Results

Descriptives

Descriptives
	Condition	T1_Distance	T2_Distance	Proportional Change in Distance 2	Proportional Change in Distance
N	NS‎/SR	29	29	29	29
	SR‎/NS	29	28	28	28
	NS‎/NS	25	23	23	23
Missing	NS‎/SR	0	0	0	0
	SR‎/NS	0	1	1	1
	NS‎/NS	0	2	2	2
Mean	NS‎/SR	206	136	29.0	29.0
	SR‎/NS	254	193	16.7	13.0
	NS‎/NS	228	181	21.6	21.6
Median	NS‎/SR	182	111	42.4	42.4
	SR‎/NS	222	152	20.6	20.6
	NS‎/NS	214	136	31.3	31.3
Standard deviation	NS‎/SR	115	102	44.5	44.5
	SR‎/NS	180	168	61.6	78.8
	NS‎/NS	112	124	41.2	41.2
Shapiro-Wilk W	NS‎/SR	0.912	0.841	0.912	0.912
	SR‎/NS	0.898	0.837	0.703	0.582
	NS‎/NS	0.930	0.925	0.951	0.951
Shapiro-Wilk p	NS‎/SR	0.020	<.001	0.020	0.020
	SR‎/NS	0.009	<.001	<.001	<.001
	NS‎/NS	0.086	0.085	0.302	0.302

Correlation Matrix

Correlation Matrix
		SCAS_Total T1	State Sleepiness Total T1	State Sleepiness T2 (child)	Trait Sleepiness Total T1	Trait Sleepiness T2 (child)	T1_Distance	T2_Distance	Proportional Change in Distance 2	Scared_Ballons_T1	Scared_Balloons_T2
SCAS_Total T1	Spearman's rho	—
	df	—
	p-value	—
State Sleepiness Total T1	Spearman's rho	0.235	—
	df	81	—
	p-value	0.032	—
State Sleepiness T2 (child)	Spearman's rho	0.305	0.476	—
	df	78	78	—
	p-value	0.006	<.001	—
Trait Sleepiness Total T1	Spearman's rho	0.243	0.727	0.582	—
	df	81	81	78	—
	p-value	0.027	<.001	<.001	—
Trait Sleepiness T2 (child)	Spearman's rho	0.346	0.697	0.648	0.691	—
	df	77	77	77	77	—
	p-value	0.002	<.001	<.001	<.001	—
T1_Distance	Spearman's rho	0.294	-0.040	0.118	-0.018	0.039	—
	df	81	81	78	81	77	—
	p-value	0.007	0.717	0.295	0.871	0.733	—
T2_Distance	Spearman's rho	0.247	0.060	0.226	0.168	0.141	0.621	—
	df	78	78	77	78	76	78	—
	p-value	0.028	0.596	0.045	0.137	0.220	<.001	—
Proportional Change in Distance 2	Spearman's rho	-0.146	-0.173	-0.238	-0.274	-0.226	0.025	-0.731	—
	df	78	78	77	78	76	78	78	—
	p-value	0.196	0.126	0.035	0.014	0.047	0.825	<.001	—
Scared_Ballons_T1	Spearman's rho	0.389	0.086	0.294	0.314	0.191	0.174	0.305	-0.236	—
	df	81	81	78	81	77	81	78	78	—
	p-value	<.001	0.438	0.008	0.004	0.091	0.115	0.006	0.035	—
Scared_Balloons_T2	Spearman's rho	0.366	0.140	0.293	0.359	0.206	0.191	0.372	-0.288	0.777	—
	df	79	79	78	79	77	79	78	78	79	—
	p-value	<.001	0.212	0.008	0.001	0.069	0.087	<.001	0.010	<.001	—

Paired Samples T-Test

Paired Samples T-Test
			Statistic	p
T1_Distance	T2_Distance	Wilcoxon W	2494ᵃ	<.001
Note. Hₐ μ_{Measure 1 - Measure 2} ≠ 0
ᵃ 1 pair(s) of values were tied

Descriptives
	N	Mean	Median	SD	SE
T1_Distance	80	229	202	143	15.9
T2_Distance	80	169	128	135	15.1

