Table 2:

Summary of preregistered hypotheses and analyses

Hypotheses	Analytic Plan*	Results
H1: Cognitive function at time 1 (indexed by the BTACT composite score) will be negatively associated with age.	Multilevel linear model controlling for education, sex, and lag between waves in years as follows: Equation 1 Level 1: ${ExecutiveFunction}_{ij}={\beta }_0+{\beta }_1{Wave}_{ij}+{\mu }_{ij}$ Level 2: $\begin{array}{l}{\beta }_0={\gamma }_{00}+{\gamma }_{01}{T1Age}_j+{\gamma }_{02}{TotalLag}_j+\\ {\gamma }_{03}{Education}_j+{\gamma }_{04}Sex+{\epsilon }_j\\ {\beta }_1={\gamma }_{10}+{\gamma }_{11}{T1Age}_j\\ \end{array}$ H1: Negative coefficient for the main effect of age at time 1 (i.e., ${\gamma }_{01}$). H2: Negative coefficient for the interaction between Age and Wave (i.e., ${\gamma }_{11}$).	H1: Supported for BTACT composite and both Executive Functioning and Episodic Memory subfactors.
H2: Within-person changes in cognitive function (indexed by time 1 to time 2 changes in BTACT composite score) will be moderated by age, such that older age will be associated with greater decline in cognitive function between time 1 and 2.		H2: Not supported.
H3: Cognitive function at time 1 (indexed by the BTACT composite score) will be positively associated with aperiodic exponent, such that flatter spectra will be associated with poorer cognitive function.	Multilevel linear model controlling for education, sex, and lag between waves in years. The placeholder “EEG” is used to represent the different EEG metrics included separately in each of the models as per hypotheses. Equation 2 Level 1: ${CognitiveFunction}_{ij}={\beta }_0+{\beta }_1{Wave}_{ij}+{\mu }_{ij}$ Level 2: $\begin{array}{l}{\beta }_0={\gamma }_{00}+{\gamma }_{01}EE{G}_j+{\gamma }_{02}{TotalLag}_j+\\ {\gamma }_{03}{Education}_j+{\gamma }_{04}Sex+{\epsilon }_j\end{array}$ $\begin{array}{ll}{\beta }_1=& {\gamma }_{10}+{\gamma }_{11}EE{G}_j\end{array}$ H3: Significant positive coefficient for the EEG metric (i.e., ${\gamma }_{01}$) when aperiodic exponent is included in the model. H4: Significant coefficient for the EEG by Wave interaction (i.e., ${\gamma }_{11}$) when aperiodic exponent is included in the model, such that flatter aperiodic spectra associated with faster decline in cognitive function. H5: Significant positive coefficient for the EEG metric (i.e., ${\gamma }_{01}$) when IAPF is included in the model. H6: Significant coefficient for the EEG by wave interaction (i.e., ${\gamma }_{11}$) when IAPF is included in the model, such that lower IAPF are associated with faster decline in cognitive function.	H3: Supported for BTACT composite and Executive Functioning subfactor.
H4: Within-person changes in cognitive function (indexed by time 1 to time 2 changes in BTACT composite score) will be moderated by the aperiodic exponent, such that flatter spectra at time 1 will be associated with greater decline in cognitive function between time 1 and 2.		H4: Not supported.
H5: Cognitive function at time 1 (indexed by the BTACT composite score) will be positively associated with IAPF, such that lower IAPF will be associated with poorer cognitive function.		H5: Not supported.
H6: Within-person changes in cognitive function (indexed by time 1 to time 2 changes in BTACT composite score) will be moderated by IAPF, such that lower IAPF at time 1 will be associated with greater decline in cognitive function between time 1 and 2.		H6: Supported for BTACT composite.
H7: The relationships between the aperiodic exponent, individual alpha peak frequency, and cognitive function outlined in H3-H6 will be moderated by age, such that greater cognitive decline will be observed in older-aged participants with flatter aperiodic exponents and lower IAPF. This hypothesis can be broken down into 4 parts (a-d) as described in the “Analytic Plan”.	Multilevel linear model controlling for education, sex, and lag between waves in years. The placeholder “EEG” is used to represent the different EEG metrics we aim to include in each of the models. Equation 3 Level 1: ${CognitiveFunction}_{ij}={\beta }_0+{\beta }_1{Wave}_{ij}+{\mu }_{ij}$ Level 2: $\begin{array}{l}{\beta }_0={\gamma }_{00}+{\gamma }_{01}EE{G}_j+{\gamma }_{02}{T1Age}_j+{\gamma }_{03}EE{G}_j\mathrm{*}\\ {T1Age}_j+{\gamma }_{04}{TotalLag}_j+{\gamma }_{05}{Education}_j+\\ {\gamma }_{06}Sex+{\epsilon }_j\end{array}$ $\begin{array}{l}{\beta }_1={\gamma }_{10}+{\gamma }_{11}EE{G}_j+{\gamma }_{12}{T1Age}_j+{\gamma }_{13}EE{G}_j\mathrm{*}\\ {T1Age}_j+{\gamma }_{14}{TotalLag}_j+{\gamma }_{15}{\text{Race}}_j+{\gamma }_{16}Sex\end{array}$ H7a: Significant coefficient for the interaction between the EEG by Age (i.e., ${\gamma }_{03}$) when aperiodic exponent is included in the model, such that older individuals with flatter aperiodic spectra will show the poorest time 1 cognitive function. H7b: Significant coefficient for the interaction between the EEG by Age (i.e., ${\gamma }_{03}$) when IAPF is included in the model, such that older individuals with lower IAPF will show the poorest time 1 cognitive function. H7c: Significant coefficient for the interaction between the EEG by Age by Wave (i.e., ${\gamma }_{13}$) when aperiodic exponent is included in the model, such that older individuals with flatter aperiodic spectra will show the steepest decline in cognitive function. H7d: Significant coefficient for the interaction between the EEG by Age by Wave (i.e., ${\gamma }_{13}$) IAPF is included in the model, such that older individuals with lower IAPF will show the steepest decline in cognitive function.	H7a: Not supported.
		H7b: Not supported.
		H7c: Not supported.
		H7d: Not supported.

^*The exact preregistered analyses were overly complicated and conservative by including lag as two separate variables (instead of a linear addition into a single variable), as well as the interaction between covariates and Wave. Additionally, after extensive testing for possible interactions with education and finding none, we decided to include education as a more appropriate covariate than race. We report the preregistered analyses in the supplemental materials, which do not change the interpretation of the findings.