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Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution
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- Опубліковано 18 сер 2024
- This statistics video explains how to perform hypothesis testing with two sample means using the t-test with the student's t-distribution and the z-test with the normal distribution table.
Confidence Intervals & Margin of Error: • How To Find The Z Scor...
Find The Z-Score Given Confidence Interval:
• How To Find The Z Scor...
Student's T-Distribution:
• Student's T Distributi...
Hypothesis Testing - Null & Alternative:
• Hypothesis Testing - N...
Type I and Type II Errors:
• How To Identify Type I...
One Tailed and Two Tailed Tests:
• One Tailed and Two Tai...
_______________________________________
Test Static For Means & Pop Proportions:
• Test Statistic For Mea...
Hypothesis Testing Problems:
• Hypothesis Testing Pro...
P-Value Method - Hypothesis Testing:
• P-Value Method For Hyp...
Hypothesis Testing - Proportions:
• Hypothesis Testing - S...
Difference of 2 Means - H Testing:
• Hypothesis Testing - D...
Cohen's D - Pooled Standard Deviation:
• How to find Cohen's D ...
Hypothesis Testing - 2 Proportions:
• Hypothesis Testing Wit...
__________________________________
Matched or Paired Samples t-Test:
• Matched or Paired Samp...
Chi Square Test:
• Chi Square Test
Chi Square Distribution Test:
• Chi Square Distributio...
Test of Independence - Chi Square Dist:
• Test of Independence U...
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You have made my first year of biotechnology biology courses much more enjoyable by teaching me in every area of science (math,statistics, chemistry and organic chemistry) that is difficult for me to grasp. May God bless you and please keep up the good work. You are a TRUE professor.
Does this guy literally teach everything in the realm of STEM? What a legend!
I am also a STEM student and he is literally my god
Hey question for two independent or depend samples, we won’t always be testing the difference right?
Degrees of freedom can also be calcuated by DF= (N1 + N2) -2
Much easier to do it that way !
No that is when variances are pooled together.
DF are N1+N2-2 if you hypotize/know that the populations of the two groups have equal variance. Viceversa, you use the formula in the video
That is for equal variances.
Nice one.
Super great video, thank you so much. It helps a lot :D!
I just wanted to add something not mentioned in the video but probably very important: when computing the t-statistic, in the denominator we compute the standard error (SE). In the video, it is assumed that the variances of both groups ARE NOT THE SAME, and hence finds the estimated SE -> sqrt(s1^2/n1 + s2ˆ2/n2)
Sometimes, depending on the case or if it is given in the problem statement, one can assume that the variances of both control groups are the same. Then the formula changes and we need to find the POOLED SE.
Yet another banger from the greatest tutor on the internet. Thank you so much.
To those learning - I highly recommend you pause the video before he begins solving the question, and try and answer it yourself. Then, unpause, compare your methods with his, and correct yourself. You learn best that way.
I'm so glad I found this channel and this awesome community. Makes me fall in love with learning all over again.
dude!!! I've tried for hours to figure this out! I watched 7 minutes of your easy, calm and totally logical teaching method and got it!! thank you thank you.
If only you posted this a day earlier, I just had a test over this😂😂
i can´t express how much it helps me. You are such a gift of god.
Sir, you need to make a Q&A video I am sure so many people want to know you.
I just wanted to say thank you. I just done doing my Performance task in math. This really helps me a lot! as in a lot! You are a hero for me to be honest. This video helps me to understand step by step, you are amazing! Thank you so much!
I'd rather watch videos from the organic chemistry tutor for HOURS more than reading ONE PAGE of my lecture book 😭 I swear.
Just a tip. When calculating dF you should round the result down and not up. So in this case 24 and not 25.
better explanation than my prof. Thanks king
Best professor ever, thank you!
I love your clear examples and computations. Great video!
The formula used, in the first example: unequal variances, for df is correct, we use df=(n1+n2)-2 when we have equal variances ( or standard deviations).
But you get the same answer?
Thanks. You saved my life for my analytical chem test tomorrow😭
For the degrees of freedom isnt it better to use n1+n2 -2 = df
You should only use df=n1+n2-2 formula if both samples have equal standard deviation. If not, you should use Satterthwaite Approximation (the formula he showed in the video) to find df.
@@MrGamingXD1 in his example i used n1+n2-2 and got the same result
@@MrGamingXD1 when he says we can use normal distribution if n is equal to or greater than 30, is he correct?
We aren't supposed to use t distribution if we aren't aware of the population Standard deviation, right?
