in your results. A higher p-value indicates a higher probability of external interference, therefore not allowing you to reject the null hypothesis. A lower p-value indicates a lower probability of external interference, therefore showing more accurate results and allowing you to reject the null hypothesis.

[@minhajuddinansari561]

Think of it in a slightly different way. In the weight example, if we consider the null hypothesis true, i.e. there is no weight difference, then what is the chance of observing a 1 kg weight difference (or more) between the two groups? In the video, this chance is 2%, which is highly unlikely, i.e. if there was no weight difference, it would be HIGHLY unlikely that we observe a difference of 1kg or more. HOWEVER, we still observe this weight difference in the samples we took, therefore, we reject the null hypothesis.

[@washington_amenuku]

You are a very good teacher. Kudos.

[@zingg7203]

The defnition would be difficult if you are making it to. 0:55 the one here is a wordy one. A much simpler one would be " what's probability of our finding is by chance." In other fancy stat bla bla jargons, assuming null hypothesis is true, what is the probability of our observed value is more extreme than a certain threshold. I am getting tired of hearing people dancing in their lingo just to hide their incompetence.

[@3453453425]

If I got it right, it would be better written like "If this were true, what is the probability of discovering a 1 kg reduction (or more) in body weight in those treated with Drug X from our sample (Group B), compared with the placebo (Group A) BY A RANDOM CHANCE (ACCIDENTALLY)" on 3:05

[@christopherbarrett9900]

Thank you so much! From what I understand, the smaller the p-value the closer one gets to the edge of the distribution, meaning that it is less likely we get something more extreme. I would just like to clarify a statement "The smaller the p-value the less likely we found this result purely by chance" Is this statement true because finding values at the edge of the distribution are extremely unlikely in the first place?

[@Corpsecreate]

All the comments are wrong. A p-value represents the probability of observing a sample statistic at least as extreme as the one actually observed under the assumption that the null hypothesis is true.

[@Saaaeeda]

thanks for the video but still confused...watched lots of videos but non was helpful to me. your video is simpler but needs some more explanation to clarify my concepts.

[@santiagodelacruzz]

Thank you very much it cleared my doubts!

[@randomsurfer007]

Should the alpha be halved when being compared to the p-value for a two-tailed hypothesis test?

[@florzinha.g]

Hi, this is incredibly well explained, but I am still a bit confused if you could please clarify something to me: Given that the p-value is the probability of the alternative hypothesis given that the null is true, why wouldnt a low p-value imply that you accept the null instead of rejecting it? For example, given that there is no difference between the weights of the two groups, the probability of it actually being different is so so low that wouldnt this imply that there is indeed essentially no difference between the weights, and hence we should accept the null? Please please help me clarify this in my brain, I would appreciate it so much.

[@philfromstatshelpdotnet1272]

Hi @Florencia Guan. The alternative hypothesis only comes into our definition of the p-value in a small way. It's mostly about probabilities under the null (not under the alternative). If that sounds like gibberish jargon, it's sometimes helpful to think of a p-value in a slightly different way. Remember the null, in this example, is that the drug behaves just like the placebo. If we get a p-value of .02, it means that the result we got is among the 2% most unlikely things that would happen if the null were true. So if the null were true, this would be a really unlikely/surprising result, so we jump to the semi-reasonable conclusion that the null isn't true.

[@philfromstatshelpdotnet1272]

(The alternative hypothesis only really comes into it, in that it can help steer us as to our idea of what should be considered "particularly surprising". The closer it is to the alternative hypothesis, the more we consider it a surprise. BUT the probabilities involved are all based on the null hypothesis. If that makes any sense...)

[@andreacastro3374]

@@philfromstatshelpdotnet1272 thank you it makes sense! So then, in the conclusion, how do we phrase it? Additionally, when and how do we accept an alternative hypothesis?

[@minhajuddinansari561]

Think of it in a slightly different way. In the weight example, if we consider the null hypothesis true, i.e. there is no weight difference, then what is the chance of observing a 1 kg weight difference (or more) between the two groups? In the video, this chance is 2%, which is highly unlikely, i.e. if there was no weight difference, it would be HIGHLY unlikely that we observe a difference of 1kg or more. HOWEVER, we still observe this weight difference in the samples we took, therefore, we reject the null hypothesis.

