## One-tailed and two-tailed tests | Inferential statistics | Probability and Statistics | Khan Academy

In the last video, our

null hypothesis was the drug had no effect. And our alternative hypothesis

was that the drug just has an effect. We didn’t say whether the drug

would lower the response time or raise the response time. We just said the drug had an

effect, that the mean when you have the drug will not

be the same thing as the population mean. And then the null hypothesis

says no, your mean with the drug’s going to be the same

thing as the population mean, it has no effect. In this situation where we’re

really just testing to see if it had an effect, whether an

extreme positive effect, or an extreme negative effect,

would have both been considered an effect. We did something called a

two-tailed test. This is called eight two-tailed test.

Because frankly, a super high response time, if you had a

response time that was more than 3 standard deviations,

that would’ve also made us likely to reject the

null hypothesis. So we were dealing with

kind of both tails. You could have done a similar

type of hypothesis test with the same experiment where you

only had a one-tailed test. And the way we could have done

that is we still could have had the null hypothesis be that

the drug has no effect. Or that the mean with the drug–

the mean, and maybe I could say the mean with the

drug– is still going to be 1.2 seconds, our mean

response time. Now if we wanted to do a

one-tailed test, but for some reason we already had maybe a

view that this drug would lower response times, then our

alternative hypothesis– and just so you get familiar with

different types of notation, some books or teachers will

write the alternative hypothesis as H1, sometimes

they write it as H alternative, either

one is fine. If you want to do one-tailed

test, you could say that the drug lowers response time. Or that the mean with the drug

is less than 1.2 seconds. Now if you do a one-tailed test

like this, what we’re thinking about is, what we want

to look at is, all right, we have our sampling

distribution. Actually, I can just use the

drawing that I had up here. You had your sampling

distribution of the sample mean. We know what the mean of that

was, it’s 1.2 seconds, same as the population mean. We were able to estimate its

standard deviation using our sample standard deviation, and

that was reasonable because it had a sample size of greater

than 30, so we can still kind of deal with a normal

distribution for the sampling distribution. And using that we saw that the

result, the sample mean that we got, the 1.05 seconds,

is 3 standard deviations below the mean. So if we look at it– let me

just re-draw it with our new hypothesis test. So this is

the sampling distribution. It has a mean right over

here at 1.2 seconds. And the result we got

was 3 standard deviations below the mean. 1, 2, 3 standard deviations

below the mean. That was what our 1.05

seconds were. So when you set it up like this

where you’re not just saying that the drug has an

effect– in that case, and that was the last view, you’d

look at both tails. But here we’re saying we only

care is does the drug lower our response time? And just like we did before, you

say OK, let’s say the drug doesn’t lower our

response time. If the drug doesn’t lower our

response time, what was the probability or what is the

probability of getting a lowering this extreme

or more extreme? So here it will only be one

of the tails that we could consider when we set our

alternative hypothesis like that, that we think it lowers. So if our null hypothesis is

true, the probability of getting a result more extreme

than 1.05 seconds, now we are only considering this tail

right over here. Let me just put it this way. More extreme than 1.05 seconds,

or let me say, lower. Because in the last video we

cared about more extreme because even a really high

result would have said, OK, the mean’s definitely

not 1.2 seconds. But in this case we care about

means that are lower. So now we care about the

probability of a result lower than 1.05 seconds. That’s the same thing as

sampling– of getting a sample from the sampling distribution

that’s more than 3 standard deviations below the mean. And in this case, we’re only

going to consider the area in this one tail. So this right here would be a

one-tailed test where we only care about one direction

below the mean. If you look at the one-tailed

test– this area over here– we saw last time that both of

these areas combined are 0.3%. But if you’re only considering

one of these areas, if you’re only considering this one over

here it’s going to be half of that, because the normal

distribution is symmetric. So it’s going to the 0.13%. So this one right here is going

to be 0.15%, or if you express it as a decimal, this

is going to be 0.0015. So once again, if you set up

your hypotheses like this, you would have said, if your null

hypothesis is correct, there would have only been a 0.15%

chance of getting a result lower than the result we got. So that would be very unlikely,

so we will reject the null hypothesis and go

with the alternative. And in this situation

your P-value is going to be the 0.0015.

first

Love it. Love you.

You are passing me in Differential Equations, Stats, AND helping me for my actuarial exam. I can not thank you enough. What a great thing you are doing.

love you dude

Really nice, one of the best videos I found so far, however if the drug is going to lower the response it means that the response will take longer. In your example you say that the response will be lower and will be less than 1.2 seconds which should be more than 1.2 seconds!

@ jessica, actually, lowering response time means that the response time will be shorter, not longer. So, lowering the response time means that the drug will cause the response time to be shorter.