Though some people say if sample size is equal to or greater than 30, z distribution approximates t distribution, it is absolutely wrong.( Reference - jbstatistics)
@@sanchitakanta1018 When sample size incerase the t-distribution approximates z-distribution. You can see it from the graph of t-distribution with different degree of freedom.
@Dominic Martin if you test if variance are equal or not using f-test (high variance/low variance) then you will find out that variance are equal. So we should use n1+n2-2 for df. What am i missing?
Man does this bring back memories from organic chem
thanks for the beautiful lecture. God bless you
literally just saved 10% of my grade ty
Thank you so much!! I needed a refresher on the df formula, I kept getting the wrong answers as I wasn't calculating each part properly. Finally done with an assignment in which we were told to come up with a research question, a hypothesis, analysis etc. Thanks to this video I just got done with that assignment!! Allahumdulillah :)
Thank you sir....thanks from India
really appreciate the effort you put into this video, it helps me a lot
Soo good information, you make it so clear!! Only got one question, we did an example at class today where the teacher used another formula because she said that's what to use when the Sd is almost the same, in your example the Sd is almost equal but you used this formula, is it something im missing?
Another amazing video
To determine if there's a significant difference between the teachers' performance, a two-sample t-test is appropriate. With a 5% significance level, calculate the t-value using the means, standard deviations, and sample sizes of both classes. The formula for the two-sample t-test is t = (mean1 - mean2) / sqrt((s1²/n1) + (s2²/n2)). Plug in the values to get t ≈ -2.86. With degrees of freedom around 25, the critical t-value (two-tailed) is roughly ±2.064. Since -2.86 is beyond this range, there's evidence to reject the null hypothesis (that the teachers' performance is the same). In conclusion, at the 5% significance level, there's a significant difference in performance between the two teachers based on the exam scores of their respective classes.
how do you know the degrees of freedom are around 25?
Thanks for the video!
God bless you organic tutor
man this was so helpful, thank you so much! got such a nice clarification :)
for question we can also use d.f.= n1 + n2 - 2 to find the degrees of freedom
I consider you the best along khan Academy
Thank you very much Dr
Extremely helpful. Thanks!
Hi, as the population variance is unknown, should we use the pooled variance method instead? thank you.
Great video! Thank you so much.(we can easier find approximation of degrees of freedom as n1 + n2 - 2)
No, that approximation only works when both the population variances are equal, here we can not say that both are equal.
Thank you very much
df could be (n1+n2)-2 :D
df=(15+12)-2=27-2=25
is this proven ?
Ashfaaq Hussein Curimbaccus this is how our prof taught us! 😊
Ah okay thanks !!!
can somebody send me a t-distribution table on ashfaaq.curimbaccus4@umail.uom.ac.mu please ????
gukkie’s ymkluvs same i was abt to say that too😂
You are father of all Subjects. 😍😍😍
Thanks for the video sir and I'm very thankful for it .. And as a ugandan i feel proud of this channel. But is it appropriate when i also use this formulae;( n1 + n2 - 2 )to get the degree of freedom?
I have a concern. In your case the calculated value was less than the standard value. You were supposed to FAIL TO REJECT the null hypothesis but instead you rejected it
isnt it because you are supossed to follow it in terms of the numbers in the number line: -3,-2.53,-2.0595, -2,-1, 0 ?
Hello. I am curious what program this is that you are using.
Before using the t-test, I think we should use the F test to determine whether it's considered as equal variance or unequal variance
Thank you for a nice presentation but I need clarification on the degree of freedom, since it refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample I think it should not be approximated to the next value. I have seen some literatures stating that even if you get 24.9 you have to make it 24 but in your example it was 24.7 but approximated to 25. Is that right?
he forget
Please anyone who has an answer can reply.
How did you conclude that the new factory was better since we only know the means are not equal and we don't know which of them is greater?
Why wee need to use a huge mathermatical formula. Degrees of freedom for a t-test is n1+n2-2 because we have two samples having n1 and n2 sizes. Am I right?
Mate, you explain very well, keep going. 🤘
the only thing I'm missing from these videos, are ways you read z./t table and when certain methods of calucalating AL should be used. When I was working through proportion calculations, i didn't understand why sometimes you read the table, why sometimes you extract value from one... Took some further research, but now it's so much easier to follow what you're doing with these values. Could be usefull :)
quick question, for number 1 for example, why does he assume that its a two tail test? He doesnt explain it and proceeds with alpha over 2. If it was one tailed he wouldve just left it as alpha
@@ghostkidgamerez3917 For a two tailed test, the null hypothesis is mean (μ) = (some number), whereas for a one tailed test, the null hypothesis is mean (μ) , ≤, ≥ (some number). This way, the shaded area, lies on both the sides of the normal distribution curve in a two tailed test, but lies either on the right or left in a one tailed test, depending on the critical value obtained, using the given level of confidence or significance.