[@samirihamk8747]

@@minhajuddinansari561 , how do significance levels come into your explanation?? (Thankyou for it by the way, it helped me!!!) As in - if the p value was higher than .02, like .06 for example, what would our conclusion be? Does it provide EVEN more evidence that we should reject the null? How does significance level affect the conclusion we make?

[@LaraGreyling]

Great explanation!

[@rogierbrussee3460]

This nice video that correctly makes the point that the p-value is a probability assuming two populations are statistically behaving equal. However there is a further small print that the video does not go into: it not only says that it is _assumed_ that the populations are statistically behaving equal, but statistically equal in the sense that they are both _independent_ samples of a a very specific _assumed_ statistical model e.g. from a normal bell shaped distribution (or for the conoisseurs depending on the test: student-t, or binomial or...). It is precisely because of such assumptions that one can _compute_ the probability of an outcome at least as skewed as was found: once you make these assumptions it is math not non unlike the proverbial math exercise that asks you to compute the probability to throw 600 or more heads when throwing a coin 1000 times assuming the coin is fair and has 50% probability to show up heads. Whether the assumption of a specific distribution is warranted depends very much on the problem (read experimental setup) and the kind of questions you ask and in particular which test you use (the so called "non parametric tests" tend to be a lot less sensitive to at least the assumption of normality). In general, no statistical power tool can substitute understanding experimental/measuring setup, and tests that work brilliantly for finding minute differences in energy by testing trillions of indistinguishable electrons, may also "prove" there is a statistical difference between groups of thousends of people, except it just shows you detect a difference assuming all the idealisations and assumptions, which may likely be impossible to organise (good luck trying to find two random populations, and treating them exactly equal), and in any case given enough people you can always find differences, but the differences between individuals are much larger! Mind you, this is not a dunk on statistical testing or on p-values! They are an extremely useful tool to keep everyone honest!

[@Divino_1]

5:02 where did the 1kg (or more) come from?

[@raymadani270]

Thanks for the contents. in my opinion, it is easier to focus on the subject if the annoying hand and the anime is removed

[@catherinemagrath]

Really efficient explanation! Thanks for sharing 👏🏼

[@jacobvandijk6525]

Of course, this efficiency-feeling is very subjective.

[@Michelethesportdietitian2b]

Thanks very much Steven!

[@clarin3318]

Best video out there

[@maryamsediqi3625]

Amazing, many thanks 🙏

[@sanjanamax]

Appreciate the explanation ❤

[@sunilshrestha8183]

I am confused. Is p value =0.02 really means 2% chance of observing the weight loss or 2% chance of observing the weight loss due to some random fluctuations and 98% certain to observe the weight loss?? If p=0.02 means 2% change of observing the weight loss, than how p

[@jsmith5764]

I understand the null hypothesis, i.e no difference with control group and the group that gets a sugar pill, but I don't get how the percentage that is arbitrarily assigned . What is that assignment based on?

[@mebrahtomyihdego2095]

Thank you very much for brief presentation.

[@AzSah000]

I think the only part that seems counterintuitive is if it's just a tiny noise (say 0.02), why should we reject the Null? It should be the other way round. Nay?

[@mdselimahamed8617]

Excellent Thank you so much for your clear explanation.

[@chanlee4143]

Many thx. It is my first understanding it.

[@tareqoweinat1761]

thank you that was so useful

[@meriyaxetri1227]

Hello. A question: if i had to interpret a p value of 10%, does that make sense when i say there is 10% chance to observe the difference in the popn given that H0 is true?? For me it somehow doesn't sound right, i mean in this case we actually accept the H0, since 0.05 our threshold. Can you please help me with it? Thank you in advance

[@mdjaffer3286]

So that difference might be due to random noise and we need to find other drug where we can reject the null hypothesis Because when we are able to obtain P P value smaller then .005 then only we can say that treatment is effective

[@wokeymcwokeface1974]

The difference can be due to variables not accounted for in the experiment. It need not be “random noise”.

