Table 4 Results of the complex models fitted in Dataset 1 and 2.

Polynomial mixed model: PE_sub
Predictor	Dataset 1			Dataset 2
Predictor	\(\hat{{\boldsymbol{\beta }}}\)	SE	Sequential P-value*	\(\hat{{\boldsymbol{\beta }}}\)	SE	Sequential P-value*
Intercept	0.05	0.14	0.01	−0.19	0.15	<0.0001
PE	−0.39	0.046	<0.0001	−0.43	0.05	<0.0001
Trial	−0.005	0.0013	<0.0001	−0.003	0.0015	0.0016
PE2	0.045	0.015	<0.0001	−0.02	0.015	<0.0001
PE3	0.002	0.001	<0.0001	0.007	0.001	<0.0001
PE4	−0.002	0.0004	<0.0001	0.00007	0.0004	0.0326
PExTrial	0.0008	0.0005	<0.0001	0.0028	0.0006	<0.0001
PE²xTrial	0.0003	0.0002	0.11	−0.0001	0.0002	0.17
PE³xTrial	0.00001	0.00002	0.61	−0.00006	0.00002	0.003
PE⁴xTrial	0.00001	0.000006	0.03	0.000006	0.000006	0.30
AIC	7019.382			7018.041
BIC	7099.065			7097.137
Log-likelihood	−3495.691			−3495.021

Predictor: the predictor variable entered into the complex model; \(\hat{{\rm{\beta }}}\): the estimated beta coefficient; SE: standard error of \(\hat{{\rm{\beta }}}\); Sequential P-value: indicates whether a predictor variable significantly predicts the data or not. Sequential P-values are more appropriate to use when interaction terms are involved because their calculation considers the other variables included in the model.

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