============================================================================== 0. DATA, VARIABLES AND GROUP DEFINITIONS ============================================================================== File: brainbodystudy-preprocessed-data-final.csv Rows: 923 (paper's analytic N = 923) Age: mean 55.24, SD 14.38, range 18 to 88 Education, binary post-secondary complete: 769 of 923 (83.3%). Paper's Table 1 reports 83%. Gender (reference = male): female 563, male 351, other 9 Pre-existing health condition covariate FOUND in the preprocessed file as 'pre_existing_health_condition'. Positive: 200 of 923. Reconstruction from dx_diabetes, dx_obesity, dx_hypertension, dx_stroke, dx_heart_attack, dx_cardiac_problems, dx_concussion reproduces it exactly: True Group definitions and counts: authors' deposited gamer_type column (paper definition) Non 316, Infrequent 378, Frequent 229 press release: 5+ hrs/week on a single genre (code >= 4) Non 368, Infrequent 373, Frequent 182 literal reconstruction: 3+ hrs/week in any genre (code >= 3) Non 368, Infrequent 270, Frequent 285 Caveats on the group variable: 1. The authors' deposited gamer_type column cannot be reproduced from the eight genre items in this file. 52 participants report 0 hours across all eight past-year genre items yet are classified as gamers by gamer_type, so that column is derived partly from questionnaire items that were not deposited in the preprocessed file. Both the authors' column and the two reconstructions are therefore reported throughout. 2. The paper's Table 2 text gives the frequent-gamer count as 239 (24.8%). 24.8% of 923 is 229, which is exactly what the deposited column gives. The percentage and the deposited column agree with each other; the printed count of 239 does not agree with either. ============================================================================== A. GROUP DIFFERENCES ON THE FIVE STANDARDIZED COMPOSITES ============================================================================== All composites are scaled to mean 0 and SD 1 within this 923-person sample, so every beta below is in within-sample SD units. Reference group is Non-gamer. p values are uncorrected; the paper judged significance against p < 0.05 Bonferroni-corrected for 14 comparisons, i.e. alpha = 0.00357, which is marked in the last column. ------------------------------------------------------------------------------ Covariate spec PAPER: paper's covariate set: age, gender, binary post-secondary education, binary pre-existing health condition formula RHS: group + age_c + C(gender) + edu_post_secondary + pre_existing_health_condition ------------------------------------------------------------------------------ Group definition: authors' deposited gamer_type column (paper definition) composite contrast beta 95% CI p < .00357 STM Frequent vs Non 0.3789 [0.213, 0.544] 8.03e-06 yes STM Infrequent vs Non 0.2053 [0.067, 0.343] 3.59e-03 no reasoning Frequent vs Non 0.3667 [0.204, 0.529] 1.07e-05 yes reasoning Infrequent vs Non 0.1348 [-0.001, 0.270] 5.12e-02 no verbal Frequent vs Non 0.0591 [-0.119, 0.238] 5.16e-01 no verbal Infrequent vs Non -0.0676 [-0.216, 0.081] 3.73e-01 no processing_speed Frequent vs Non 0.3610 [0.213, 0.509] 2.04e-06 yes processing_speed Infrequent vs Non 0.1864 [0.063, 0.310] 3.14e-03 yes overall Frequent vs Non 0.4813 [0.336, 0.626] 1.28e-10 yes overall Infrequent vs Non 0.1869 [0.066, 0.308] 2.49e-03 yes Group definition: press release: 5+ hrs/week on a single genre (code >= 4) composite contrast beta 95% CI p < .00357 STM Frequent vs Non 0.4296 [0.261, 0.598] 6.58e-07 yes STM Infrequent vs Non 0.1787 [0.046, 0.312] 8.46e-03 no reasoning Frequent vs Non 0.3542 [0.188, 0.520] 3.04e-05 yes reasoning Infrequent vs Non 0.1566 [0.026, 0.288] 1.91e-02 no verbal Frequent vs Non 0.0246 [-0.158, 0.207] 7.91e-01 no verbal Infrequent vs Non -0.0383 [-0.182, 0.106] 6.02e-01 no processing_speed Frequent vs Non 0.3984 [0.248, 0.549] 2.57e-07 yes processing_speed Infrequent vs Non 0.2147 [0.096, 0.334] 