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Pooled-Variance t Tests and Confidence Intervals: Introduction
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- Опубликовано: 5 июн 2013
- An introduction to pooled-variance t tests and confidence intervals (in the setting of inference for two means). I don't work through an example in this video. My video working through an example can be found at: • Pooled-Variance t Test...
The shame/young offender data is simulated data with the same summary statistics as found in:
Owen, T., Fox, S. (2011). Experiences of shame and empathy in violent and non-violent young offenders. The Journal of Forensic Psychiatry & Psychology, 22(4):551-563.
I'm so grateful there are people like you who will take the time to put such useful videos on RUclips
I'm not sure if you're still checking comments - but I just wanted to say that your videos are amazing and (statistically significantly) much easier to understand than the course content for the Uni Stats course I'm doing. Thanks to you I feel confident in my final exam!
I’m here 7 years later. Still great and relevant
You are simply an angel! Thank you very much for the excellent job.
Who on earth downvotes this ? So many stats students would be lost without this guy !
It goes without saying these videos are incredibly awesome! It would've been cherry on top if the concept of confidence interval was intuitively connected with the hypothesis testing somehow. For example the video mentions we can say with an (1-α)*100% probability that the difference (μ1-μ2) lies within the range tα±SE(x1bar-x2bar) from any obtained value of (x1bar-x2bar). Which made me think the hypothesis testing would go something like the probability of finding zero within this tα±SE(x1bar-x2bar) range, which would mean the two population means were the same. But instead it doesn't expand on the point of confidence interval anymore and goes to regular method of P value calculation. Amazing content regardless!
Wow!! such clear explanation. Terminologies are so accurate. All your videos are awesome. Thanks a ton. I would love to see a video from you explaining Bessel correction and degrees of freedom. is there one already?
You are very welcome, and thanks for the kind words! I do discuss the use of n-1 in the sample variance formula, in a couple of different ways:
The Sample Variance: Why Divide by n-1? available at ruclips.net/video/9ONRMymR2Eg/видео.html
and
Proof that the Sample Variance is an Unbiased Estimator of the Population Variance, available at ruclips.net/video/D1hgiAla3KI/видео.html
+jbstatistics I need to determine whether there's a significant difference between 2 sample's variance. They are both the same size from the same population. Does the information in this video relate to my task? I'm finding myself getting very lost between what's in this video, F-test and chi^2 test, to produce my test.
Hi, is the pooled-variance t procedure the same as the student's t test? Also, as mentioned early in the video, there are 3 assumptions to the pooled-variance t procedure but I want to ask how to actually determine whether the data to be analyzed hold these assumptions.For the first assumption of independence, do I use a test for auto correlation on the dependent variable values? For the second assumption, how large is large? n=500? n=20? also is there a calculation or rule of thumb for this? For the third assumption, I feel that assuming equal variances can unrealistic, and may cause unfavorable results in some cases. Is there a guideline as to when to use unpooled variances or the Welch test that you mentioned earlier?
Thank you very much!
P.S. I often have a hard time learning statistics all because of all the abstraction present in mathematics. I am often worried that the results that I obtain from an analysis may not be accurate--which kind of defeats the purpose of performing a statistical analysis.
Watching at 2019 from India 🇮🇳 😄
Thank you!
Many thanks
You are my God
What do you use for the alpha to search for in the T table? Especially if there is no alpha given
I typically use the p-value approach (and not the rejection region approach), so we find the p-value and report it. I'm of the school of thought that we don't need to use a fixed alpha level - we report the p-value and go from there. Not everyone agrees with that approach.
If you need to choose an alpha level, then it gets a little trickier. The appropriate choice of alpha depends on the specifics of the problem at hand, but people often forget all that and just say "bah, use 0.05". But that's not what I recommend or how I go about it.
I need to determine whether there's a significant difference between 2 sample's variance. They are both the same size from the same population. Does the information in this video relate to my task? I'm finding myself getting very lost between what's in this video, F-test and chi^2 test, to produce my test. Thanks for any help
This video involves inference for the *means* of two populations, and not the variances. I have some other videos that discuss inference for variances. Cheers.
the second assumption is not that important for large samples. but shouldn't we use a test based on normal distribution for large samples ? t-test is for small samples
No, the t test is not only for small samples. If we're sampling from normally distributed populations, and the population variances are not known (and that part is essentially always the case), then we should use t procedures regardless of the sample sizes. Lots of folks will tell you to use z if n > 30 or something, but I think that's silly and leads to confusion like this.
Why couldn't you be my stat professor...
I think at 4:30 you meant to say "variance" not "mean" ... should be "lost one degree of freedom when we estimated each *variance* " ... right?
No, I meant what I said. Every variance estimator has degrees of freedom attached. If we happened to know the true population mean for group 1, then we'd estimate the variance with sum(x_i - mu_1)^2/n_1, and this would have n_1 degrees of freedom. But, we almost never know the true population mean, and so we estimate the variance with sum(x_i - mu_1)^2/(n_1-1). The "-1" in the denominator comes from the fact that we used the data to estimate the true mean, and in so doing lost a degree of freedom (when estimating the variance rolls around). In this video we do that twice (since we have two groups), and thus lost two degrees of freedom along the way.
very helpful !!!
Thanks!
amazing
Thanks!
mu_2 = mewtwo
You haave a beautiful voice bebe
Shame, shame, shame! Oh wait this isn't a game of thrones scene...