Statistics How To

Statistics Definitions > The monotone likelihood ratio (MLR) represents a useful data generating process; one where there’s a clear relationship between the magnitude of observed variables and the probability distribution they are drawn from. This clear relationship makes many statistical processes possible, including identifying uniformly most powerful processes. The MLR is defined as follows: If … Read more

Internal Consistency Reliability > Average inter-item correlation is a way of analyzing internal consistency reliability. It is a measure of if individual questions on a test or questionnaire give consistent, appropriate results; different items that are meant to measure the same general construct or idea are checked to see if they give similar scores. For … Read more

Item response theory > What is a Graded Response Model? Graded response model (or Ordered Categorical Responses Model) is a family of mathematical models for grading responses. Specifically, responses with ordered polytomous categories. Ordered means that there is a specific order, or ranking, of responses. Polytomous means that these response are divided into more than … Read more

Probability > Axiomatic probability is a unifying probability theory. It sets down a set of axioms (rules) that apply to all of types of probability, including frequentist probability and classical probability. These rules, based on Kolmogorov’s Three Axioms, set starting points for mathematical probability. Kolmogorov’s Three Axioms The three axioms are: For any event A, … Read more

Bayesian Statistics > What is The Principle of Indifference? The principle of indifference is a rule which tells us how to assign probabilities when we don’t have any special knowledge of a situation. It is also known as the principle of insufficient reason. Let’s say there are a number of different alternative possibilities. The rule … Read more

Excel for statistics > How to Load the Microsoft Excel Data Analysis ToolPak Contents (click to skip to that section): Load the Excel Data Analysis Toolpak in Excel 2013-current Load the Excel Data Analysis ToolPak in Excel 2007-2010 Notes on using the ToolPak What’s included in the Toolpak? How to Load the Data Analysis Toolpak … Read more

Statistics Definitions > Nearest neighbor matching is a solution to a matching problem that involves pairing a given point with another, ‘closest’ point. It is important in many very different fields, from data compression to DNA sequencing. Searching for a Nearest Neighbor Nearest neighbor matching can be carried out on most statistics software through a … Read more

Statistics Definitions > What is a Tolerance Level? The term “tolerance level” has a few different meanings, depending on the context of where the term is being used: Setting Limits As a Measure of Error Measuring Collineariy 1. Setting Limits In general use, tolerance level is used to set an upper limit of how much … Read more

Time Series > What is a Spectral Plot? A spectral plot is a graph which allows us to examine the cyclic structure, in the frequency domain, of a time series. A time series represents a progression of some parameter in time. We can think of it as a function of time, but it is typically … Read more

Statistics Definitions > A combined mean is a mean of two or more separate groups, and is found by : Calculating the mean of each group, Combining the results. Combined Mean Formula Watch the video for two worked examples using the combined mean formula: Can’t see the video? Click here to watch it on YouTube … Read more