Textbook - Essential STATISTICS for the BEHAVIORAL SCIENCES BY Gregory J. Privitera

1. Define the Pearson Correlation Coefficient.

2. Define correlation.

3. Define a scatter plot.

4. Define the Point-biserial Correlation Coefficient.

5. Define the Phi Correlation Coefficient.

6. Define the Spearman rank-order correlation coefficient (rs), or Spearman's rho.

7. Define Data Points.

Please participate (respond) to the classmates answers with notable and educational input. (200 word minimum Reponses)

1. Kelly:Like all correlation analyses the Point-Biserial Correlation measures the strength of association or co-occurrence between two variables. Correlation analyses express this strength of association in a single value, the correlation coefficient.

The Point-Biserial Correlation Coefficient is a correlation measure of the strength of association between a continuous-level variable (ratio or interval data) and a binary variable. Binary variables are variables of nominal scale with only two values. They are also called dichotomous variables or dummy variables in Regression Analysis. Binary variables are commonly used to express the existence of a certain characteristic (e.g., reacted or did not react in a chemistry sample) or the membership in a group of observed specimen (e.g., male or female). If needed for the analysis, binary variables can also be created artificially by grouping cases or recoding variables. However it is not advised to artificially create a binary variable from ordinal or continuous-level (ratio or scale) data because ordinal and continuous-level data contain more variance information than nominal data and thus make any correlation analysis more reliable. For ordinal data use the Spearman Correlation Coefficient rho, for continuous-level (ratio or scale) data use Pearson's Bivariate Correlation Coefficient r. Binary variables are also called dummy. The Point-Biserial Correlation Coefficient is typically denoted as rpb .
Like all Correlation Coefficients (e.g. Pearson's r, Spearman's rho), the Point-Biserial Correlation Coefficient measures the strength of association of two variables in a single measure ranging from -1 to +1, where -1 indicates a perfect negative association, +1 indicates a perfect positive association and 0 indicates no association at all. All correlation coefficients are interdependency measures that do not express a causal relationship.

Mathematically, the Point-Biserial Correlation Coefficient is calculated just as the Pearson's Bivariate Correlation Coefficient would be calculated, wherein the dichotomous variable of the two variables is either 0 or 1--which is why it is also called the binary variable. Since we use the same mathematical concept, we do need to fulfill the same assumptions, which are normal distribution of the continuous variable and homoscedasticity. ("Statistics Solutions", 2016).

Statistics solutions. (2016). Retrieved from http://www.statisticssolutions.com/point-biserial-correlation/