Statistics How To

Hypothesis Testing > Results from a statistical tests will fall into one of two regions: the rejection region— which will lead you to reject the null hypothesis, or the acceptance region, where you provisionally accept the null hypothesis. The acceptance region is basically the complement of the rejection region; If your result does not fall … Read more

Statistics Definitions > In a general sense, infinitely divisible means that any section of time and space can be divided into an infinite number of smaller and smaller pieces. For example, 10 feet can be subdivided into 1 foot sections, 0.1 foot sections, 0.00001 foot sections…and so on. However, infinite divisibility in probability theory has … Read more

Confounding Variables > What are History Graded Influences? Normative history graded influences are events experienced by a particular culture at a certain period of time. The term normative* here means that the majority of a culture experiences the events — as opposed to a small group of people. These events create generational differences in a … Read more

Graph Theory > A Hamiltonian cycle is a closed loop on a graph where every node (vertex) is visited exactly once. A loop is just an edge that joins a node to itself; so a Hamiltonian cycle is a path traveling from a point back to itself, visiting every node en route. If a graph … Read more

Statistics Definitions > Illusory association happens when an association between two attributes is not direct; The association is dependent on a third, hidden or unrecorded attribute. Example “What one Christian does is his own responsibility, what one Jew does is thrown back at all Jews.” Anne Frank, May 22, 1944 (Frank, 1993, p. 239) Major … Read more

Combinatorics > What is Queuing Theory? Queuing theory is the study of queues and the random processes that characterize them. It deals with making mathematical sense of real-life scenarios. For example, a mob of people queuing up at a bank or the tasks queuing up on your computer’s back end. In queuing theory we often … Read more

Probability > In statistics, an urn model is an idealized way of modeling real-life problems as if they were problems which involve drawing balls out of an urn, or box. The urn contains balls of two or more colors. Depending on the problem being studied, the balls may be: Replaced after each draw (called sampling … Read more

Types of Sampling > Adaptive sampling (also called response-adaptive designs) is where you adapt your selection criteria as the experiment progresses, based on preliminary results as they come in. Adaptive sampling is especially important in medical research, where traditional sampling and research techniques may lead to ethical dilemmas and clinical trials that are not in … Read more

Graph Theory > What is the Traveling Salesman Problem? The Traveling Salesman Problem answers the question “Given a list of cities you want to visit, what’s the shortest possible distance to visit all of them and return to your starting point?“. The problem was first described in an 1832 traveling salesman’s manual and has since … Read more

Statistics Definitions > Order Statistics Order Statistics Definition Order statistics are sample values placed in ascending order. The study of order statistics deals with the applications of these ordered values and their functions. Let’s say you had three weights: X1 = 22 kg, X2 = 44 kg, and X3 = 12 kg. To get the … Read more