Synonyms for point_biserial_correlation or Related words with point_biserial_correlation

spearman_correlation              σph              cesàro_equation              glaisher_kinkelin_constant              hellinger_distance              nörlund_rice_integral              chernoff_inequality              hyperbolic_tangent_function              pearson_correlation_coefficient              hotelling_squared_distribution              autocovariance_function              δy              logarithmic_derivative              sample_covariance_matrix              differintegral              ramanujan_tau_function              youden              δij              variance_covariance              isothermal_compressibility              ricci_curvature_tensor              δu              gudermannian_function              mmse_estimator              fisher_noncentral_hypergeometric_distribution              quantile_function              bispectrum              bessel_correction              gaussian_binomial              wilks_lambda_distribution              trinomial_expansion              landau_ramanujan_constant              shannon_entropy              cumulant_generating_function              landé_factor              studentized_range              rényi_entropy              σp              frobenius_norm              λd              rayleigh_quotient              nonparametric_skew              dirichlet_eta_function              multinomial_coefficient              deltap              bhattacharyya_coefficient              scalar_curvature              viscous_damping              homological_equivalence              ks_pme             

Examples of "point_biserial_correlation"
where formula_62 is the point biserial correlation of item "i". Thus, if the assumption holds, where there is a higher discrimination there will generally be a higher point-biserial correlation.
Also the square of the point biserial correlation coefficient can be written:
Phi is related to the point-biserial correlation coefficient and Cohen's "d" and estimates the extent of the relationship between two variables (2×2).
The point-biserial correlation is mathematically equivalent to the Pearson (product moment) correlation, that is, if we have one continuously measured variable "X" and a dichotomous variable "Y", "r" = "r". This can be shown by assigning two distinct numerical values to the dichotomous variable.
It is worth also mentioning some specific similarities between CTT and IRT which help to understand the correspondence between concepts. First, Lord showed that under the assumption that formula_60 is normally distributed, discrimination in the 2PL model is approximately a monotonic function of the point-biserial correlation. In particular:
To calculate "r", assume that the dichotomous variable "Y" has the two values 0 and 1. If we divide the data set into two groups, group 1 which received the value "1" on "Y" and group 2 which received the value "0" on "Y", then the point-biserial correlation coefficient is calculated as follows:
Commonly used measures of association for the chi-squared test are the Phi coefficient and Cramér's V (sometimes referred to as Cramér's phi and denoted as "φ"). Phi is related to the point-biserial correlation coefficient and Cohen's "d" and estimates the extent of the relationship between two variables (2 x 2). Cramér's V may be used with variables having more than two levels.
The point biserial correlation coefficient ("r") is a correlation coefficient used when one variable (e.g. "Y") is dichotomous; "Y" can either be "naturally" dichotomous, like whether a coin lands heads or tails, or an artificially dichotomized variable. In most situations it is not advisable to dichotomize variables artificially. When you artificially dichotomize a variable the new dichotomous variable may be conceptualized as having an underlying continuity. If this is the case, a biserial correlation would be the more appropriate calculation.
It's important to note that this is merely an equivalent formula. It is not a formula for use in the case where you only have sample data. There is no version of the formula for a case where you only have sample data. The version of the formula using "s is useful if you are calculating point-biserial correlation coefficients in a programming language or other development environment where you have a function available for calculating "s, but don't have a function available for calculating "s".
Reliability provides a convenient index of test quality in a single number, reliability. However, it does not provide any information for evaluating single items. Item analysis within the classical approach often relies on two statistics: the P-value (proportion) and the item-total correlation (point-biserial correlation coefficient). The P-value represents the proportion of examinees responding in the keyed direction, and is typically referred to as "item difficulty". The item-total correlation provides an index of the discrimination or differentiating power of the item, and is typically referred to as "item discrimination". In addition, these statistics are calculated for each response of the oft-used multiple choice item, which are used to evaluate items and diagnose possible issues, such as a confusing distractor. Such valuable analysis is provided by specially-designed psychometric software.
A specific case of biserial correlation occurs where "X" is the sum of a number of dichotomous variables of which "Y" is one. An example of this is where "X" is a person's total score on a test composed of "n" dichotomously scored items. A statistic of interest (which is a discrimination index) is the correlation between responses to a given item and the corresponding total test scores. There are three computations in wide use, all called the "point-biserial correlation": (i) the Pearson correlation between item scores and total test scores including the item scores, (ii) the Pearson correlation between item scores and total test scores excluding the item scores, and (iii) a correlation adjusted for the bias caused by the inclusion of item scores in the test scores. Correlation (iii) is