An introduction to the concept of independent events, pitched at a level appropriate for the probability section of a typical introductory statistics course. I give the definition of independence, work through some simple examples, and attempt to illust...

From jbstatistics

Conditional probability example problems, pitched at a level appropriate for a typical introductory statistics course. I assume that viewers have already been introduced to the concepts of conditional probability and independence, but I do review the con...

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An introductory discussion of unions, intersections, and complements in the context of basic probability. I include a discussion of mutually exclusive events, as well as the addition rule. I work through a simple die rolling example, and also an example...

From jbstatistics

(Recorded in 2013, but misplaced and not released until now.)
I work through an example of a one-sample t test on a mean, and (intentionally) make many false statements. Some of them might sound pretty reasonable. The lesson is: Get your statistics hel...

From jbstatistics

A discussion of De Morgan's laws, in the context of basic probability. I illustrate De Morgan's laws using Venn diagrams, describe their meaning in a worded example, and show how they might be useful in a probability calculation.
I will get back to stat...

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An introduction to conditional probability, pitched at a level appropriate for a typical introductory statistics course. I work through some simple examples in this introductory video, and a I briefly touch on the concept of independence in an example a...

From jbstatistics

Are mutually exclusive events independent? I get asked variants of this question frequently, so itâ€™s evident that some students confuse these two concepts. The one sentence summary: If A and B are mutually exclusive events, then they are independent if...

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Usually, Venn diagrams are not very useful for illustrating independence, as the sizes of the circles and their intersections have no meaning. It can help to illustrate independence if we force the area of each region to be equal to its probability of oc...

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An introduction to the expected value and variance of discrete random variables. The formulas are introduced, explained, and an example is worked through.
This is an updated and refined version of an earlier video. Those looking for the original vers...

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A discussion of the sampling distribution of the ratio of sample variances. I begin by discussing the sampling distribution of the ratio of sample variances when sampling from normally distributed populations, and then illustrate, through simulation, the...

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I work through an example of a confidence interval and a hypothesis test for the ratio of population variances, using F procedures that are based on the assumption of normally distributed populations.
The example in this video involves tail lengths of ...

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A discussion of the sampling distribution of the sample variance. I begin by discussing the sampling distribution of the sample variance when sampling from a normally distributed population, and then illustrate, through simulation, the sampling distribut...

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I derive the appropriate formula for a confidence interval for the ratio of two population variances (when we are sampling from normally distributed populations). I do not do any calculations or look at any examples in this video, I simply derive the app...

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An introduction to confidence intervals and hypothesis tests for the ratio of two population variances (using F procedures based on the assumption of normally distributed populations). I introduce the methods, and take a quick look at an example and disc...

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I derive the appropriate formula for a confidence interval for a population variance (when we are sampling from a normally distributed population). I do not do any calculations or look at any examples in this video, I simply derive the appropriate confid...

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I discuss confidence intervals and hypothesis tests for a variance when sampling from a normally distributed population. I discuss the logic behind the procedures, discuss some characteristics of the sampling distribution of the sample variance, and give...

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I discuss the sampling distribution of the difference in sample proportions, and confidence intervals and hypothesis tests for the difference in population proportions (using large sample Z procedures based on the normal approximation).
The male birth ...

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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...

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I work through an example of a confidence interval and a hypothesis test for a single proportion, using normal approximation methods (Z test and confidence interval).
The data on the proportion of male births is from:
Koshy et al. (2010). Parental smokin...

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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 i...

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An introduction to the geometric distribution. I discuss the underlying assumptions that result in a geometric distribution, the formula, and the mean and variance of the distribution. I work through an example of the calculations and then discuss the c...

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An informal discussion of why we divide by n-1 in the sample variance formula. I give some motivation for why we should divide by something less than n, and (casually) discuss the concept of degrees of freedom (in the context of the sample variance). I ...

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An introduction to z-scores as a descriptive measure of relative standing. (I don't do any probability calculations in this video.) I do a simple calculation example, discuss the empirical rule in the context of z-scores, and illustrate what the z-scor...

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A brief introduction to measures of central tendency. The mean, median, and mode are introduced and calculated for a simple example. The relationship between the mean and median for different shapes of distributions is then discussed.
The guinea pig...

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An introduction to measures of variability. I discuss the range, mean absolute deviation, variance, and standard deviation, and work through a simple example of calculating these quantities. I then discuss interpreting the standard deviation, including ...

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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 illustrate the relationship between...

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A brief introduction to the chi-square distribution. I discuss how the chi-square distribution arises, its pdf, mean, variance, and shape....

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I work through a few probability examples based on some common discrete probability distributions (binomial, Poisson, hypergeometric, geometric -- but not necessarily in this order). I assume that you've been previously introduced to these distributions ...

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A brief overview of some common discrete probability distributions (Bernoulli, Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson). I discuss when these distributions arise and the relationships between them. I do not do any calculations in...

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An introduction to the Poisson distribution. I discuss the conditions required for a random variable to have a Poisson distribution. work through a simple calculation example, and briefly discuss the relationship between the binomial distribution and th...

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An introduction to the binomial distribution. I discuss the conditions required for a random variable to have a binomial distribution, discuss the binomial probability mass function and the mean and variance, and look at two examples involving probabilit...

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I discuss the sampling distribution of the sample mean, and work through an example of a probability calculation. (I only briefly mention the central limit theorem here, but discuss it in more detail in another video).
The mean and standard deviation of...

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An introduction to the hypergeometric distribution. I briefly discuss the difference between sampling with replacement and sampling without replacement. I describe the conditions required for the hypergeometric distribution to hold, discuss the formula,...

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I discuss standardizing normally distributed random variables (turning variables with a normal distribution into something that has a standard normal distribution). I work through an example of a probability calculation, and an example of finding a perce...

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I derive the mean and variance of the binomial distribution. I do this in two ways. First, I assume that we know the mean and variance of the Bernoulli distribution, and that a binomial random variable is the sum of n independent Bernoulli random variab...

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An example of calculating power and the probability of a Type II error (beta), in the context of a two-tailed Z test for one mean. Much of the underlying logic holds for other types of tests as well.
I have a related video with a one-tailed Z test exa...

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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 simulati...

From jbstatistics