General Linear Model

Model Info
Info
Model Type	Linear Model	OLS Model for continuous y
Model	lm	T1_Distance ~ 1 + Condition + `State Sleepiness Total T1` + `Trait Sleepiness Total T1`
Distribution	Gaussian	Normal distribution of residuals
Omnibus Tests	F
Sample size	83
Converged	yes
Y transform	none
C.I. method	Bootstrap percent	1000 bootstrap samples
Note. All covariates are centered to the mean
[3]

Model Results

Model Fit
R²	Adj. R²	df	df (res)	F	p
0.027	0.000	4	78	0.535	0.711
[4]

ANOVA Omnibus tests
	SS	df	F	p
Model	43011.628	4	0.535	0.711
Condition	37980.346	2	0.944	0.393
State Sleepiness Total T1	8834.335	1	0.439	0.509
Trait Sleepiness Total T1	3927.687	1	0.195	0.660
Residuals	1568339.890	78
Total	1611351.518	82

Parameter Estimates (Coefficients)
				95% Confidence Intervals
Names	Effect	Estimate	SE	Lower	Upper	β	df	t	p
(Intercept)	(Intercept)	229.039	15.604	201.527	259.456	-0.001	78	14.678	<.001
Condition1	SR‎/NS - NS‎/SR	55.311	40.507	-32.000	136.078	0.395	78	1.365	0.176
Condition2	NS‎/NS - NS‎/SR	22.504	40.053	-46.827	83.916	0.161	78	0.562	0.576
State Sleepiness Total T1	State Sleepiness Total T1	-2.346	3.539	-10.867	5.846	-0.116	78	-0.663	0.509
Trait Sleepiness Total T1	Trait Sleepiness Total T1	1.752	3.964	-7.367	9.669	0.080	78	0.442	0.660
[5]

Estimated Marginal Means

Estimate Marginal Means - Condition
				95% Confidence Intervals
Condition	Mean	SE	df	Lower	Upper
NS‎/SR	203.101	27.609	78	162.378	251.476
SR‎/NS	258.412	27.533	78	195.112	325.165
NS‎/NS	225.605	28.669	78	179.511	276.483

General Linear Model

Model Info
Info
Model Type	Linear Model	OLS Model for continuous y
Model	lm	T2_Distance ~ 1 + Condition + `State Sleepiness Total T1` + `Trait Sleepiness Total T1` + `State Sleepiness T2 (child)`
Distribution	Gaussian	Normal distribution of residuals
Omnibus Tests	F
Sample size	79
Converged	yes
Y transform	none
C.I. method	Bootstrap percent	1000 bootstrap samples
Note. All covariates are centered to the mean
[3]

Model Results

Model Fit
R²	Adj. R²	df	df (res)	F	p
0.142	0.083	5	73	2.42	0.044
[4]

ANOVA Omnibus tests
	SS	df	F	p
Model	205475.104	5	2.419	0.044
Condition	136377.321	2	4.014	0.022
State Sleepiness Total T1	27348.481	1	1.610	0.209
Trait Sleepiness Total T1	13811.266	1	0.813	0.370
State Sleepiness T2 (child)	99688.797	1	5.868	0.018
Residuals	1240108.567	73
Total	1445583.671	78

Parameter Estimates (Coefficients)
				95% Confidence Intervals
Names	Effect	Estimate	SE	Lower	Upper	β	df	t	p
(Intercept)	(Intercept)	169.976	14.731	143.733	201.648	0.011	73	11.539	<.001
Condition1	SR‎/NS - NS‎/SR	102.910	38.476	8.392	204.421	0.756	73	2.675	0.009
Condition2	NS‎/NS - NS‎/SR	85.683	39.005	17.281	161.878	0.629	73	2.197	0.031
State Sleepiness Total T1	State Sleepiness Total T1	-4.301	3.390	-11.757	2.220	-0.221	73	-1.269	0.209
Trait Sleepiness Total T1	Trait Sleepiness Total T1	3.517	3.901	-3.146	10.253	0.166	73	0.902	0.370
State Sleepiness T2 (child)	State Sleepiness T2 (child)	6.058	2.501	0.937	12.135	0.336	73	2.422	0.018
[5]