4.12e-04 yes overall Frequent vs Non 0.4899 [0.342, 0.638] 1.34e-10 yes overall Infrequent vs Non 0.1951 [0.078, 0.312] 1.08e-03 yes Group definition: literal reconstruction: 3+ hrs/week in any genre (code >= 3) composite contrast beta 95% CI p < .00357 STM Frequent vs Non 0.3285 [0.181, 0.476] 1.32e-05 yes STM Infrequent vs Non 0.1836 [0.039, 0.328] 1.27e-02 no reasoning Frequent vs Non 0.3184 [0.174, 0.463] 1.69e-05 yes reasoning Infrequent vs Non 0.1197 [-0.022, 0.261] 9.78e-02 no verbal Frequent vs Non 0.0256 [-0.133, 0.184] 7.51e-01 no verbal Infrequent vs Non -0.0616 [-0.217, 0.094] 4.37e-01 no processing_speed Frequent vs Non 0.3377 [0.206, 0.469] 5.51e-07 yes processing_speed Infrequent vs Non 0.2059 [0.077, 0.335] 1.77e-03 yes overall Frequent vs Non 0.4067 [0.277, 0.536] 9.84e-10 yes overall Infrequent vs Non 0.1678 [0.041, 0.295] 9.55e-03 no ------------------------------------------------------------------------------ Covariate spec NO_HEALTH: age + gender + binary education only (health condition dropped) formula RHS: group + age_c + C(gender) + edu_post_secondary ------------------------------------------------------------------------------ Group definition: authors' deposited gamer_type column (paper definition) composite contrast beta 95% CI p < .00357 STM Frequent vs Non 0.3707 [0.206, 0.536] 1.18e-05 yes STM Infrequent vs Non 0.1991 [0.061, 0.337] 4.64e-03 no reasoning Frequent vs Non 0.3684 [0.206, 0.530] 9.13e-06 yes reasoning Infrequent vs Non 0.1361 [0.001, 0.271] 4.83e-02 no verbal Frequent vs Non 0.0365 [-0.143, 0.215] 6.89e-01 no verbal Infrequent vs Non -0.0848 [-0.234, 0.064] 2.65e-01 no processing_speed Frequent vs Non 0.3629 [0.215, 0.511] 1.67e-06 yes processing_speed Infrequent vs Non 0.1878 [0.065, 0.311] 2.84e-03 yes overall Frequent vs Non 0.4677 [0.323, 0.613] 4.01e-10 yes overall Infrequent vs Non 0.1766 [0.056, 0.298] 4.28e-03 no Group definition: press release: 5+ hrs/week on a single genre (code >= 4) composite contrast beta 95% CI p < .00357 STM Frequent vs Non 0.4184 [0.251, 0.586] 1.15e-06 yes STM Infrequent vs Non 0.1731 [0.040, 0.306] 1.06e-02 no reasoning Frequent vs Non 0.3557 [0.191, 0.521] 2.57e-05 yes reasoning Infrequent vs Non 0.1573 [0.027, 0.288] 1.83e-02 no verbal Frequent vs Non -0.0042 [-0.186, 0.178] 9.64e-01 no verbal Infrequent vs Non -0.0526 [-0.197, 0.092] 4.75e-01 no processing_speed Frequent vs Non 0.3997 [0.250, 0.550] 2.04e-07 yes processing_speed Infrequent vs Non 0.2154 [0.097, 0.334] 3.83e-04 yes overall Frequent vs Non 0.4717 [0.324, 0.619] 5.71e-10 yes overall Infrequent vs Non 0.1861 [0.069, 0.303] 1.85e-03 yes Group definition: literal reconstruction: 3+ hrs/week in any genre (code >= 3) composite contrast beta 95% CI p < .00357 STM Frequent vs Non 0.3182 [0.172, 0.465] 2.21e-05 yes STM Infrequent vs Non 0.1796 [0.035, 0.324] 1.48e-02 no reasoning Frequent vs Non 0.3195 [0.176, 0.463] 1.41e-05 yes reasoning Infrequent vs Non 0.1201 [-0.021, 0.262] 9.61e-02 no verbal Frequent vs Non -0.0018 [-0.161, 0.157] 9.82e-01 no verbal Infrequent vs Non -0.0723 [-0.229, 0.084] 3.64e-01 no processing_speed Frequent vs Non 0.3391 [0.208, 0.470] 4.28e-07 yes processing_speed Infrequent vs Non 0.2064 [0.078, 0.335] 1.70e-03 yes overall Frequent vs Non 0.3894 [0.260, 0.518] 4.36e-09 yes overall Infrequent vs Non 0.1610 [0.034, 0.288] 1.30e-02 no ------------------------------------------------------------------------------ Covariate spec EDU5_NO_HEALTH: age + gender + 5-level education factor, no health condition (sensitivity check only, not the paper's spec) formula RHS: group + age_c + C(gender) + C(education) ------------------------------------------------------------------------------ Group definition: authors' deposited gamer_type column (paper definition) composite contrast beta 95% CI p < .00357 STM Frequent vs Non 0.3615 [0.196, 0.527] 2.06e-05 yes STM Infrequent vs Non 0.1897 [0.052, 0.328] 7.19e-03 no reasoning Frequent vs Non 0.3715 [0.209, 0.534] 8.20e-06 yes reasoning Infrequent vs Non 0.1451 [0.009, 0.281] 3.60e-02 no verbal Frequent vs Non 0.0352 [-0.144, 0.215] 7.01e-01 no verbal Infrequent vs Non -0.0805 [-0.230, 0.069] 2.91e-01 no processing_speed Frequent vs Non 0.3604 [0.212, 0.509] 2.21e-06 yes processing_speed Infrequent vs Non 0.1879 [0.064, 0.312] 2.99e-03 yes overall Frequent vs Non 0.4636 [0.318, 0.609] 6.23e-10 yes overall Infrequent vs Non 0.1780 [0.057, 0.299] 4.09e-03 no Group definition: press release: 5+ hrs/week on a single genre (code >= 4) composite contrast beta 95% CI p < .00357 STM Frequent vs Non 0.4117 [0.244, 0.580] 1.81e-06 yes STM Infrequent vs Non 0.1648 [0.032, 0.298] 1.54e-02 no reasoning Frequent vs Non 0.3532 [0.188, 0.519] 3.09e-05 yes reasoning Infrequent vs Non 0.1638 [0.033, 0.295] 1.44e-02 no verbal Frequent vs Non -0.0110 [-0.194, 0.172] 9.06e-01 no verbal Infrequent vs Non -0.0482 [-0.193, 0.097] 5.13e-01 no processing_speed Frequent vs Non 0.3963 [0.246, 0.547] 2.97e-07 yes processing_speed Infrequent vs Non 0.2151 [0.096, 0.334] 4.24e-04 yes overall Frequent vs Non 0.4637 [0.316, 0.612] 1.20e-09 yes overall Infrequent vs Non 0.1867 [0.069, 0.304] 1.85e-03 yes Group definition: literal reconstruction: 3+ hrs/week in any genre (code >= 3) composite contrast beta 95% CI p < .00357 STM Frequent vs Non 0.3116 [0.165, 0.459] 3.41e-05 yes STM Infrequent vs Non 0.1703 [0.025, 0.315] 2.13e-02 no reasoning Frequent vs Non 0.3183 [0.174, 0.462] 1.61e-05 yes reasoning Infrequent vs Non 0.1282 [-0.014, 0.270] 7.71e-02 no verbal Frequent vs Non -0.0062 [-0.165, 0.153] 9.39e-01 no verbal Infrequent vs Non -0.0663 [-0.223, 0.091] 4.07e-01 no processing_speed Frequent vs Non 0.3362 [0.205, 0.467] 6.07e-07 yes processing_speed Infrequent vs Non 0.2064 [0.077, 0.336] 1.82e-03 yes overall Frequent vs Non 0.3832 [0.254, 0.512] 8.21e-09 yes overall Infrequent vs Non 0.1626 [0.035, 0.290] 1.25e-02 no Reading of section A. The frequent-versus-non-gamer gap on the overall composite sits between about +0.41 and +0.49 SD across these specifications. Dropping the health-condition covariate moves it very little. Replacing the binary education variable with the 5-level factor moves it a little more. The group definition moves it more than the covariates do. ============================================================================== B. AGE CURVE ON THE OVERALL COMPOSITE: LINEAR VERSUS QUADRATIC ============================================================================== Any conversion of an SD gap into years of age assumes something about the shape of the age curve. The simplest assumption, one constant slope for every age, is testable. It is tested here two ways: with no covariates, and inside the paper's covariate specification alongside the group term. (i) No covariates, no group term linear overall ~ age age slope = -0.03965 SD/year, p = 1.330e-80 adj R2 = 0.3240 quadratic overall ~ age + age^2 age slope at sample mean = -0.04218 SD/year age^2 term = -0.000321 QUADRATIC TERM p = 0.0039 adj R2 = 0.3294 likelihood-ratio test of the quadratic term: LR(1) = 8.344, p = 0.0039 Local slope of the fitted curve, in SD per year of age: at age 40: -0.03239 at age 55: -0.04203 at age 70: -0.05166 (ii) Paper's covariate set, group term present (authors' gamer_type) age slope at sample mean = -0.03609 SD/year age^2 term = -0.000288 QUADRATIC TERM p = 0.0087 Conclusion of section B. The quadratic term is significant in both forms. The decline in the overall composite accelerates with age: it is roughly 1.6 times as steep at age 70 as at age 40. A single linear age slope is therefore not a defensible basis for a single years-equivalent figure, and any such figure has to name the age it is anchored at. ============================================================================== C / D. YEARS-EQUIVALENT CONVERSIONS, BY ANCHOR AGE AND DEFINITION ============================================================================== WARNING, and it applies to every number in this section. 