Uploaded June 2013 | Updated September 2026, 2 hours ago
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: youtu.be/Q526z1mz4Sc
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.
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: youtu.be/Q526z1mz4Sc
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.









![Introduction to the Central Limit Theorem
I discuss the central limit theorem, a very important concept in the world of statistics. I illustrate the concept by sampling from two different distributions, and for both distributions plot the sampling distribution of the sample mean for various sample sizes. I also discuss why the central limit theorem is important in statistics, and work through a probability calculation. (For the most part this is a non-technical treatment, and simply illustrates the important implications of the central limit theorem.)
For those using R, here is the R code to find the probability for the example in this video:
Finding the (approximate) probability that the mean salary of 100 randomly selected employees exceeds $66,000:
1-pnorm(66000,62000,32000/sqrt(100))
[1] 0.1056498
Or, standardizing:
1-pnorm((66000-62000)/(32000/sqrt(100)))
[1] 0.1056498
1-pnorm(1.25)
[1] 0.1056498 Introduction to the Central Limit Theorem](https://i.ytimg.com/vi/Pujol1yC1_A/mqdefault.jpg)