Estimated Marginal Means

Estimate Marginal Means - Condition
				95% Confidence Intervals
Condition	Mean	SE	df	Lower	Upper
NS‎/SR	107.111	26.308	73	56.812	154.741
SR‎/NS	210.022	25.801	73	148.671	279.712
NS‎/NS	192.794	27.763	73	142.670	244.742

Estimate Marginal Means - State Sleepiness T2 (child)
				95% Confidence Intervals
State Sleepiness T2 (child)	Mean	SE	df	Lower	Upper
Mean-1·SD	124.234	23.744	73	80.100	162.040
Mean	169.976	14.731	73	143.733	201.648
Mean+1·SD	215.717	24.152	73	161.782	281.326

Results Plots

Plot: T2_Distance ~ Condition ✻ State Sleepiness T2 (child)

Assumption Checks

Test for Homogeneity of Residual Variance
Test	Statistics	df1	df2	p
Breusch-Pagan Test	10.64	5		0.059
Levene's Test	1.42	2	76	0.248
Note. Levene's test is done only for factors.

General Linear Model

Model Info
Info
Model Type	Linear Model	OLS Model for continuous y
Model	lm	`Proportional Change in Distance 2` ~ 1 + Condition + `Trait Sleepiness Total T1` + `State Sleepiness Total T1` + `State Sleepiness T2 (child)`
Distribution	Gaussian	Normal distribution of residuals
Omnibus Tests	F
Sample size	79
Converged	yes
Y transform	none
C.I. method	Wald
Note. All covariates are centered to the mean
[3]

Model Results

Model Fit
R²	Adj. R²	df	df (res)	F	p
0.125	0.065	5	73	2.09	0.076
[4]

ANOVA Omnibus tests
	SS	df	F	p	η²p
Model	24636.628	5	2.091	0.076	0.125
Condition	8377.650	2	1.777	0.176	0.046
Trait Sleepiness Total T1	2274.935	1	0.965	0.329	0.013
State Sleepiness Total T1	75.309	1	0.032	0.859	0.000
State Sleepiness T2 (child)	4457.016	1	1.891	0.173	0.025
Residuals	172033.682	73
Total	196670.310	78

Parameter Estimates (Coefficients)
				95% Confidence Intervals
Names	Effect	Estimate	SE	Lower	Upper	β	df	t	p
(Intercept)	(Intercept)	22.508	5.487	11.573	33.443	-0.008	73	4.102	<.001
Condition1	SR‎/NS - NS‎/SR	-25.210	14.331	-53.771	3.351	-0.502	73	-1.759	0.083
Condition2	NS‎/NS - NS‎/SR	-21.776	14.528	-50.730	7.178	-0.434	73	-1.499	0.138
Trait Sleepiness Total T1	Trait Sleepiness Total T1	-1.427	1.453	-4.323	1.468	-0.183	73	-0.983	0.329
State Sleepiness Total T1	State Sleepiness Total T1	-0.226	1.263	-2.742	2.291	-0.031	73	-0.179	0.859
State Sleepiness T2 (child)	State Sleepiness T2 (child)	-1.281	0.932	-3.138	0.575	-0.193	73	-1.375	0.173
[5]

Descriptives

Descriptives
	Scared_Ballons_T1
N	83
Missing	0
Mean	1.96
Median	2
Standard deviation	0.956
Minimum	1
Maximum	5

Descriptives

Descriptives
	Scared_Ballons_T1
N	83
Missing	0
Mean	1.96
Median	2
Standard deviation	0.956
Minimum	1
Maximum	5

Frequencies

Frequencies of Scared_Ballons_T1
Scared_Ballons_T1	Counts	% of Total	Cumulative %
Not at all scared	31	37.3%	37.3%
Mostly not scared	30	36.1%	73.5%
A bit scared	18	21.7%	95.2%
Quite scared	2	2.4%	97.6%
Very scared	2	2.4%	100.0%

