Two-sample t test for difference of means | AP Statistics | Khan Academy

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Hypothesis test for the difference between means of two populations.
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AP Statistics on Khan Academy: Meet one of our writers for AP¨_ Statistics, Jeff. A former high school teacher for 10 years in Kalamazoo, Michigan, Jeff taught Algebra 1, Geometry, Algebra 2, Introductory Statistics, and AP¨_ Statistics. Today he's hard at work creating new exercises and articles for AP¨_ Statistics.
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[@125dudeman]

tough for the donations they want, I really wish I could but most people watching are broke college students :( one day ill get you guys back if you're still around.

[@Tazerbob]

surely man! 👏

[@blessingobiora3983]

Yours is more comprehensive than the ones I av watched. Thank you

[@3607458]

Two-Sample T-Test and CI Sample N Mean StDev SE Mean 1 22 1.300 0.500 0.11 2 24 1.600 0.300 0.061 Difference = μ (1) - μ (2) Estimate for difference: -0.300 95% CI for difference: (-0.550, -0.050) T-Test of difference = 0 (vs ≠): T-Value = -2.44 P-Value = 0.020 DF = 33

[@johnnyroc]

why are you reading the comments. back to studying.

[@aaryanjain312]

@@kriti5276 can u do both tho

[@vainca3192]

Why did you click on answers?!

[@aaryanjain312]

@@kriti5276 what a flex!!! 😎

[@aaryanjain312]

@@vainca3192 what? Clicking on answers is what you are supposed to do as a highschool student 😎

[@aaryanjain312]

@@vainca3192 then like what

[@Levelworm]

One caveat I found out about pretty much all STAT tutorials and textbooks is that there is few real-life examples, especially business ones. It's either something like this that you can immediately put numbers into the formula, or something that is related to medical experiments. What I think that is really needed is how to APPLY that knowledge to a usual business question.

[@MakeMultiplayerGames]

This is needed in some user research experiments, which is used to validate business hypothesis, e.g. in MVT or A/B testing. Two versions of a landing page / feature/ logo are tested on samples of users, and you want to compare how those two versions score in X property to keep the better one.

[@zoezhang7661]

Hi, please may I ask what app are you using as for the calculator?

[@oudviola]

A helpful tutorial. However, I ran two different online t-tests with these mean, std and Ns, and both gave the same result which however is slightly different than the calculation here. They both gave a two-tailed p-value of 0.0165. Graphpad also gives the degrees of freedom, which was 44. That's pretty different than the estimated 22 (or 24?) here, maybe that is the reason. But the t-statistic was also a bit different, 2.4919.

[@sohamsantra7548]

I got the same value for the T statistic. I think he used exact values, that's why he's getting a different answer upon rounding.

[@sixtysixx3933]

I liked that you have used an uneven size for the two samples. Learned something new today xd

[@minhquanduong7121]

Felix Carpio is this the same thing as the welch’s t test?

[@ilirose6456]

is there a way to calculate the p value by hand without the calculator function? We are only allowed to use a very basic calculator that does not have tcdf in our exam. Thanks for the help!

[@grandpazhongli3657]

so will i arrive at the same answer if i use the welch t test?

[@steverensen2551]

I guess just looking at the mean versus the standard deviation you went with the unequal variance t-test. Otherwise we would have to conduct a F-test to determine if a pooled estimate could be used. I wish you mentioned something on this.

[@DmanGaming]

bruh if you know that much then why does it matter?

[@jenjp7853]

because I was confused and @steverensen2551 explained why I was confused, the comment was helpful@@DmanGaming

[@alivegaming438]

When your University professor just links this video for online class instead of actually teaching it himself

[@veerakanneboina8086]

For a two samples t test if it is not given whether the population variances are not equal or not. Then which formula do I have to use to find degrees of freedom

[@bjlenny3889]

How do you calculate the minimum sample size you need to compare 2 sets of data?

[@WirTrivedi]

I can say he is a very good artist please reply ☺️

[@aroobashafique1921]

I have data of two rivers. River a and river b. The data is of before and after the application of the chemical. One sample set is bigger than the other. I need to know in which sample the chemical was more successful in removing parasite than the other. Which test should i use. ? Please please please guide

[@mastermax7777]

Okay I understand the steps, But I don't understand some things like how do we determine the significance level? (Where did you get 0.05? out of thin air?)

[@bjlenny3889]

from my understanding 0.05 is the default p-value for this sort of test. This represents 2 standard deviations (95% probability). However you could theoretically use any p-value.