Thanks for such a great video!

hey sorry man i realy dont get your teaching…it so confusing…hmmm sory man

I thought in a one tailed test you would look at the 3% percentile of the lower tail, not 1.5% AND disregard the other extreme. Were as in the two tailed test you are looking at both ends equally, that is 1.5% percentile on both extremes.

thanks for helping me with my homework! You really help me understand what's going on rather than just memorizing equations. And it's awesome that i can pause you and make you repeat things over and over! ha ha

i think im ganna fail anyway…

i have to ask, for test of independency (chi-square test) with df=1 do we have to mention wether it is one tailed or two tailed? what is the logic of having one tailed chi square or two tailed chi square test when the chi square pdf of df=1 is asymmetrical??. i am doing an assignment where i have to mention wether im doing one-tailed or two tailed test statistic

Hypotheses, no? As in "hip-poth-eh- seez" . Although, "hypothesisis-sis" is kind of cute :3

TEST TOMORROW. thank you for your help! i may actually do well! AP stats ftw…

thank you for the video

Indeed.

Holy crap. You don't realize how over-complicated my textbook made this whole concept. And yet in 15 minutes, I now completely understand. This is easy. ðŸ™‚

is two-tailed, and one-tailed just another way of saying "one sided confidence interval" and "two sided confidence interval" or are those completely separate things?

two tailed test is appropriate because we are checking if the means are different, i.e., higher or lower does not matter

Null must go because p is low, therefore, the means are significantly different

t statistic is above t-critical, therefore reject null which means that the means are significantly different

Hey i have a simple question:

So if the question says "what are the chances it will be lower than the population mean" you would do a 1-tailed test?

While if the question said "what are the chances it will stray from the population mean" you would do a 2-tailed test?

mr khan, what settings do you have your pen on? is it a tablet? if so, what kind? i just got one and i like how your lines

Is 1.2 the sample mean? it looks like the population mean from the question, and formula used seems to be (pop mean – sample mean)/sd?

Could you please edit the videos? Take out the mistakes. It becomes confusing.

dear sir,I think for the two tailed test significant level should be alpha/2 for each tail which is .003/2 for each tail….plz right me if im wrong.

for one tailed test significant level is alpha which is .003

other than I think your explaination couldnt be better than that.

thnx

Salman Khan IS THE MAN

sal, you have no idea how many tests you helped me pass in my mechanical engineering course. than you!

Thanks man, that's really useful. But I've got P-value = Â 0.13% (from z table), is't correct?

Thank You Khan Academy for these helpful videos.Â

Age: 34

Major: MBA

Class: QNT 561 (Statistics and Research)Â

I understood your teaching style, and taking this one step at a time.

thank you it was very helpful

Lost me. Why doesn't H1 state < 1.05? You have it as <1.2 and then spend you time talking about <1.05. So confusing!

I wish you lessons were numbered so someone 1st that lands on a video like this could easily find the prior video. Also you all blue thumb nails are also unhelpful.

I have a test-stat of 2.303164609, df 8, alpha .05. Doing a two tailed test (in excel) I got p-values of .05022 (>.05000), and for a one tailed test I got .02511 (<.05000). Am I interpreting my results correctly that in the 2-tailed test we keep the null but in the one tailed we reject it? Does the critical point change when you go from a 2 to a 1 tailed test?

selling humans poison laser then charge them, illegal.Â law class

But then you could also have made the H1 hypothesis as it was greater than the mu+0.15=1.35 (since mu-1.05=0.15) and then get the same p-value right? As the normal distribution is symmetric and the right tail has the same probabilty as the left tail you just calculated. Which would be clearly a bad result and you would accept the H1 hypothesis then as well and conclude that it lowers the response rate. Am I right?

I know this video is from 5 years ago, but I am desperate to know how to compute the p-value without a TI-84. I have excel, two calculator apps.. where did 0.15%, or 0.0015 come from??? Perhaps I should try to find the first video..you might explain it there.

Why did he subtract x bar from mu? Shouldn't it be the other way around?

this example is very relevant because I'd guess that a lot of us are currently addy'd out. Or I should say I am 95% confident that a lot of us are addy'd out

just looked at the statistics of this video being watched and saw that how lazy people pile up over and over just before their exams lol.

sir I have a problem of stats but I am not getting how to solve problem is

two batches of animals each are given test of inoculation , one batch was inoculated and the other was not the numbers of dead and surviving animals are given in the following table for both cases can the inoculation be regarded as effective against the decease at 5â„… level of significance

dead. survival. total

inoculated. 2. 10. 12

non inoculated. 8. 4. 12

total. 10. 14. 24

can please anyone solve this for me

This is the first Khan video I've ever struggled with. If the null hypothesis is that the drug has no effect on the mean response time of 1.2 seconds, why are we focused on the probability of getting a response time of 1.05 seconds or lower? I don't understand how we can reject the null hypothesis based on the knowledge that there's a .15% chance of getting < 1.05 seconds. It still doesn't tell us if the drug has any effect at all.

You explained this better than my professor. Why am I paying for university again???…

Ooooooooh. Now I get it. So much simpler than I was thinking.

nice…..

i like this in statistics woow

thank you for the video. However, shouldn't the null hypothesis state that Ho: mean>=1.2 in this case?

There's some crucial part of reasoning missing in this video. What would happen if I set my alternative hypothesis H1 as Drug raises response time : mu>1.2 s. Why the very same reasoning would fail?

for it's one. two. three standard deviations below the mean. at the old. ball. gameeeeee

I just want to know how you differentiate two-tailed one-tailed

Do i spare time if played on 1.5 speed and get less lazy afterwards?