1. The published paper reports NO years-equivalent figure. It reports group differences in SD units. Every figure in this section is our arithmetic on the paper's data, not a finding of the paper. 2. A years-equivalent figure is ANCHOR DEPENDENT. Because the age curve is significantly quadratic (section B), the same gap buys many more years of age at 40 than at 70. No figure here should ever be quoted without both its anchor age and its model. 3. These are cross-sectional between-person differences in a self-selected, older, unusually educated sample. Converting them into years of ageing is an illustrative rescaling, not a measure of how much anyone's ageing was slowed. 4. All conversions divide the group gap by an age slope taken from the SAME regression that produced the gap. Mixing an adjusted gap with an unadjusted marginal age slope gives a different and internally inconsistent answer. ============================================================================== Group definition: authors' deposited gamer_type column (paper definition) Covariate set: paper's covariate set: age, gender, binary post-secondary education, binary pre-existing health condition ============================================================================== LINEAR AGE MODEL (one constant slope at every age) frequent vs non-gamer gap on overall : 0.4813 SD, 95% CI [0.336, 0.626], p = 1.28e-10 age slope, same model : -0.03375 SD per year years-equivalent : 14.26 years 95% CI (delta method) : [9.15, 19.37] years MODEL AND ANCHOR: linear age model, which has NO anchor age. This single figure is what you get only if you assume the decline rate is the same at every age, and section B rejects that assumption at p < 0.01. QUADRATIC AGE MODEL (decline accelerates with age; age^2 p = 0.0087) frequent vs non-gamer gap on overall : 0.4871 SD age slope at sample mean age 55.2 : -0.03609 SD per year age^2 coefficient : -0.000288 anchor age local slope years (exact 95% CI years (local implied SD/year curve solve) (bootstrap) slope approx) age 40 -0.02732 23.80 [11.8, 34.6] 17.83 16.2 55 -0.03595 15.46 [9.8, 24.0] 13.55 39.5 70 -0.04459 11.83 [7.6, 17.1] 10.92 58.2 "years (exact curve solve)" solves the fitted age curve for the number of years younger at which normal age-related performance rises by the size of the gaming gap, starting from the named anchor age. "years (local slope approx)" is the first-order shortcut, gap divided by the slope at the anchor. The two differ because the curve is curved, and the gap is large enough to travel a long way along it. EXTRAPOLATION NOTE: at anchor age(s) 40 the implied age falls below 18, the youngest person in this sample. The curve is being read outside the data there, which is a further reason the large figures at young anchor ages should not be quoted as findings. ============================================================================== Group definition: press release: 5+ hrs/week on a single genre (code >= 4) Covariate set: paper's covariate set: age, gender, binary post-secondary education, binary pre-existing health condition ============================================================================== LINEAR AGE MODEL (one constant slope at every age) frequent vs non-gamer gap on overall : 0.4899 SD, 95% CI [0.342, 0.638], p = 1.34e-10 age slope, same model : -0.03451 SD per year years-equivalent : 14.20 years 95% CI (delta method) : [9.22, 19.17] years MODEL AND ANCHOR: linear age model, which has NO anchor age. This single figure is what you get only if you assume the decline rate is the same at every age, and section B rejects that assumption at p < 0.01. QUADRATIC AGE MODEL (decline accelerates with age; age^2 p = 0.0085) frequent vs non-gamer gap on overall : 0.4983 SD age slope at sample mean age 55.2 : -0.03687 SD per year age^2 coefficient : -0.000288 anchor age local slope years (exact 95% CI years (local implied SD/year curve solve) (bootstrap) slope approx) age 40 -0.02808 23.35 [12.1, 34.4] 17.75 16.6 55 -0.03673 15.44 [9.9, 23.5] 13.57 39.6 70 -0.04538 11.88 [7.7, 17.0] 10.98 58.1 "years (exact curve solve)" solves the fitted age curve for the number of years younger at which normal age-related performance rises by the size of the gaming gap, starting from the named anchor age. "years (local slope approx)" is the first-order shortcut, gap divided by the slope at the anchor. The two differ because the curve is curved, and the gap is large enough to travel a long way along it. EXTRAPOLATION NOTE: at anchor age(s) 40 the implied age falls below 18, the youngest person in this sample. The curve is being read outside the data there, which is a further reason the large figures at young anchor ages should not be quoted as findings. ============================================================================== Group definition: literal reconstruction: 3+ hrs/week in any genre (code >= 3) Covariate set: paper's covariate set: age, gender, binary post-secondary education, binary pre-existing health condition ============================================================================== LINEAR AGE MODEL (one constant slope at every age) frequent vs non-gamer gap on overall : 0.4067 SD, 95% CI [0.277, 0.536], p = 9.84e-10 age slope, same model : -0.03474 SD per year years-equivalent : 11.71 years 95% CI (delta method) : [7.43, 15.98] years MODEL AND ANCHOR: linear age model, which has NO anchor age. This single figure is what you get only if you assume the decline rate is the same at every age, and section B rejects that assumption at p < 0.01. QUADRATIC AGE MODEL (decline accelerates with age; age^2 p = 0.0104) frequent vs non-gamer gap on overall : 0.4108 SD age slope at sample mean age 55.2 : -0.03705 SD per year age^2 coefficient : -0.000282 anchor age local slope years (exact 95% CI years (local implied SD/year curve solve) (bootstrap) slope approx) age 40 -0.02847 17.44 [9.6, 28.7] 14.43 22.6 55 -0.03692 12.28 [7.8, 18.2] 11.13 42.7 70 -0.04537 9.63 [6.2, 14.0] 9.06 60.4 "years (exact curve solve)" solves the fitted age curve for the number of years younger at which normal age-related performance rises by the size of the gaming gap, starting from the named anchor age. "years (local slope approx)" is the first-order shortcut, gap divided by the slope at the anchor. The two differ because the curve is curved, and the gap is large enough to travel a long way along it. ============================================================================== SUMMARY OF SECTION C / D: every years figure with its anchor and model ============================================================================== All rows use the paper's covariate set. Years figures are never comparable across rows unless the anchor age and model match. group definition gap SD model anchor years 95% CI paper (gamer_type) 0.4813 linear (no anchor) none 14.26 [9.1, 19.4] 0.4871 quadratic, exact solve 40 23.80 [11.8, 34.6] 0.4871 quadratic, exact solve 55 15.46 [9.8, 24.0] 0.4871 quadratic, exact solve 70 11.83 [7.6, 17.1] 0.4871 quadratic, local slope 40 17.83 not computed 0.4871 quadratic, local slope 55 13.55 not computed 0.4871 quadratic, local slope 70 10.92 not computed press release (5+ hr) 0.4899 linear (no anchor) none 14.20 [9.2, 19.2] 0.4983 quadratic, exact solve 40 23.35 [12.1, 34.4] 0.4983 quadratic, exact solve 55 15.44 [9.9, 23.5] 0.4983 quadratic, exact solve 70 11.88 [7.7, 17.0] 0.4983 quadratic, local slope 40 17.75 not computed 0.4983 quadratic, local slope 55 13.57 not computed 0.4983 quadratic, local slope 70 10.98 not computed literal 3+ hr rebuild 0.4067 linear (no anchor) none 11.71 [7.4, 16.0] 0.4108 quadratic, exact solve 40 17.44 [9.6, 28.7] 0.4108 quadratic, exact solve 55 12.28 [7.8, 18.2] 0.4108 quadratic, exact solve 70 9.63 [6.2, 14.0] 0.4108 quadratic, local slope 40 14.43 not computed 0.4108 quadratic, local slope 55 11.13 not computed 0.4108 quadratic, local slope 70 9.06 not computed What the table shows. Within a single group definition and a single covariate set, the years-equivalent figure moves by roughly a factor of two across the three anchor