## 7.1 Inference for Two Means: Introduction

I introduce inference procedures for the difference between two means in the case where the population standard deviations are known. I discuss the sampling distribution of the difference in the sample means, and discuss the confidence interval formula and the hypothesis test of the equality of population means.

## 7.2 The Sampling Distribution of the Difference in Sample Means

I discuss the characteristics of the sampling distribution of the difference in sample means (X1 – X2). I then work through an example of a probability calculation that involves these concepts. The values for male and female heights are based on information in the 2009-2011 Canadian Health Measures Survey.

## 7.3 Pooled-Variance t Tests and Confidence Intervals: Introduction

An introduction to pooled-variance t tests and confidence intervals (in the setting of inference for two means). 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, … Read more

## 7.4 Pooled-Variance t Tests and Confidence Intervals: An Example

I work through an example of a pooled-variance t test and confidence interval (in the setting of inference for two means). The MENT/PTSD data is simulated data with the same summary statistics as found in: Geraerts et al. (2009). Detecting deception of war-related posttraumatic stress disorder. The Journal of Forensic Psychiatry & Psychology, 20(2):278-285.

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

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.

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

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.

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

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.

## 7.8 An Introduction to Paired-Difference Procedures

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 … Read more

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

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 … Read more

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

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.