Statistics How To

Statistics Definitions > What is a Parameter Space? Statistical inference concerns an unknown parameter θ. Sometimes we know nothing about θ but most of the time we have an idea about what kinds of numbers θ can take on: real numbers, subsets of real numbers, complex numbers, even higher-dimensions. Those possible values for θ are … Read more

Effect Size > Cohen’s f statistic is used as a measure of effect size in ANOVA and ANCOVA. The statistic gives an estimate of the proportion of variance explained by the categorical variable. Cohen’s f is a ratio between two interim sums of squares: the term-sum-of-squares and error-sum-of-squares (or proportion of variance accounted for relative … Read more

Probability Distributions > Logarithmic distribution Contents: What is a Logarithmic Distribution? Other “Logarithmic Distribution” Types What is a Logarithmic Distribution? The logarithmic distribution (also called the logarithmic series distribution or log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion. It has one parameter β, which ranges from 0 to 1, and … Read more

Probability Distributions > Multivariate distributions show comparisons between two or more measurements and the relationships among them. For each univariate distribution with one random variable, there is a more general multivariate distribution. For example, the normal distribution is univariate and its more general counterpart is the multivariate normal distribution. While the multivariate normal model is … Read more

Probability Distributions > The modified geometric distribution gives the number of failures until the first success in a series of independent trials. The modified geometric distribution starts at zero—that’s why it’s sometimes called the zero-modified (or zero-truncated) geometric distribution; a special case is the zero-modified negative binomial [1]. Geometric vs. Modified Geometric Distribution Both the … Read more

Probability in Real Life > Experimental probability is the results from an actual experiment of repeated trials. In class, examples are sometimes given with coin tosses or dice rolling. For example, you could toss a coin 50 times to see the probability of getting heads (your results should come close to the theoretical probability of … Read more

Probability in Real Life > A probability tree diagram is one way to study the sample space of an experiment. They are often helpful for studying outcomes and probabilities for multistage experiments. Any situation where an “experiment” is multistage can serve as a tree diagram real life example. Tree Diagram Real Life Example List Accepting … Read more

Probability in Real Life > Real Life Examples of the Geometric Distribution The Geometric distribution tells us the probability of a certain number of failures to get the first success in k Bernoulli trials (where the only two possible outcomes are success or failure). In class, you’re often given an example with dice rolls or … Read more

Probability > Key Takeaways: Epistemic probability is incomplete information about how probabilities arise. The field bridges the gap between known measurements and what is thought to be true. An example is classical statistical mechanics. Epistemic probability concerns “…our possession of knowledge, or information.” It is incomplete knowledge about the mechanism from which the probabilities are … Read more

Probability > An uncountable set is a set that isn’t countable. It’s a bit more complicated than simply deciding whether a set contains a countable number of items (or not). Infinity and The Uncountable Set While you can’t imagine counting an infinite set (i.e., start at zero and count to infinity), an infinite set actually … Read more