Results

Repeated Measures ANOVA

Within Subjects Effects
	Sum of Squares	df	Mean Square	F	p	η²_p
Size/Distance	405083.92	1	405083.92	8.9016	0.004	0.146
Size/Distance ✻ Modality	699581.68	1	699581.68	15.3732	< .001	0.228
Residual	2.37e+6	52	45506.67
Identity	1.24e+6	1	1.24e+6	70.9219	< .001	0.577
Identity ✻ Modality	6943.92	1	6943.92	0.3980	0.531	0.008
Residual	907256.61	52	17447.24
Viewing	359891.33	1	359891.33	6.1898	0.016	0.106
Viewing ✻ Modality	138761.40	1	138761.40	2.3866	0.128	0.044
Residual	3.02e+6	52	58142.44
Size/Distance ✻ Identity	2217.00	1	2217.00	0.3236	0.572	0.006
Size/Distance ✻ Identity ✻ Modality	25116.35	1	25116.35	3.6662	0.061	0.066
Residual	356236.43	52	6850.70
Size/Distance ✻ Viewing	539872.12	1	539872.12	20.1541	< .001	0.279
Size/Distance ✻ Viewing ✻ Modality	82888.76	1	82888.76	3.0943	0.084	0.056
Residual	1.39e+6	52	26787.21
Identity ✻ Viewing	9965.77	1	9965.77	0.9915	0.324	0.019
Identity ✻ Viewing ✻ Modality	48801.50	1	48801.50	4.8552	0.032	0.085
Residual	522667.65	52	10051.30
Size/Distance ✻ Identity ✻ Viewing	5.61	1	5.61	6.33e-4	0.980	0.000
Size/Distance ✻ Identity ✻ Viewing ✻ Modality	294.66	1	294.66	0.0333	0.856	0.001
Residual	460358.43	52	8853.05
Note. Type 3 Sums of Squares

[3]

Between Subjects Effects
	Sum of Squares	df	Mean Square	F	p	η²_p
Modality	19438	1	19438	0.0505	0.823	0.001
Residual	2.00e+7	52	384814
Note. Type 3 Sums of Squares

Assumptions

Homogeneity of Variances Test (Levene's)
	F	df1	df2	p
D Bi small/near Rub	0.2288	1	52	0.634
D Mon small/near Rubiks	1.1452	1	52	0.289
D Bi small/near Die	0.0177	1	52	0.895
D Mon small/near Die	0.8513	1	52	0.360
D Bi large/far Rubik	0.0595	1	52	0.808
D Mon large/far Rubik	0.3803	1	52	0.540
D Bi Large/far Die	0.7251	1	52	0.398
D Mon large/far Die	0.3920	1	52	0.534

Post Hoc Tests

Post Hoc Comparisons - Size/Distance ✻ Viewing
Comparison
Size/Distance	Viewing		Size/Distance	Viewing	Mean Difference	SE	df	t	p
Small/Near	Binoc	-	Small/Near	Monoc	-13.20	30.5	52.0	-0.433	0.667
		-	Large/Far	Binoc	-134.27	29.1	52.0	-4.610	< .001
		-	Large/Far	Monoc	-3.58	30.0	52.0	-0.119	0.906
	Monoc	-	Large/Far	Binoc	-121.06	33.0	52.0	-3.674	< .001
		-	Large/Far	Monoc	9.63	23.2	52.0	0.415	0.680
Large/Far	Binoc	-	Large/Far	Monoc	130.69	26.5	52.0	4.940	< .001

Post Hoc Comparisons - Size/Distance ✻ Modality
Comparison
Size/Distance	Modality		Size/Distance	Modality	Mean Difference	SE	df	t	p
Small/Near	VR	-	Small/Near	REAL	95.6	65.8	52.0	1.452	0.152
		-	Large/Far	VR	19.6	32.2	52.0	0.609	0.545
		-	Large/Far	REAL	-48.7	64.5	52.0	-0.754	0.454
	REAL	-	Large/Far	VR	-76.0	63.9	52.0	-1.188	0.240
		-	Large/Far	REAL	-144.2	26.7	52.0	-5.409	< .001
Large/Far	VR	-	Large/Far	REAL	-68.2	62.6	52.0	-1.090	0.281

[4]

References

[1] The jamovi project (2021). jamovi. (Version 1.6) [Computer Software]. Retrieved from https://www.jamovi.org.

[2] R Core Team (2020). R: A Language and environment for statistical computing. (Version 4.0) [Computer software]. Retrieved from https://cran.r-project.org. (R packages retrieved from MRAN snapshot 2020-08-24).

[3] Singmann, H. (2018). afex: Analysis of Factorial Experiments. [R package]. Retrieved from https://cran.r-project.org/package=afex.

[4] Lenth, R. (2020). emmeans: Estimated Marginal Means, aka Least-Squares Means. [R package]. Retrieved from https://cran.r-project.org/package=emmeans.