Statistics How To

Regression Analysis > A tuning parameter (λ), sometimes called a penalty parameter, controls the strength of the penalty term in ridge regression and lasso regression. It is basically the amount of shrinkage, where data values are shrunk towards a central point, like the mean. Shrinkage results in simple, sparse models which are easier to analyze … Read more

Post Hoc Tests > Duncan’s Multiple Range Test What is Duncan’s MRT? When you run Analysis of Variance (ANOVA), the results will tell you if there is a difference in means. However, it won’t pinpoint which means are different. Duncan’s Multiple Range test (DMRT) is a post hoc test to measure specific differences between pairs … Read more

Post Hoc > Studentized Range Contents: Studentized Range & Distribution Q Table Studentized Range & Distribution The Studentized Range (q) is the difference between the largest and smallest data point in a sample, measured in terms of sample standard deviations. The studentized range distribution is the probability distribution of studentized ranges for independent, identically distributed … Read more

Statistics Definitions > You may want to read this article first: What is the multinomial coefficient? The multinomial theorem provides an easy way to expand the power of a sum of variables. As “multinomial” is just another word for polynomial, this could also be called the polynomial theorem. It tells us that when you expand … Read more

Regression Analysis > Bilinear regression is an informal term (i.e. there is no set definition for its meaning). Therefore, it might mean something different depending on who is using the term and in what context. General Class of Regressions One way to define bilinear regression is as a membership to the class of regressions on … Read more

Statistics Definitions > Binomial coefficients tell us how many ways there are to choose k things out of larger set. More formally, they are defined as the coefficients for each term in (1+x)n. Written as , (read n choose k), where is the binomial coefficient of the xk term of the polynomial. An alternate notation … Read more

Statistics Definitions > You may want to read this article first: What is a Factorial(!)? The multinomial coefficient, used in combinatorics, is an extension of the binomial coefficient. It’s used to find permutations when you have repeating values or duplicate items. The formula is: In formal terms, the multinomial coefficient formula gives the expansion of … Read more

Statistics Definitions > The minimal detectable difference is the smallest difference, or change, that can be statistically detected in a given study. It is dependent on your desired significance level, and has been defined as the smallest difference δ where p (δ) ≤ α. In clinical trials, the minimal detectable difference is the smallest difference … Read more

Sampling > General Definition Direct sampling is a somewhat informal term that can refer to when the sample is taken from the actual population and not, for example, some kind of related record like driver’s license’s, voter registration cards, or census forms. Although the concept sounds simple, direct sampling isn’t always possible. It may be … Read more

Types of Variables > An active variable is a variable that is manipulated by the investigator. It’s designed to shine light on some part of a question or problem, and its usefulness comes in the way it can be controlled by a researcher. Because of that, an active variable changes in a well-defined and carefully … Read more