Two Sample t-Test:Equal vs Unequal Variance Assumption| Statistics Tutorial #24| MarinStatsLectures

In this statistics tutorial, we learn about the assumption of equal variance (or standard deviation) vs non-equal variance (or standard deviation). When working with the 2 sample t-test, we must make one of those two assumptions. We also learn how to decide if we can assume equal variance or if we should assume unequal variance. We cover making this decision both in a subjective way, as well as describing more formal tests that can be used. Assuming equal variance is also referred to as 'pooling', or a 'pooled estimate' of the variance. This video also shows how to calculate the standard error for the difference in means under each of the assumptions, although the focus is on what each assumption means, in concept, and not on the calculations. 

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Content Creator: Mike Marin (B.Sc., MSc.) Senior Instructor at UBC.
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[amydalasmusic]

is nobody going to comment on how this man is writing backwards, thats insane lol

[aravindssingapore]

Hello amydalasmusic:
I admire how this teacher is left-handed too. I cannot even imagine myself being able to write with the left hand

[asiatrigonopoulou]

thank you for the video really good explanations. helped me a lot!

[fidelestevesdonascimento]

Hi, very nice lesson. I am here thinking... In S_pooled, the denominator should'nt be n_1 + n_2 - 1?! Would be the same as using the union of the two samples in order to make the standard deviation estimative.

[Rubiking]

What is the meaning of a 0 valued pooled variance?

[TheMishmak]

Excellent explanation, thanks very much!

[hopetdudusola]

Thank you so much, just to be clear if for instance my standard deviation for sample 1 is 8.0026 and my standard deviation for sample two is
3.015 which if i divide is greater than 2, then it means i proceed to use an unequal assumption of variance right?

[gbganalyst]

Thank you so much for this awesome tutorial. I got it right now!

[AnuragTK]

Hi, Thanks a ton for all the videos but I have a question.
In a video where you derive the equation for standard error, you state a property as var(x1+x2)= var(x1) + var(x2), even in that case x1 and x2 are independant. So how is this different from that? Why does the sign change from + to -. Thanks again

[yshulz]

Hello, may I ask why you write that the variance of the sample mean is equal to the sample variance / n as opposed to variance/n? (here I write variance to mean the exact variance of the data which we do not know, rather than the sample variance). Presumably the next stage is to apply the 2-sample t test by dividing by calculated variances, but this will cause an issue because to assume a t distribution we require that the numerator is standard normally distributed, which we do not immediately obtain by dividing by sample SD (we would have to divide by the true SD, and then hope for cancellations with the Chi-squared distribution of the denominator to remove unknown values). How valid is this approximation in practice for the case of unequal standard deviations, since there is no such cancellation?

[chrisg]

Excellent tutorial - thank you. Question, I have 2 groups with 10 samples in each. They have been compared and shown to have equal variance allowing the experiment to start i.e. the groups are considered to be from the same population. After a treatment the variances are no longer equal. As the treatment wears off the variances again become equal. Due to this the stats package creates a new, and much lower, DoF value for the treatment significance calculation. I understand why non-equal variance could cause lower DoF. But as the test started and ended with equal variance I would have thought the DoF should not change throughout the test? The un-equal variance appears to point to outliers (either treatment variability or method variability). Is the change in DoF a stats package anomaly? Thanks for your help.

[whoo]

i am wondering why there is no distinguish on equal and non-equal variance in paired t-test. l:

[abhishek-shrm]

Sir, you have forgot to add Mann Whitney U in this playlist.

[divyaaarr]

Sir, if we are giving a score chart to a group of people for a survey between 2 independent food samples how to know, if we want to perform one tailed test or two tailed test?