[@otmanalami6621]

Please how I know the standard deviation ( at 100 trials ) of an outcome that has 78% probability of occurring ?

[@willliam1420]

More important is how you come up with the p value. Can it be manipulated?

[@catmom1322]

A great review! Thanks.

[@thor4164]

Brilliantly explained

[@megaloschemos9113]

This is very helpful, thanks

[@Shghyghmszdh]

Incredibly perfect

[@nabil7sleiman]

How do you calculate the p-value?

[@StevenBradburn]

That will vary as there are various statistical tests you can perform. The type of data you have and the hypothesis you are testing will determine the appropriate test

[@brazilfootball]

Is the p-value based on the idea of hypothetically repeating the experiment a bunch of times? (Which we don’t do)

[@pmo4325]

Yes that's correct. If the p-value is 0.05 that means that if you were to run the experiment 20 times over you might expect to see the observed difference once out of those 20 times just by chance (because 20 x 0.05 = 1). The lower the p-value is, the less likely it is that the observed difference is just down to chance.

[@Arslanqadri]

Can we say this : while settling for Ho (no difference), p is just the chance of an anomaly i.e. the chance that a difference may exists? If we set a threshold alpha, then were a saying that if this percentage of anomaly is gt alpha then we are not going to go with Ho?

[@mathewskambani9116]

Well presented

[@saulomenezes4047]

Awesome! Great job!

[@coliv2]

These people make this notion complicated, but it is not: p-value is the PROBABILITY of having the current sample observation under the assumptions of the null hypothesis. If this probability is low, below some threshold, we can reject the null hypothesis. That's all it is, everything else is just to complicate. Usually the null hypothesis will be given in terms of normal distribution, that's why you can use the normal distribution tables, etc.

[@JakeRichardsong]

Subscribed. To reduce coincidence of random sampling, in this case, would the researchers filter out people with that gene before conducting the study?

[@texasflood1295]

Yes you could exclude those people. Also, if you use a good method to randomize subjects to the two groups, you could assume there are equal numbers with the gene in each group.

[@SAINIVEDH]

Why does a low p-value indicates stronger evidence against null hypothesis. The opposite must be true right ?. As the p-value is the probability of getting result atleast as extreme as those measured when H0 is true. So, the high probability value indicates higher chances of getting data contradicting H0. Please clarify this.

[@nachiketpargaonkar8646]

What I'm understanding from the video is, p value = probability/percentage of the event happening by chance alone. So, if p value is low, the chance of event occuring *by chance alone* is low, indirectly, the event most likely occurred by intention/intervention. Null hypothesis claims that the difference caused by the intervention is null. So if low p-value means that the chance of getting the result by coincidence alone is low, the null hypothesis has to be wrong & the difference occurred because of intervention

[@priyalgoel4644]

@@nachiketpargaonkar8646 Hey, I have a doubt here. Does p value indicate the nature of event that contradicts the null hypothesis? Let's say, if the p-value is 0.9432, then according to your definition, if the chances of occurrence of the event by chance are 94%, then with intention, won't it be much greater? Maybe, I have a lack of conceptual understanding here. Can you please explain?

[@nachiketpargaonkar8646]

@@priyalgoel4644 See most of our studies tend to follow the normal distribution curve. P-value represents the values that occur at the tail ends of the curve. P value of 0.94 would mean that there's a high probability (of 94%) that the event has occurred by chance. This doesn't mean that by intention it will be more than 94%, it means that the out of 100 events, the chance of getting this X result is 94 times, whereas by intention it is 6 times. One recent article (mentioned in another comment) has pointed out another necessary thing: P value is an observation, not an interpretation. That is, just because P value is 94% it does not necessarily mean that 94% is due to chance alone only. It signifies that it _could be_ due to chance alone.

[@valiarodriguez2330]

The video is right. Let me explain with two examples. 1- p=0.1 means that given that H0 is true you will still have a 10% chance of observing a difference between the samples (due to sampling noise, that is, a difference that actually does not exist), 2- however, a p=0.01 means that given that H0 is true you will only have a 1% chance to observe a difference due to sampling noise. Therefore, the lower the p, there is more evidence to reject H0.