ages, and by a further one to two years depending on whether the curve is solved exactly or approximated by its local slope. The linear-model figure has no anchor age at all, so it cannot correctly be described as applying "at the sample's mean age"; the figure that does apply at the mean age comes from the quadratic model and is a different number. Any sentence that attaches a linear-model estimate to an anchored phrase is combining two different models. The spread across anchor ages is larger than the difference between any two covariate specifications in section A, and comparable to the width of the confidence interval. The years framing is not a stable quantity. ============================================================================== E. THE VERBAL COMPOSITE: NO GAMER ADVANTAGE ============================================================================== The paper reports a significant gaming association on four of five composites and explicitly not on verbal. This section checks that under every combination of covariate set and group definition used above, because it is the caveat most often dropped when this study is summarised as "gamers have better cognition". covariate spec group definition beta 95% CI p PAPER group_paper 0.0591 [-0.119, 0.238] 0.516 PAPER group_press 0.0246 [-0.158, 0.207] 0.791 PAPER group_literal3h 0.0256 [-0.133, 0.184] 0.751 NO_HEALTH group_paper 0.0365 [-0.143, 0.215] 0.689 NO_HEALTH group_press -0.0042 [-0.186, 0.178] 0.964 NO_HEALTH group_literal3h -0.0018 [-0.161, 0.157] 0.982 EDU5_NO_HEALTH group_paper 0.0352 [-0.144, 0.215] 0.701 EDU5_NO_HEALTH group_press -0.0110 [-0.194, 0.172] 0.906 EDU5_NO_HEALTH group_literal3h -0.0062 [-0.165, 0.153] 0.939 Under the paper's covariate set and the authors' own group column, the frequent-versus-non-gamer difference on verbal is +0.0591 SD, 95% CI [-0.119, 0.238], p = 0.516. The interval includes zero, and it includes it under every specification above. "Cognition" in this study means short-term memory, reasoning and processing speed. It does not mean language, and nothing in this dataset measures school performance. ============================================================================== CLOSING NOTES FOR ANYONE CITING THESE NUMBERS ============================================================================== 1. The "13.7 years younger" figure is not in PLOS ONE 20(10): e0334924. Searching the published article for "13.7", "years younger" and "5.2" returns nothing. The figure comes from the October 2024 press cycle around an earlier preprint with roughly 1,000 completers, not from the 923-person published analysis. Exact reproduction from this file should not be expected, and a residual difference is not evidence of an error by anyone. 2. The press release and the paper do not use the same group definition. The release's frequent gamer is 5 or more hours a week on a single type of game; the paper's is 3 or more hours a week in one or more genres. The figures above are reported under both, and they differ. 3. There is no IQ conversion in this script. The composites are standardised within a 923-person, 83%-post-secondary, mean-age-55 self-selected sample. A within-sample SD is not an IQ SD, and the paper makes no IQ claim. 4. Never quote a years-equivalent figure without its anchor age and model. Section C shows the same gap is worth roughly twice as many years at age 40 as at age 70. A figure derived from a sample whose mean age is 55 carries no implication at all for children. 5. This is cross-sectional. People with better cognition may play more games. The authors state this limitation themselves, along with self-reported gaming hours, two-item mental-health screeners, a sample skewed older, more educated and more active than the population, and too few action-game players to test any genre effect. ============================================================================== END OF OUTPUT ==============================================================================