Results

Reliability Analysis

Alpha for the DOI

Scale Reliability Statistics
		Cronbach's α
scale		0.783

[3]

Reliability Analysis

Alpha for the fractions measure

Scale Reliability Statistics
		Cronbach's α
scale		0.830

[3]

Reliability Analysis

Alpha for matrix reasoning

Scale Reliability Statistics
		Cronbach's α
scale		0.703

[3]

Reliability Analysis

Alpha for all conditional reasoning items (the variables are accuracies)

Scale Reliability Statistics
		Cronbach's α
scale		0.352
Note. items 'MT1', 'MP1', 'MP2', 'MP3', 'MT2', 'MT3', 'MP4', and 'MT4' correlate negatively with the total scale and probably should be reversed

[3]

Reliability Analysis

Alpha for all conditional reasoning items excluding MT

Scale Reliability Statistics
		Cronbach's α
scale		0.689
Note. items 'MP1', 'MP2', 'MP3', and 'MP4' correlate negatively with the total scale and probably should be reversed

[3]

Reliability Analysis

Alpha for MT items on conditional inference test only

Scale Reliability Statistics
		Cronbach's α
scale		0.510

[3]

Correlation Matrix

Correlation between MP+DA+AC and MT on conditional inference test

Correlation Matrix
		MP_DA_AC	MT.total
MP_DA_AC	Pearson's r	—
	df	—
	p-value	—
MT.total	Pearson's r	-0.444	—
	df	962	—
	p-value	< .001	—

Descriptives

Descriptives
	DOI_score	GHQ_av	Matrix.total	Rational_Number_Test_Score	MP.total	DA.total	AC.total	MT.total	CI.total	MP_DA_AC
Mean	-4.50	1.05	57.8	71.7	0.939	0.409	0.231	0.645	55.6	0.526
Standard deviation	3.18	0.542	25.2	22.5	0.152	0.340	0.294	0.296	12.5	0.186
Minimum	-20.6	0.00	0	0.00	0.00	0.00	0.00	0.00	25.0	0.167
Maximum	0.00	2.92	100	100	1.00	1.00	1.00	1.00	100	1.00

Correlation Matrix

Correlation Matrix
	DOI_score		GHQ_av		Matrix.total		Rational_Number_Test_Score		CI.total		MP_DA_AC		MT.total	Age	Education
DOI_score	—
GHQ_av	-0.091	**	—
Matrix.total	0.208	***	0.039		—
Rational_Number_Test_Score	0.102	**	-0.014		0.329	***	—
CI.total	0.109	***	0.013		0.271	***	0.257	***	—
MP_DA_AC	0.078	*	-0.021		0.214	***	0.186	***	0.849	***	—
MT.total	0.039		0.062		0.055		0.086	**	0.096	**	-0.444	***	—
Age	0.137	***	-0.211	***	0.007		-0.108	***	-0.049		-0.026		-0.034	—
Education	-0.124	***	-0.118	***	0.059		0.095	**	0.064	*	0.082	*	-0.045	-0.030	—
Note. * p < .05, p < .01, * p < .001

One Sample T-Test

Are the four inference scores from the CIT significantly different to chance levels? (Footnote 1).

One Sample T-Test
		Statistic	df	p
DA.total	Student's t	-8.33	963	< .001
AC.total	Student's t	-28.39	963	< .001
MP.total	Student's t	89.85	963	< .001
MT.total	Student's t	15.24	963	< .001
Note. Hₐ μ ≠ 0.5

Partial Correlation

Are Rational Number Test scores related to Conditional Inference controlling for various covariates? (Footnote 2.)

Partial Correlation
		Rational_Number_Test_Score	CI.total	MP_DA_AC	MT.total
Rational_Number_Test_Score	Pearson's r	—
	p-value	—
CI.total	Pearson's r	0.174	—
	p-value	< .001	—
MP_DA_AC	Pearson's r	0.110	0.841	—
	p-value	< .001	< .001	—
MT.total	Pearson's r	0.081	0.087	-0.466	—
	p-value	0.012	0.007	< .001	—
Note. controlling for 'Matrix.total', 'Sex01', 'Education', and 'Age'

[4]

Linear Regression

Model Fit Measures
			Overall Model Test
Model	R	R²	F	df1	df2	p
1	0.133	0.0178	8.70	2	961	< .001

Model Coefficients - DOI_score
						95% Confidence Interval
Predictor	Estimate	SE	t	p	Stand. Estimate	Lower	Upper
Intercept	-6.5611	0.50989	-12.87	< .001
Rational_Number_Test_Score	0.0111	0.00468	2.38	0.017	0.0788	0.0139	0.144
CI.total	0.0226	0.00839	2.70	0.007	0.0892	0.0243	0.154

Linear Regression

Hierarchical regression with control variables in block 1 and main variables in block 2.

Model Fit Measures
			Overall Model Test
Model	R	R²	F	df1	df2	p
1	0.282	0.0796	20.6	4	955	< .001
2	0.296	0.0874	15.2	6	953	< .001

Model Comparisons
Comparison
Model		Model	ΔR²	F	df1	df2	p
1	-	2	0.00777	4.06	2	953	0.018

Model Specific ResultsModel 1Model 2

Model Coefficients - DOI_score
						95% Confidence Interval
Predictor	Estimate	SE	t	p	Stand. Estimate	Lower	Upper
Intercept	-5.5052	0.55421	-9.933	< .001
Age	0.0320	0.00770	4.151	< .001	0.1290	0.0680	0.1900
Sex01	0.1027	0.20175	0.509	0.611	0.0159	-0.0453	0.0771
Education	-0.3240	0.07557	-4.287	< .001	-0.1337	-0.1949	-0.0725
Matrix.total	0.0275	0.00393	6.987	< .001	0.2178	0.1566	0.2790

