Statistics How To

Statistics Definitions > Rank-Biserial Correlation What is Rank-Biserial Correlation? Rank-biserial correlation (rank biserial r or rrb) is used when you want to find a correlation between dichotomous (binary) nominal data and ordinal (ranked) data. It is a special case of Somers’ D. Formula The formula (assuming there are no tied ranks) is: rrb = 2 … Read more

Statistics Definitions > Guttman’s lambda-2 What is Guttman’s lambda-2? Guttman’s lambda-2 (Guttman’s λ2) is a reliability estimate. λ-2 is the second in a series of 6 lambda’s proposed by Guttman in 1945. Lambda-1 was intended as a starting point for reliability analysis. From the 6 lambdas, lambda-2 and lambda-3 (which is equivalent to Cronbach’s alpha) … Read more

Statistics Definitions > Reliability and Validity Contents: Overview What is Reliability? The Reliability Coefficient What is Validity? Curricular Validity Overview of Reliability and Validity Outside of statistical research, reliability and validity are used interchangeably. For research and testing, there are subtle differences. Reliability implies consistency: if you take the ACT five times, you should get … Read more

Statistics Definitions > Spearman-Brown Formula What is the Spearman-Brown Formula? The Spearman-Brown Formula (also called the Spearman-Brown Prophecy Formula) is a measure of test reliability. It’s usually used when the length of a test is changed and you want to see if reliability has increased. The formula is: rkk = k(r11) / [1 + (k … Read more

Correlation Coefficients > Contents: Partial Correlation Semi-Partial Correlation What is Partial Correlation? Partial correlation measures the strength of a relationship between two variables, while controlling for the effect of one or more other variables. For example, you might want to see if there is a correlation between amount of food eaten and blood pressure, while … Read more

Outliers > Modified Thompson Tau Test What is the modified Thompson Tau Test? The modified Thompson Tau test is a way to find outliers in a data set. The data set must be a single variable (e.g. x1, x2,…xn). One potential outlier is tested at a time using a version of the t-test. Roughly speaking, … Read more

Statistics Definitions > Thurstone Scale What is the Thurstone Scale? A Thurstone scale has a number of “agree” or “disagree” statements. It is a unidimensional scale to measure attitudes towards people. Developing the scale is time consuming and relatively complex compared to other scales (like the Likert scale); You can find the steps below. Although … Read more

Statistics Definitions > Cauchy-Schwarz Inequality What is the Cauchy-Schwarz Inequality? The Cauchy-Schwarz Inequality (also called Cauchy’s Inequality, the Cauchy-Bunyakovsky-Schwarz Inequality and Schwarz’s Inequality) is useful for bounding expected values that are difficult to calculate. It allows you to split E[X1, X2] into an upper bound with two parts, one for each random variable (Mukhopadhyay, 2000, … Read more

Design of Experiments > Randomization What is Randomization? Randomization in an experiment is where you choose your experimental participants randomly. For example, you might use simple random sampling, where participants names are drawn randomly from a pool where everyone has an even probability of being chosen. You can also assign treatments randomly to participants, by … Read more

Bias in Statistics > Accidental Bias What is Accidental Bias? Accidental bias is the introduction of one or more nuisance variables into your experiment. These nuisance variables may be known or unknown to the researcher. But in either case they are unwanted and systematically affect your experimental units — which means you must take them … Read more