jbstatistics

I discuss the relationship between a (two-sided) confidence interval and a two-sided hypothesis test. I discuss the relationship in terms of inference for one mean, but the same concept holds in many other settings as well.

A look at what factors influence the power of a hypothesis test. This discussion is in the setting of a one-sample Z test on the population mean, but the concepts hold for many other types of test as well. I discuss what...

An example of a t test on one population mean. I first work through an example of a t test, then briefly investigate the influence of 3 outliers on the conclusions.

The sleep misperception index data is simulated data w...

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 alterna...

An example of calculating power and the probability of a Type II error (beta), in the context of a Z test for one mean. Much of the underlying logic holds for other types of tests as well.

An ultra-brief summary of hypothesis testing. (Just for fun.)

A brief discussion of the meaning of statistical significance, and how it is strongly related to the sample size.

A discussion of when to use a one-sided alternative hypothesis and when to use a two-sided alternative hypothesis in hypothesis testing. I assume that the viewer has already had a brief introduction to the notion of one-s...

An example of a Z test on the population mean mu. This test is appropriate when sampling from a normally distributed population, when the population standard deviation sigma is known.

A discussion of Type I errors, Type II errors, their probabilities of occurring, and the power of a hypothesis test.

An introduction to the concept of the p-value in a Z test. This video discusses the p-value in the context of a Z test for one mean, but the same logic holds for other tests.

An introduction to the rejection region approach to reaching a conclusion in a Z test. This video discusses the rejection region in the context of a Z test for one mean, but the same logic holds for other Z tests.

An introduction to Z tests for a population mean mu. These tests are appropriate when sampling from a normally distributed population where sigma is known. I discuss the hypotheses and the underlying logic, and work thro...

A first look at hypothesis testing.

An introduction to the concept of the p-value, in the context of one-sample Z tests for the population mean. Much of the underlying logic holds for other tests as well. I discuss what a p-value is, then using simulation ...

I derive the appropriate formula for a confidence interval for the population mean mu, when sampling from a normally distributed population with a known value of sigma.

(The purpose of this video is to show the rationa...

An introduction to normal quantile-quantile (QQ) plots (a graphical method for assessing whether a set of observations is approximately normally distributed). I discuss the motivation for the plot, the construction of th...

An introduction to confidence intervals.

I introduce the chi-square test for one-way tables (sometimes called a goodness-of-fit test), and work through an example.

The data used here is from a classic 1905 genetics experiment by William Bateson and Reginald Punnet.

I introduce the chi-square test of independence and work through an example.

The binge drinking data is from:

Wechsler H, Lee JE, Kuo M, Lee H. (2000). College Binge Drinking in the 1990s: A Continuing Problem — Resul...

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...

I discuss the concept of sampling distributions (an important concept that underlies much of statistical inference), and illustrate the sampling distribution of the sample mean in a simple example.

I work through an example of finding the median, areas under the curve, and the cumulative distribution function for a continuous probability distribution. I assume a basic knowledge of integral calculus. I derive the...

I work through an example of deriving the mean and variance of a continuous probability distribution. I assume a basic knowledge of integral calculus.

A brief introduction to the (continuous) uniform distribution. I discuss its pdf, median, mean, and variance. I also work through an example of finding a probability and a percentile. I don't do any integration in this v...

An introduction to the t distribution, a common continuous probability distribution. I discuss how the t distribution arises, its pdf, its mean and variance, and its relationship to the standard normal distribution. I il...

An introduction to the normal distribution, often called the Gaussian distribution. The normal distribution is an extremely important continuous probability distribution that arises very frequently in probability and stat...

An introduction to continuous random variables and continuous probability distributions. I briefly discuss the probability density function (pdf), the properties that all pdfs share, and the notion that for continuous ran...

A brief introduction to leverage and influence in simple linear regression. This video is about the basic concepts, and only briefly mentions numerical measures of leverage and influence near the end of the video.

I discuss estimating the mean of Y and predicting a single value of Y for a given value of X in simple linear regression. I discuss the form of the confidence interval for the mean and prediction interval for a single val...

A look at the relationship between the pooled-variance t test and simple linear regression. I illustrate how the pooled-variance t test can be done as a regression, by declaring an appropriate indicator variable. I assum...

An introduction to the multinomial distribution, a common discrete probability distribution. I discuss the basics of the multinomial distribution and work through two examples of probability calculations. For comparison ...

An introduction to the negative binomial distribution, a common discrete probability distribution. In this video I define the negative binomial distribution to be the distribution of the number of *trials* needed to obtai...

An introduction to the Bernoulli distribution, a common discrete probability distribution.

A look at transformations in the context of simple linear regression. I look at two examples where taking a transformation (applying a function to the response and/or explanatory variables) can help to satisfy the assumpt...

A look at the Pearson correlation coefficient (r), the coefficient of determination (r^2), some of their properties and a few examples. (This is discussed in the context of measuring the strength of the linear relationshi...

I work through an example relating eggshell thickness to DDT concentration, fitting the least squares line, using the line for prediction, interpreting the coefficient of determination, checking the residual plots and carr...

I work through an example of finding a confidence interval and carrying out a hypothesis test on the slope parameter.

The data used is estimated from a figure in:

Singer et al. (2004). Empathy for pain involves the aff...

I show the formulas (and work through some of the underlying logic) for confidence intervals and hypothesis tests on the slope parameter in simple linear regression.

A quick look at a few cautions about simple linear regression.

Anscombe's quartet can be found in:

Anscombe, F. (1973). Graphs in statistical analysis. American Statistician, 27:17--21.

The fuel use vs speed data is fo...

An investigation of the normality, constant variance, and linearity assumptions of the simple linear regression model through residual plots.

The pain-empathy data is estimated from a figure given in:

Singer et al. (200...

A look at the assumptions on the epsilon term in our simple linear regression model.

A look at the interpretation of the parameters (beta_0, beta_1, sigma^2), and their corresponding estimates in simple linear regression.

An introduction to the least squares regression line in simple linear regression.

The pain-empathy data is estimated from a figure given in:

Singer et al. (2004). Empathy for pain involves the affective but not sensory ...

An introduction to simple linear regression.

The pain-empathy data is estimated from a figure given in:

Singer et al. (2004). Empathy for pain involves the affective but not sensory components of pain. Science, 303:1157...

I work through an example of finding the p-value for a chi-square test, using both the table and R.

Finding significance in a one-way ANOVA F test means there is strong evidence that not all population means are equal. Which are different? We can explore that with a multiple comparison procedure. Here we look at the s...

An example of finding the p-value in one-way ANOVA. The p-value (the area to the right of the F test statistic) is found using both the F table and the statistical software R.

A one-way ANOVA example. The example and data used here is based on information and summary statistics from:

Grattan-Miscio, K. and Vogel-Sprott, M. (2005). Alcohol, intentional control, and inappropriate behavior: Regu...