. Author manuscript; available in PMC: 2024 May 1.

Published in final edited form as: J Int Neuropsychol Soc. 2023 Nov 28;30(4):389–401. doi: 10.1017/S1355617723000760

Table 2.

Individual and incremental percentage variance explained (R ²*100) for each demographic variable and the full regression model (combined).

	Individual variable R^{2 a}				Incremental (Partial) R^{2 b}					Combined R²

Measure (Raw Scores)	Age	Age Squared	Sex	Educ	Age	Age Squared	Sex	Educ	Shared^c	All

Category Fluency Total	16.25	16.93	5.33	7.83	12.30	0.75	7.36	5.21	2.61	28.23
Animals	14.68	15.26	0.10	8.75	10.73	0.54	0.01	4.61	4.14	20.03
Fruit	12.01	12.31	9.95	4.13	9.60	0.32	12.03	3.04	1.05	26.04
Vegetables	5.98	6.43	13.08	2.64	4.59	0.79	15.10	2.53	0.02	23.03
Boston Naming Test	5.74	7.03	1.76	9.76	3.22	4.12	0.79	5.99	3.81	17.93
TMT-A seconds, reversed	24.58	26.46	0.22	3.58	21.71	3.10	0.53	0.76	2.81	28.91
TMT-A errors	0.00	0.00	0.29	0.17	0.02	0.00	0.36	0.26	0.00	0.55
TMT-B seconds, reversed	25.06	27.36	0.00	7.30	20.56	4.14	0.14	2.66	4.63	32.13
TMT-B errors	5.04	5.54	0.12	2.51	3.81	0.93	0.01	1.14	1.38	7.27
AVLT Sum of Trials^d	25.50	26.19	9.39	5.21	21.60	0.75	11.52	2.61	2.89	39.37
WAIS-R Digit Symbol	33.18	33.79	4.32	8.04	27.74	0.57	6.10	3.71	4.39	42.51
WAIS-R Block Design	23.07	23.49	2.24	8.83	18.24	0.30	1.26	3.22	5.57	28.59
WAIS-R Picture Completion	12.33	13.62	2.50	7.86	8.93	2.34	1.50	3.46	4.40	20.63
WMS-R Logical Memory I	7.85	8.36	0.08	7.37	5.15	0.62	0.44	4.80	2.56	13.57
WMS-R Logical Memory II	10.13	10.63	0.26	6.86	7.17	0.55	0.76	4.16	2.69	15.33
WMS-R Visual Reprod. I	16.61	17.95	0.00	6.04	13.17	2.18	0.08	2.48	3.56	21.47
WMS-R Visual Reprod. II	26.69	28.37	0.05	7.12	22.07	2.36	0.33	2.51	4.61	31.88

Individual variable (e.g., univariate) variance explained, which reflects the amount of variance explained when a single predictor is in the model. These R²*100 values reported are equivalent to Pearson Correlation Coefficients, Squared. The majority of P values for Pearson correlation coefficients (before squaring) are p < .001, except as follows: associations with age differed from p < .001 for TMT-A errors (p=0.752); associations with age squared differed from p < .001 for TMT-A errors (p=0.763); associations with sex differed from p < .001 for Animal fluency (p=.039), TMT-A seconds (p=.002), TMT-B seconds (p=.999), TMT-B errors (p=0.027), LM-I (p=.059), VR-I (p=.787), and VR-II (p=.139); associations with education differed from p < .001 for TMT-A errors (p=0.007).

We performed a series of hierarchical multiple regressions for each test variable in which all but one demographic predictor was included in step one (e.g., age, age squared and sex) and the remaining variable (e.g, education) is entered in a second step. Thus, the incremental (i.e., marginal) variance explained is the amount of variance accounted for by each variable (e.g., education) beyond that explained by the other variables. This allows us to understand the incremental variance accounted for by each predictor, which is the partial R².

Shared = overlapping variance explained by a combination of all 4 model predictors simultaneously; this is calculated as combined variance explained - sum of incremental variance explained for all 4 predictors. For example, shared variance for category fluency total = 28.23 - (12.30 + 0.75 + 7.36 + 5.21) = 2.61

Auditory Verbal Learning Test Sum of Trials (Trials 1–5 + Trial 6 Short-Delay + 30-minute delayed recall) was included here to provide the incremental variance explained data for this primary AVLT variable that was the focus of our prior work (Stricker et al., 2021) using the same sample.