One-Way ANOVA

One-Way ANOVA (Fisher's)
	F	df1	df2	p
Scared_Ballons_T1	0.260	2	80	0.772
Scared_Balloons_T2	0.530	2	78	0.591

Assumption Checks

Homogeneity of Variances Test (Levene's)
	F	df1	df2	p
Scared_Ballons_T1	0.142	2	80	0.868
Scared_Balloons_T2	0.967	2	78	0.385
[6]

Post Hoc Tests

Tukey Post-Hoc Test – Scared_Ballons_T1
		NS‎/SR	SR‎/NS	NS‎/NS
NS‎/SR	Mean difference	—	0.138	-0.0400
NS‎/SR	p-value	—	0.850	0.987
SR‎/NS	Mean difference		—	-0.1779
SR‎/NS	p-value		—	0.778
NS‎/NS	Mean difference			—
NS‎/NS	p-value			—

Tukey Post-Hoc Test – Scared_Balloons_T2
		NS‎/SR	SR‎/NS	NS‎/NS
NS‎/SR	Mean difference	—	0.172	-0.148
NS‎/SR	p-value	—	0.829	0.884
SR‎/NS	Mean difference		—	-0.321
SR‎/NS	p-value		—	0.565
NS‎/NS	Mean difference			—
NS‎/NS	p-value			—

Descriptives

Descriptives
	Scared_Ballons_T1	Scared_Balloons_T2
N	83	81
Missing	0	2
Mean	1.96	2.05
Median	2	2
Standard deviation	0.956	1.12
Range	4	4
Minimum	1	1
Maximum	5	5

Frequencies

Frequencies of Scared_Ballons_T1
Scared_Ballons_T1	Counts	% of Total	Cumulative %
Not at all scared	31	37.3%	37.3%
Mostly not scared	30	36.1%	73.5%
A bit scared	18	21.7%	95.2%
Quite scared	2	2.4%	97.6%
Very scared	2	2.4%	100.0%

Frequencies of Scared_Balloons_T2
Scared_Balloons_T2	Counts	% of Total	Cumulative %
Not at all scared	33	40.7%	40.7%
Mostly not scared	23	28.4%	69.1%
A bit scared	16	19.8%	88.9%
Quite scared	6	7.4%	96.3%
Very scared	3	3.7%	100.0%

Descriptives

Descriptives
	SCAS_Total T1
N	83
Missing	0
Mean	5.58
Median	5.00
Standard deviation	3.62
Minimum	0.00
Maximum	19.0

Descriptives

Descriptives
	Scared_Ballons_T1
N	83
Missing	0
Mean	1.96
Median	2
Standard deviation	0.956
Minimum	1
Maximum	5

Descriptives

Descriptives
	Condition	State Sleepiness Total T1	Trait Sleepiness Total T1	State Sleepiness T2 (child)
N	NS‎/SR	29	29	28
	SR‎/NS	29	29	29
	NS‎/NS	25	25	23
Missing	NS‎/SR	0	0	1
	SR‎/NS	0	0	0
	NS‎/NS	0	0	2
Mean	NS‎/SR	18.9	20.3	21.9
	SR‎/NS	18.8	16.2	17.0
	NS‎/NS	16.2	16.4	15.8
Median	NS‎/SR	16.0	20.0	22.5
	SR‎/NS	19.0	15.0	16.0
	NS‎/NS	16.0	15.0	15.0
Standard deviation	NS‎/SR	6.73	6.62	7.04
	SR‎/NS	7.23	5.48	6.93
	NS‎/NS	6.81	6.44	7.40
Minimum	NS‎/SR	7.00	7.00	7.00
	SR‎/NS	7.00	7.00	7.00
	NS‎/NS	7.00	7.00	7.00
Maximum	NS‎/SR	34.0	33.0	33.0
	SR‎/NS	33.0	27.0	35.0
	NS‎/NS	32.0	33.0	31.0

Mediation

Mediation Estimates
Effect	Estimate	SE	Z	p
Indirect	31.2	14.6	2.14	0.032
Direct	-85.0	31.8	-2.67	0.008
Total	-53.8	31.2	-1.72	0.085