[@veerakanneboina8086]

What if I calculate the t value as XB-XA. Will that make difference in conclusion

[@micahsnow346]

There is a way to reject/accept the null hypothesis based only on confidence intervals instead of the p-value, right?

[@d2xr]

Yes

[@mihai.ciorobita]

Sir, what do I do if I want to test mean(A) > mean(B) ?

[@__evanhart5320]

based on the laws, why are you not pooling the variances

[@qaisarkhan1326]

Where we use pooled Estimate of standard deviance (Sp)

[@VK-sp4gv]

No, he doesn't use a pooled estimate, but he doesn't explain why.

[@roger2bro]

Thank you

[@xiebustillo3521]

What type of calculation app was used?

[@FrankRomerophoto]

Where can I get the TI-84 Plus CE in software? Thanks

[@vanessajaime7538]

i’m just trying to look for one that isn’t the conservative approach for the df because my teacher doesn’t use that🤦🏽‍♀️

[@lumpi806]

Interesting video, but you don't explain if you assume the variance are equal or NOT. You don't axplain if you use the welch method, or NOT. And your formula for the degree of freedom is curious.

[@qwertytwerqy2440]

True, watching the video left me with more questions than before I watched it.

[@shanggao9970]

Thank you! Super helpful! A quick question: why is the df = min(sample size)-1 ?

[@michaellovin3522]

Good question. Though you have two samples, you are comparing their means. Therefore, this is a single variable analysis and degrees of freedom is n - 1. Now recall that a chain is only as strong as its weakest link, a group of runners that must run as a group is only as fast as its slowest runner, and a statistical test is only as strong as its weakest test. In statistics, more data is better. Therefore, you must adopt the lower of the two values as your basis for degrees of freedom.

[@vincenttsai5344]

I got a question, what if the two sample number is very different? ex: N1 = 24 N2 = 2500 the DF still min(sample size)-1, in this case, DF = 24-1 = 23 ?

[@robertmei8881]

I checked wiki, it should be N1 -1+ N2 -1 for the independent two sample test

[@juliusceasarhortelano7020]

Hi, are you not going to take the absolute value of the differences of the two means (numerator)?

[@mariselcantiga1860]

What app did u use in solving the p-value?

[@TilmanVogel]

1:26 Why are you talking about the alternative hypothesis after already having set the null-hypothesis? If that one is set, you don't have a choice anymore: It's just the complementary hypothesis that the null-hypothesis does not hold, so if you want to discuss the hypothesis, do so when you fix the first.

[@adasun1777]

I think the df should be 44, am I wrong?

[@harrisontichenor2092]

Doesn't the test statistic and degrees of freedom depend on whether variance is known or unknown? And then there are two more approaches if unknown, assume variances equal, assume variances not equal

[@fangmin2890]

what is the equation for p-value calculation? (can this be done in excel?), thanks

[@prasadkedar30]

for calculating p-value in excel with t-value known ...you can use the function T.DIST(tvalue, n-1, TRUE). this will give the p-value for left tailed test. for right tailled test, you can subtract this value from 1. similarly for two tailed test, use 2* the pvalue obtained by using the function.

[@d2xr]

So this is like a shortcut?

[@mccnlightx4495]

KAITO MOMOTA LUMINARY OF THE STARS 🌟 ‼️ is growing tomato plants atm

[@brandonwarren5644]

Is there an online calculator like the one he is using?

[@missjunanne87]

best statistic calculator online

[@missjunanne87]

You will just encode the values then it will give you answers

[@temmygrace2786]

My question is how did you get the value for X1 and X2, S1 and S2. I'm using data from fresh sample

[@karannchew2534]

2:04 std dev of the sampling distribution of the differences of the sample means

[@felixmugire6583]

Degree of freedom = n1+n2 -2

[@dol2han]

I think so too

[@ayashabeg911]

If we find significant by applying t statistic between two groups ,then how do we decide that the significant difference is recorded in which group as compared other group?

[@Patwardhan622]

As sample size are large so I should use z test????

[@lanasaleh6569]

Yes And must n1=n2

[@Princess-zu9eo]

Yes if the sample size in above 30, you should use z test

[@mariselcantiga1860]

So i should use z test? Since my sample size is 102

[@anisabhita]

what if the number of sample is bigger than 30 (large sample)? should i still using this formula?

