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. 2021 Oct 18;12:727761. doi: 10.3389/fpsyg.2021.727761

Table 6.

Statistical tests for research question 3: non-standard versus standard word problems.

Fixed effects LL #p LR χ2 df p
Hypothesis 3a
M0 - −6617.3 3
M1 Grade −6460.0 6 M1-M0 314.624 3 <0.001
M2 Steps+Grade −6456.7 7 M2-M1 6.606 1 0.010
M3 Steps+Grade+Pr.Type −6456.4 8 M3-M2 0.640 1 0.42
M5 Steps+Grade*Pr.Type −6453.7 11 M4-M3 5.372 3 0.15
Hypothesis 3b: reading comprehension process (MOCCA)
M5a Steps+Grade+Pr.Type −6431.2 8
M6a Steps+Grade+Pr.Type+MOCCA −6396.8 9 M6a-M5a 68.718 1 < 0.001
M7a Steps+Grade+Pr.Type*MOCCA −6395.7 10 M7a-M6a 2.282 1 0.13
M8a Steps+Grade*Pr.Type*MOCCA −6394.7 16 M8a-M7a 2.026 6 0.92
Hypothesis 3b: reading comprehension product (CITO)
M5a Steps+Grade+Pr.Type −5364.8 8
M6a Steps+Grade+Pr.Type+CITO −5330.0 9 M6b-M5b 69.726 1 < 0.001
M7a Steps+Grade+Pr.Type*CITO −5329.9 10 M7b-M6b 0.056 1 0.81
M8a Steps+Grade*Pr.Type*CITO −5327.1 16 M8b-M7b 5.720 6 0.46
Hypothesis 3b: non-verbal reasoning (RAVEN)
M5a Steps+Grade+Pr.Type −6456.4 8
M6a Steps+Grade+Pr.Type+RAVEN −6407.7 9 M6cb-M5c 97.412 1 <0.001
M7a Steps+Grade+Pr.Type*RAVEN −6406.8 10 M7c-M6c 1.720 1 0.19
M8a Steps+Grade*Pr.Type*RAVEN −6403.9 16 M8c-M7c 5.858 6 0.44
Hypothesis 3b: working memory (WM)
M4d Steps+Grade+Pr.Type −6303.3 8
M5d Steps+Grade+Pr.Type+WM −6270.2 9 M6d-M5d 66.314 1 <0.001
M6d Steps+Grade+Pr.Type*WM −6269.9 10 M7d-M6d 0.486 1 0.49
M7d Steps+Grade*Pr.Type*WM −6266.8 16 M8d-M7d 6.202 6 0.40

LL, log-likelihood; #p, number of parameters; LR, likelihood ratio test; χ2, test statistic LR-test; Steps, number of arithmetic steps (one or two); Pr.Type, problem type (standard or non-standard word problem).