Path Estimates
			Estimate	SE	Z	p
Condition - Sleep Restriction Time 2	→	State Sleepiness T2 (child)	5.50	1.65	3.33	<.001
State Sleepiness T2 (child)	→	T2_Distance	5.67	2.03	2.79	0.005
Condition - Sleep Restriction Time 2	→	T2_Distance	-84.97	31.82	-2.67	0.008

Mediation

Mediation Estimates
Effect	Estimate	SE	Z	p
Indirect	-9.45	8.58	-1.10	0.271
Direct	47.68	30.98	1.54	0.124
Total	38.23	31.52	1.21	0.225

Path Estimates
			Estimate	SE	Z	p
Condition - Sleep Restriction Time 1	→	State Sleepiness T2 (child)	-2.25	1.75	-1.29	0.198
State Sleepiness T2 (child)	→	T2_Distance	4.20	1.98	2.13	0.033
Condition - Sleep Restriction Time 1	→	T2_Distance	47.68	30.98	1.54	0.124

Mediation

Mediation Estimates
Effect	Estimate	SE	Z	p
Indirect	-15.1	10.5	-1.435	0.151
Direct	32.4	33.4	0.971	0.332
Total	17.3	33.4	0.517	0.605

Path Estimates
			Estimate	SE	Z	p
Condition - Control	→	State Sleepiness T2 (child)	-3.60	1.81	-1.987	0.047
State Sleepiness T2 (child)	→	T2_Distance	4.20	2.02	2.076	0.038
Condition - Control	→	T2_Distance	32.40	33.37	0.971	0.332

Moderation

Moderation Estimates
	Estimate	SE	Z	p
Condition - Sleep Restriction Time 2	-76.99	30.34	-2.54	0.011
State Sleepiness T2 (child)	5.64	1.88	2.99	0.003
Condition - Sleep Restriction Time 2 ✻ State Sleepiness T2 (child)	-4.83	4.24	-1.14	0.254

Simple Slope Analysis

Simple Slope Estimates
	Estimate	SE	Z	p
Average	-77.0	30.6	-2.513	0.012
Low (-1SD)	-40.7	48.9	-0.832	0.406
High (+1SD)	-113.2	39.0	-2.906	0.004
Note. shows the effect of the predictor (Condition - Sleep Restriction Time 2) on the dependent variable (T2_Distance) at different levels of the moderator (State Sleepiness T2 (child))

Simple Slope Plot

Descriptives

Descriptives
	State Sleepiness Total T1	Trait Sleepiness Total T1	State Sleepiness T2 (child)	Trait Sleepiness T2 (child)
N	83	83	80	79
Missing	0	0	3	4
Mean	18.1	17.7	18.4	17.5
Median	17.0	17.0	18.0	17.0
Standard deviation	6.95	6.41	7.50	6.97
Minimum	7.00	7.00	7.00	7.00
Maximum	34.0	33.0	35.0	35.0
Shapiro-Wilk W	0.966	0.968	0.961	0.960
Shapiro-Wilk p	0.028	0.034	0.015	0.015

References

[1] The jamovi project (2024). jamovi. (Version 2.6) [Computer Software]. Retrieved from https://www.jamovi.org.

[2] R Core Team (2024). R: A Language and environment for statistical computing. (Version 4.4) [Computer software]. Retrieved from https://cran.r-project.org. (R packages retrieved from CRAN snapshot 2024-08-07).

[3] Gallucci, M. (2019). GAMLj: General analyses for linear models. [jamovi module]. Retrieved from https://gamlj.github.io/.

[4] Gallucci, M. (2020). Model goodness of fit in GAMLj. . link.

[5] Lüdecke, Ben-Shachar, Patil & Makowski (2020). Extracting, Computing and Exploring the Parameters of Statistical Models using R. CRAN. link.

[6] Fox, J., & Weisberg, S. (2023). car: Companion to Applied Regression. [R package]. Retrieved from https://cran.r-project.org/package=car.