JB An introduction to t tests for one population mean. I briefly discuss when we use the test, and when we would use a z test instead. I also briefly discuss the hypotheses of the test, and the p-value for different alternatives. I then work through an example. (If you are comfortable with the basics of … Read more
of a t test, then briefly investigate the influence of 3 outliers on the conclusions. The sleep misperception index data is simulated data with the same summary statistics as found in: Manconi et al. (2010). Measuring the error in sleep estimation in normal subjects and in patients with insomnia. Journal of Sleep Research, 19:478–486.
A discussion of the assumptions of the t test on one mean. (The assumptions are the same as those of the t confidence intervals for one mean.) The assumptions are discussed, and the effect of different violations of the normality assumption is investigated through simulation.
I look at at what influences the choice of the t statistic or z statistic in one-sample hypothesis tests on the population mean mu, then work through an example of a t test. I compare the p-value of the t test to what we would have found had we (incorrectly) used a z test.
I work through examples of finding the p-value for a one-sample t test using the t table. (It’s impossible to find the exact p-value using the t table. Here I illustrate how to find the appropriate interval of values in which the p-value must lie.)
Here I work through two examples of finding areas under the t distribution, using both R and the t table.
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.
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.
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
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.