7:24
df = 24.7 which is approximately equal to 25.
What if degree of freedom is a decimal number such as 24.25 it must be 25 or 24 (round up or round down ?)
it must be 24 right ? round to the nearest number.
If df = 24.5
it must be 25 right sir ?
Yes, that's how rounding off numbers works
good job and go on
thank u. its more helpfull.
God bless you abundantly
Thank you so much, sir.
saved my day
thank you. love you pal
actually the GOAT
Please do explain how we can determine the Z critical point when we have left side hypotheses test as no one has explained this yet and I don’t know how to calculate it as our Z value table is right test only
For degree of freedom you can use, (n1 + n2 - 2)
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
Pengujian hipotesis tentang
selisih
rata
-rata
dua
populasi
independen , 𝜎12 = 𝜎12 (Ragam
populasi
ke
-1 sama
dgn ragam
populasi ke-2) tetapi
nilainya
diketahui
thank you for this video, but the least you can do is to explain WHY you use the welch method for the first part of the video.
I don’t understand, how did u get the rejection region of 0.5 for number 2 problem?
Thank you
Bro thank you!!!!!!! 😭😭😭
in the DF
u can use n1+n2-2
You have made the process tougher. I couldn't understand df formula
also, you can find df of 2 sample sizes by just subtracting them by 2. regardless, great video though :)
Thank you sir for your explanations.
I just confused when I have two samples and every one consists of 27 experiments. However when I Calculated the degrees of freedom I found it is 59 . I couldn't find a value of t_critical in table corresponded to 59 degrees on freedom. Can you help me ?
for the second example, you use the z-distribution, not the t-distribution, since the sample sizes are greater than 30
But I thought alpha value of O.O5, Not O.O25 should be used to calculate critical t value?
How we know use pooled variance from unpooled from question?
Thanks for your videos. Kindly use white background since the blue is not visible with a black background 😢
What if one sample have 200 observations, and second sample have 20 ? Will we use normal distribution or t-distribution ?
In the first example, why was degree of freedom had to be calculated using a special formula, what not n-1, also 15 -1 =14
I don't get it my question just feels different. Mine is telling me to assume the data is normally distributed. I just don't understand how to do a difference of two means with normal distribution. My teacher only ever covered examples with t distribution?.. But when it came to an assignment I am stuck. Both my random samples are less than 30 however the question is telling me to assume that its normally distributed. I just don't get what I am supposed to do at that point.
the equation for calculating df is very complex. cant we use df=n1+n2-2 in this context?
How could we use a z test in the second example if we don't have the population standard deviation?
sir please make a video on annova
How come we're not using Central Limit Theorem for Q2 where n1 and n2 >= 30
why is the formula for the degree of freedom so big? i thought it was n-1, or is that the df for a different sample?
what is standard deviation and how do i get it?
Hi, why can't I just use the formula for t = (mean1-mean2/(sqrt((s1 squared/n1)+ (s2 squared/n2)? Thanks.
why did we took degree of freedom in example one, and not in example 2 ?
Am I the only one who hears kittens meowing around 16:55? :D
You are surely only one not focused on lesson very well
thank you :)
This maybe stupid since i dont know much, but what to do when one sample size is less than 30 and the other sample size is 30 or more?
The degrees of freedom should rounded down to the nearest integer. It should be 24 not 25
why is class1 - class 2 and the the opposite?
How do I choose which one is "class 1"
for df could you just add 15 + 12 the subtract 2
to figure out the df you could have done df=n-2 which is 27-2=25 simple
Why was the left tail rejection region added to the acceptance region when calculating the critical value
Please anyone?
Enjoying Statistics 2
The best!!!!
he tSTAT test statistic follows a t distribution with n1 + n2 - 2 degrees of freedom
DF = N1-1 +N2-1 is a much easier formula
How can I decide which significance level I used?
why not taking the pondarate value for x1 & x2: ((x1*n1-x2*n2)/(n1+n2)-(u1-u2))/sqrt(....)
Is the difference between two means the same as saying 2 populations ?
what distribution is it if n1 < 30 and n2 > 30
someone please buy this man a car!