If the sample is normally distributed (i.e., conditions for the computation of the biserial exist), then to obtain the biserial correlation from the point-biserial for dichotomous data:

Biserial = Point-biserial * f(proportion-correct-value)

 

Example: Specify PTBISERIAL=Yes and PVALUE=Yes. Display Table 14.

+-------------------------------------------------------------------------------------+

|ENTRY    RAW                   MODEL|   INFIT  |  OUTFIT  |PTBSE| P-  |              |

|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZSTD|MNSQ  ZSTD|CORR.|VALUE| TAP          |

|------------------------------------+----------+----------+-----+-----+--------------|

|     8     27     34   -2.35     .54| .59  -1.3| .43   -.2| .65| .77| 1-4-2-3      |

 

Point-biserial = .65. proportion-correct-value = .77. Then, from the Table below, f(proportion-correct-value) = 1.3861, so Biserial correlation = .65 * 1.39 = 0.90

 

Here is the Table of proportion-correct-value and f(proportion-correct-value).

p-va f(p-val) p-va f(p-val)

0.99 3.7335   0.01 3.7335

0.98 2.8914   0.02 2.8914

0.97 2.5072   0.03 2.5072

0.96 2.2741   0.04 2.2741

0.95 2.1139   0.05 2.1139

0.94 1.9940   0.06 1.9940

0.93 1.8998   0.07 1.8998

0.92 1.8244   0.08 1.8244

0.91 1.7622   0.09 1.7622

0.90 1.7094   0.10 1.7094

0.89 1.6643   0.11 1.6643

0.88 1.6248   0.12 1.6248

0.87 1.5901   0.13 1.5901

0.86 1.5588   0.14 1.5588

0.85 1.5312   0.15 1.5312

0.84 1.5068   0.16 1.5068

0.83 1.4841   0.17 1.4841

0.82 1.4641   0.18 1.4641

0.81 1.4455   0.19 1.4455

0.80 1.4286   0.20 1.4286

0.79 1.4133   0.21 1.4133

0.78 1.3990   0.22 1.3990

0.77 1.3861   0.23 1.3861

0.76 1.3737   0.24 1.3737

0.75 1.3625   0.25 1.3625

0.74 1.3521   0.26 1.3521

0.73 1.3429   0.27 1.3429

0.72 1.3339   0.28 1.3339

0.71 1.3256   0.29 1.3256

0.70 1.3180   0.30 1.3180

0.69 1.3109   0.31 1.3109

0.68 1.3045   0.32 1.3045

0.67 1.2986   0.33 1.2986

0.66 1.2929   0.34 1.2929

0.65 1.2877   0.35 1.2877

0.64 1.2831   0.36 1.2831

0.63 1.2786   0.37 1.2786

0.62 1.2746   0.38 1.2746

0.61 1.2712   0.39 1.2712

0.60 1.2682   0.40 1.2682

0.59 1.2650   0.41 1.2650

0.58 1.2626   0.42 1.2626

0.57 1.2604   0.43 1.2604

0.56 1.2586   0.44 1.2586

0.55 1.2569   0.45 1.2569

0.54 1.2557   0.46 1.2557

0.53 1.2546   0.47 1.2546

0.52 1.2540   0.48 1.2540

0.51 1.2535   0.49 1.2535

0.50 1.2534   0.50 1.2534

 

To obtain the biserial correlation from a point-biserial correlation, multiply the point-biserial correlation by SQRT(proportion-correct-value*(1-proportion-correct-value)) divided by the normal curve ordinate at the point where the normal curve is split in the same proportions.

 

There is no direct relationship between the point-polyserial correlation and the polyserial correlation.