# Blog

## 8.2 The Sampling Distribution of the Sample Proportion

Posted by on Jan 4th, 2015 in 8. Inference for Proportions | 0 comments

A discussion of the sampling distribution of the sample proportion. I discuss how the distribution of the sample proportion is related to the binomial distribution, discuss its mean and variance, and illustrate that the sample proportion is approximately normally distributed for large sample sizes.

## 4.5 Proof that the Sample Variance is an Unbiased Estimator of the Population Variance

Posted by on Jan 4th, 2015 in 4. Sampling Distributions | 0 comments

A proof that the sample variance (with n-1 in the denominator) is an unbiased estimator of the population variance. In this proof I use the fact that the sampling distribution of the sample mean has a mean of mu and a variance of sigma^2/n. If you need that to be shown as well, I show that in this video: http://youtu.be/7mYDHbrLEQo.

## 1.17 Poisson or Not? (When does a random variable have a Poisson distribution?)

Posted by on Jan 4th, 2015 in 1. Discrete Probability Distributions | 0 comments

A not-too-technical look at the conditions required for a random variable to have a Poisson distribution. It can be difficult to determine whether a random variable actually has a Poisson distribution, so here I look at a few examples and some visual illustrations that may help. There are no probability calculations carried out in this video. I assume that the viewer has already been introduced to the Poisson distribution, but I do a brief review at the start.

## 7.10 Pooled-Variance t Procedures: Investigating the Normality Assumption

Posted by on Oct 27th, 2013 in 7. Inference for Two Means | 0 comments

A discussion of the assumptions of pooled-variance t tests and confidence intervals for the difference in means. The assumptions are briefly discussed, and the effects of different violations of the normality assumption are investigated through simulation. The quick summary: Pooled-variance t procedures are more robust to violations of the normality assumption than their one-sample counterparts.

## 7.9 An Example of a Paired-Difference t Test and Confidence Interval

Posted by on Oct 27th, 2013 in 7. Inference for Two Means | 0 comments

An example of a paired-difference t test and confidence interval. The data used in this video is from: Penetar et al. (2012). The isoflavone puerarin reduces alcohol intake in heavy drinkers: A pilot study. Drug and Alcohol Dependence, 126:256-261. Values used in this video are simulated values based on the summary statistics found in the paper. (The summary statistics, test statistic, p-value, and overall conclusions are the same.)

## 7.8 An Introduction to Paired-Difference Procedures

Posted by on Oct 27th, 2013 in 7. Inference for Two Means | 0 comments

An introduction to paired-difference procedures. I briefly discuss how paired difference scenarios arise, and briefly outline how we can use the paired-difference t procedure to construct confidence intervals and carry out hypothesis tests. (Paired difference procedures are sometimes referred to as matched-pairs procedures, depending on the setting.) The alcohol/reaction time data is loosely based on information in: Anderson et al. (2011). Functional Imaging of Cognitive Control During Acute Alcohol Intoxication. Alcoholism: Clinical and...

## 7.7 Pooled or Unpooled Variance t Tests and Confidence Intervals? (To Pool or not to Pool?)

Posted by on Oct 27th, 2013 in 7. Inference for Two Means | 0 comments

I discuss the assumptions of both the pooled-variance and Welch (unpooled variance) t tests and confidence intervals, and their advantages and disadvantages. I illustrate some of pros and cons using the results of two simulations.

## 7.6 Welch (Unpooled Variance) t Tests and Confidence Intervals: An Example

Posted by on Oct 27th, 2013 in 7. Inference for Two Means | 0 comments

I work through an example of a Welch (unpooled variance) t test and confidence interval (in the setting of inference for two means). The antivenom/swelling data is found in: Offerman et al. (2009). Subcutaneous crotaline Fab antivenom for the treatment of rattlesnake envenomation in a porcine model. Clinical Toxicology, 47: 61-68.

## 7.5 Welch (Unpooled Variance) t Tests and Confidence Intervals: Introduction

Posted by on Oct 27th, 2013 in 7. Inference for Two Means | 0 comments

An introduction to Welch (unpooled variance) t tests and confidence intervals. (Inference for two means.) The Cairo traffic police officer data is simulated data with the same summary statistics as found in: Kamal, A., Eldamaty, S., and Faris, R. (1991). Blood level of Cairo traffic policemen. Science of the Total Environment, 105:165-170.