[@Blackcomb1-h9e]

The lower the p value the more valid the evidence. Glad it didn't do only my head in learning this.

[@RXP91]

Thanks for this!

[@keppela1]

All made sense until 4:40. Don't you mean at p=0.02 there's only a 2% chance the weight loss would be LESS than 1kg (i.e. closer to the null hypothesis)?

[@juanjesusarandaromero7699]

Just Thanks!

[@drsamiruladanargungu368]

Thank you very much.

[@123shainz]

Thank you very much dear

[@StevenBradburn]

Most welcome 😊

[@texaspolygraph]

Thanks so much that was a great explanation.

[@YasminA-jm9zs]

very helpful!

[@rm9994]

3.32, yes but why. The counter intuitive aspect is not addressed. A lawyer having smaller amounts of evidence would not lead to a conviction.

[@dee.2848]

What’s the difference between a “p-value” and the “actual significance level”?

[@Jeff-zc6rr]

no one ever explains that hypothesis testing is the inverse problem of a confidence interval.

[@GamingShiiep]

Not gonna lie, this one confused me: "P-Value measures the strength of evidence against the 0 hypothesis" and "the smaller the p-value, the stronger the cevidence against the null hypothesis"" confused me a bit. Let's say the p-value is 0.002. then the null hypothesis is correct by 0.998. even smaller p-value, much much higher value for 0-hypothesis, because it's the most likely then. If p-value = 0.4, then its incredibly lickely, that the null hypothesis is wrong, right?

[@MuffinsAPlenty]

A p-value works under the assumption that the null hypothesis is true. If you _assume_ that the null hypothesis is true of the general population, what is the probability that you just so happened to get a sample which gave the results you obtained (or even less representative of the population)? That's what a p-value is. It's the conditional probability of obtaining the results you obtained given that the null hypothesis is true. If you got a p-value of 0.4, this would mean that you would have a 40% of getting the data you got if the null hypothesis is true. If you got a p-value of 0.03, this would mean that you would have a 3% of getting the data you got if the null hypothesis is true. A smaller p-value is more "anomalous". So, if you got a p-value of 0.03, the questions are this: did I get a results that would only happen 3% of the time, or is my assumption that the null hypothesis is true wrong?

[@JohnXie-e9f]

@@MuffinsAPlenty a small p-value can be obtained for more than the two reasons you just specified (i.e., H0 is false; or random fluctuation while H0 is true): other things equal but a very large sample size; some assumption condition of the proposed test is violated. The researcher who applies the test cannot tell which of the possible reasons has caused a small p-value. Hence, your statement ' A smaller p-value is more "anomalous". So, if you got a p-value of 0.03, the questions are this: did I get a results that would only happen 3% of the time, or is my assumption that the null hypothesis is true wrong?' is incorrect. Actually, since p-value is obtained by assuming H0 is true (as a precondition), it is logically not defensible that p-value contains information to estimate the likelihood of H0 - it is Bayesian statistics posterior probability.

[@KaiusKing]

Good Video

[@alimenhem3348]

I mean if something has an effect(which is opposite to null hypo) and its proved why should there be a P value(iff null hypo is true) like it's not logical null hypo isn't true why say if null hypo is true what is probability gett9ng results

[@soukkhanhsila134]

drug X is my favorite. the p-value of that is pretty high.

[@larissacury7714]

loved it!

[@exotiknuella]

Thanks!

[@WilliamPeck1958]

nice! good job

[@Takeitlightly6]

I dont think you can draw all these perfectly so fast

[@francmittelo6731]

P-value = the probability of saying there is a tiger in the bushes, when in reality there is no tiger in the bushes. If I am wrong, please correct me.

[@0x8badbeef]

I prefer contrasting examples with obvious formatting: He got hit by a snowball in hell for taking the pill which has a p-value of 0.00. He got hit by a car on a busy highway for taking the pill which has a p-value of 1.00.

[@wolfgangamadeusmozart1816]

Surely the null hypothesis should be: "There is no significant difference as a result of the pill"