Model Coefficients - DOI_score
						95% Confidence Interval
Predictor	Estimate	SE	t	p	Stand. Estimate	Lower	Upper
Intercept	-6.73446	0.70493	-9.553	< .001
Age	0.03423	0.00772	4.431	< .001	0.1382	0.07699	0.1994
Sex01	0.16642	0.20300	0.820	0.413	0.0257	-0.03587	0.0873
Education	-0.34311	0.07567	-4.535	< .001	-0.1416	-0.20289	-0.0803
Matrix.total	0.02302	0.00423	5.449	< .001	0.1826	0.11681	0.2483
CI.total	0.01599	0.00830	1.928	0.054	0.0631	-0.00113	0.1274
Rational_Number_Test_Score	0.00828	0.00479	1.730	0.084	0.0587	-0.00789	0.1252

Linear Regression

First regression mentioned in footnote 4.

Model Fit Measures
			Overall Model Test
Model	R	R²	F	df1	df2	p
1	0.282	0.0796	20.6	4	955	< .001
2	0.291	0.0845	17.6	5	954	< .001

Model Comparisons
Comparison
Model		Model	ΔR²	F	df1	df2	p
1	-	2	0.00491	5.11	1	954	0.024

Model Specific ResultsModel 1Model 2

Model Coefficients - DOI_score
						95% Confidence Interval
Predictor	Estimate	SE	t	p	Stand. Estimate	Lower	Upper
Intercept	-5.5052	0.55421	-9.933	< .001
Age	0.0320	0.00770	4.151	< .001	0.1290	0.0680	0.1900
Sex01	0.1027	0.20175	0.509	0.611	0.0159	-0.0453	0.0771
Education	-0.3240	0.07557	-4.287	< .001	-0.1337	-0.1949	-0.0725
Matrix.total	0.0275	0.00393	6.987	< .001	0.2178	0.1566	0.2790

Model Coefficients - DOI_score
						95% Confidence Interval
Predictor	Estimate	SE	t	p	Stand. Estimate	Lower	Upper
Intercept	-6.3837	0.67585	-9.446	< .001
Age	0.0328	0.00769	4.269	< .001	0.1326	0.07162	0.1935
Sex01	0.1206	0.20148	0.599	0.549	0.0187	-0.04249	0.0798
Education	-0.3327	0.07551	-4.407	< .001	-0.1373	-0.19847	-0.0762
Matrix.total	0.0250	0.00407	6.155	< .001	0.1985	0.13522	0.2618
CI.total	0.0185	0.00818	2.261	0.024	0.0730	0.00965	0.1363

Linear Regression

First regression mentioned in footnote 4.

Model Fit Measures
			Overall Model Test
Model	R	R²	F	df1	df2	p
1	0.282	0.0796	20.6	4	955	< .001
2	0.290	0.0838	17.5	5	954	< .001

Model Comparisons
Comparison
Model		Model	ΔR²	F	df1	df2	p
1	-	2	0.00421	4.39	1	954	0.036

Model Specific ResultsModel 1Model 2

Model Coefficients - DOI_score
						95% Confidence Interval
Predictor	Estimate	SE	t	p	Stand. Estimate	Lower	Upper
Intercept	-5.5052	0.55421	-9.933	< .001
Age	0.0320	0.00770	4.151	< .001	0.1290	0.0680	0.1900
Sex01	0.1027	0.20175	0.509	0.611	0.0159	-0.0453	0.0771
Education	-0.3240	0.07557	-4.287	< .001	-0.1337	-0.1949	-0.0725
Matrix.total	0.0275	0.00393	6.987	< .001	0.2178	0.1566	0.2790

Model Coefficients - DOI_score
						95% Confidence Interval
Predictor	Estimate	SE	t	p	Stand. Estimate	Lower	Upper
Intercept	-6.06567	0.61455	-9.870	< .001
Age	0.03376	0.00773	4.367	< .001	0.1363	0.07506	0.1976
Sex01	0.16027	0.20326	0.788	0.431	0.0248	-0.03690	0.0865
Education	-0.33778	0.07572	-4.461	< .001	-0.1394	-0.20073	-0.0781
Matrix.total	0.02467	0.00414	5.954	< .001	0.1956	0.13116	0.2601
Rational_Number_Test_Score	0.00989	0.00472	2.095	0.036	0.0700	0.00442	0.1357

Linear Regression

Main analysis with conditional inference scores split into MP+DA+AC and MT.

Model Fit Measures
Model	R	R²
1	0.136	0.0184

Model Coefficients - DOI_score
						95% Confidence Interval
Predictor	Estimate	SE	t	p	Stand. Estimate	Lower	Upper
Intercept	-6.6858	0.53626	-12.47	< .001
MP_DA_AC	1.6599	0.63138	2.63	0.009	0.0969	0.02458	0.169
MT.total	0.8135	0.39085	2.08	0.038	0.0757	0.00433	0.147
Rational_Number_Test_Score	0.0109	0.00469	2.33	0.020	0.0773	0.01218	0.142

References

[1] The jamovi project (2022). jamovi. (Version 2.3) [Computer Software]. Retrieved from https://www.jamovi.org.

[2] R Core Team (2021). R: A Language and environment for statistical computing. (Version 4.1) [Computer software]. Retrieved from https://cran.r-project.org. (R packages retrieved from MRAN snapshot 2022-01-01).

[3] Revelle, W. (2019). psych: Procedures for Psychological, Psychometric, and Personality Research. [R package]. Retrieved from https://cran.r-project.org/package=psych.

[4] Kim, S. (2015). ppcor: Partial and Semi-Partial (Part) Correlation. [R package]. Retrieved from https://cran.r-project.org/package=ppcor.