[@oooooo-kr4ep]

One way ANOVA test: between groups sum aquare = 66636.83; df= 2; mean square%=33318.41; f= 11.710 and sig=.000. Within groups = 189577.87; df=669; mean square= 283.37 what is the answer?

[@satyamgupta4808]

very nice video

[@randomplay4623]

Why you use t test? The summ of the sample wize is greater than 30/ n>30, you should use z-test instead 9f t test

[@muhaha21]

so basically you are assuming that the groups variances are not equal right ?

[@aurangzebrathore5001]

There is no assumption. It is stated that the two have different standard deviations.

[@Cardboard0G]

@@aurangzebrathore5001 that doesnt mean that the population standard deviations are different. There are two different tests that can be used to test if the population means are different. One test is for when the population variances are different and one when they are the same. In this instance Dr. Khan is using the method for when the population variances are different. thats like saying the population means are different because the sample means are stated as different

[@ritamsarkar7753]

degree of freedom = n1+n2 -2 = 22+24 -2 = 44 , Please reply why it is 21 ?

[@felixmugire6583]

i also doubted that.

[@nadiansnazar1248]

what if the sample is equal?

[@RJG989]

You use a pooled t-test I am pretty sure

[@mariselcantiga1860]

Can i used t-test when my sample is 100?

[@mariselcantiga1860]

Please answer me😭

[@RaviSingh-xx2wq]

No. You'll use Z test as T-test is used when sample size is usually under 30

[@3607458]

Please look at the below solution and confirm for difference in P-value: Difference = μ (1) - μ (2) Estimate for difference: -0.300 95% CI for difference: (-0.550, -0.050) T-Test of difference = 0 (vs ≠): T-Value = -2.44 P-Value = 0.020 DF = 33

[@manushreemishra3998]

Can you please ellaborate on DF?

[@mariselcantiga1860]

My two sample t-statistic is -3.02 What is my p-value?

[@mihai.ciorobita]

If you are still interested to find the value of p you need the degree of freedom too. As in the video was specified it is the lowest size of the two samples -1. And finally to calculate the value you can use matlab function tcdf(t, df). df - degree of freedom

[@xiaowenxu5720]

lack the assumption that the height follows normal distribution to apply CLT?

[@carolinesnell6026]

god bless you sal

[@abelbiju7269]

why am i getting -1.7875 for 't'

[@portmax95]

I think you forgot polled variance

[@yuhanglin1547]

Well, these tomato plants taken are just samples instead of original populations. So should the variance s^2A and s^2B used be the unbiased estimators instead of variance of the samples?

[@MrSajjad1989]

Thank brother you made it easy

[@mariselcantiga1860]

My two sample t statistic is -7.14 Can someone tell me what is the p-value?

[@mihai.ciorobita]

I also need the degree of freedom

[@lookaway8496]

What if the two samples are the same?

[@mihai.ciorobita]

nothing change, I guess...

[@hadijutt2960]

Mistake 0.3^2=0.9

[@mikegardetto5536]

.3 *.3 is 0.09 I believe its your mistake.

[@lemyul]

thanks vulcano

[@sq9779]

Is the two sample t test the same as the student t test?

[@Mersch20]

According to my statistics book, t-Test has 1 sample. The 2 sample test is called Pooled-t or non-pooled, depending on the sample size or standard deviation.

[@oooooo-kr4ep]

One way Anova test

[@lanasaleh6569]

In t dist we use Sp and we cant use the standard division S ?🤔🤔

[@mersancanonigo1018]

me too

[@JamTik734]

nice

[@jannahtesl]

Why did you calculate 0.9 and not 0.09?

[@karthikeyans1646]

0.3 the whole square is 0.9 tata y he calculated mistakenly he wrote as 0.09 dude

[@joyleemorrondoz8745]

0.3^2=0.09 this is not mistakenly calculated.

[@dami9475]

is this a two sample paired t test?

[@Mersch20]

Yes, it says it in the title of the video

[@benjaminjordan2330]

Okay... what's your point?

[@Dissandou]

To teach statistics learners how to apply a t-distribution to a difference of means problem

[@sajeewakalhara5623]

Sweety

[@cynthiasimpson6469]

First!

[@cynthiasimpson6469]

.

[@AntonioDTorres]

2:58- When you square 0.3 equals 0.9 not 0.09.

[@fguintu]

.3^2 = .09 He’s not wrong

[@VK-sp4gv]

Squaring a number which is less than 1 makes that number smaller, not bigger.

[@forevershampoo]

I really have never liked this guys voice