Gender-age effects in assessing attitudes toward statistics among undergraduate students: structural equation approach

Figures & data

Table 1: Descriptive statistics of construct/items.

Construct	Item	Mean	SD	Skwness	z-score	p-value	Kurtosis	z-score	p-value
Affect	AF1	3.26	1.08	–0.37	–4.8	<0.001	–0.76	–4.88	<0.001
	AF2	3.15	1.05	–0.31	–3.95	<0.001	–0.72	–4.67	<0.001
	AF3	2.89	1.08	0.08	1.01	0.311	–0.9	–5.79	<0.001
	AF4	2.98	1.09	–0.08	–0.97	0.332	–0.96	–6.21	<0.001
Cognitive	CO1	3.06	1.13	–0.27	–3.46	0.001	–0.94	–6.1	<0.001
	CO2	2.98	1.22	–0.18	–2.34	0.02	–1.16	–7.48	<0.001
	CO3	2.7	1.12	0.19	2.4	0.016	–0.91	–5.91	<0.001
	CO4	3.07	1.2	–0.29	–3.76	<0.001	–1.06	–6.88	<0.001
	CO5	3.25	1.17	–0.5	–6.51	<0.001	–0.81	–5.22	<0.001
Value	VA1	3.21	1.19	–0.1	–1.22	0.221	–1.15	–7.45	<0.001
	VA2	2.99	1.25	0.17	2.25	0.024	–1.16	–7.49	<0.001
	VA3	3.02	1.11	–0.12	–1.59	0.112	–1.12	–7.21	<0.001
	VA4	2.98	1.07	–0.1	–1.23	0.219	–1.01	–6.56	<0.001
	VA5	2.93	1.11	0.08	1.02	0.308	–1.1	–7.1	<0.001
Difficulty	DI1	3.41	0.95	–0.47	–6.04	<0.001	–0.46	–2.99	0.003
	DI2	3.61	0.88	–0.73	–9.44	<0.001	0.28	1.78	0.076
	DI3	3.51	0.91	–0.62	–8.04	<0.001	–0.04	–0.28	0.778
	DI4	3.62	0.95	–0.69	–8.86	<0.001	–0.02	–0.11	0.909
Interest	IN1	3.04	1.03	–0.02	–0.24	0.808	–0.88	–5.67	<0.001
	IN2	3.06	1.06	–0.07	–0.86	0.389	–0.94	–6.07	<0.001
	IN3	2.98	1.13	–0.05	–0.68	0.495	–0.99	–6.4	<0.001
	IN4	3.13	1.07	–0.33	–4.28	<0.001	–0.94	–6.06	<0.001
Effort	EF1	3.59	1.09	–0.66	–8.48	<0.001	–0.32	–2.09	0.037
	EF2	3.36	1.1	–0.47	–6.02	<0.001	–0.71	–4.59	<0.001
	EF3	3.58	1.03	–0.75	–9.73	<0.001	–0.12	–0.8	0.426

Table 2: Standardized regression loading and multiple r squared.

Item	Mean	S. E	Loading	R-Squared
Value
VA3	3.02	0.04	0.86	0.74
VA4	2.98	0.03	0.85	0.72
VA5	2.93	0.04	0.86	0.74
Cognitive
CO2	2.98	0.04	0.68	0.47
CO4	3.07	0.04	0.94	0.89
CO5	3.25	0.04	0.90	0.81
Interest
IN1	3.04	0.03	0.86	0.74
IN2	3.06	0.03	0.92	0.85
IN3	2.98	0.04	0.86	0.74
Difficulty
DI1	3.41	0.03	0.83	0.69
DI2	3.61	0.03	0.82	0.67
DI3	3.51	0.03	0.89	0.79
DI4	3.62	0.03	0.84	0.70
Affect
AF1	3.26	0.03	0.96	0.92
AF2	3.15	0.03	0.77	0.59
EF2	3.36	0.04	0.55	0.36
EF3	3.58	0.03	0.94	0.83

Note: S.E refers to the standard error of the mean.

Table 3: Model validity with and without demographic profile (gender and age).

	Summary statistics			With gender & age			Without gender & age
Constructs	M	SD	CR	AVE	SR(AVE)	CR	AVE	SR(AVE)
Value	2.98	0.92	0.956	0.880	0.938	0.892	0.733	0.856
Cognitive	3.10	0.93	0.921	0.798	0.893	0.884	0.720	0.849
Interest	3.03	0.90	0.917	0.788	0.888	0.913	0.777	0.881
Difficulty	3.54	0.94	0.927	0.760	0.872	0.909	0.713	0.844
Affect	3.21	0.90	0.892	0.806	0.898	0.858	0.754	0.868
Effect	3.47	0.83	0.835	0.731	0.855	0.916	0.869	0.932

Note: SR represents the square root of AVE. SR(AVE) refers to square root of Average Variance Extracted (AVE); ^†p < 0.100; *p < 0.050; **p < 0.010; ***p < 0. 001.

Table 5: Correlation among SATS constructs with age and gender.

	Cov(X,Y)	ρ(X, Y)	S.E	C.R	p-value
Value↔Cognitive	0.422	0.531	0.035	12.076	<0.001
Value↔Interest	–0.132	–0.157	0.030	–4.408	<0.001
Value↔Difficulty	0.088	0.116	0.027	3.258	0.001
Value↔Affect	0.481	0.490	0.039	12.369	<0.001
Effect↔Value	0.075	0.138	0.025	2.970	0.003
Cognitive↔Interest	–0.110	–0.149	0.026	–4.257	<0.001
Cognitive↔Difficulty	–0.078	–0.118	0.023	–3.359	<0.001
Effect↔Value	0.075	0.138	0.025	2.970	0.003
Cognitive↔Affect	0.157	0.184	0.030	5.191	<0.001
Effect↔Cognitive	0.032	0.067	0.015	2.056	0.040
Interest↔Difficulty	–0.061	–0.087	0.024	–2.504	0.012
Interest↔Affect	–0.064	–0.070	0.032	–2.012	0.044
Effect↔Interest	–0.037	–0.074	0.016	–2.263	0.024
Difficulty↔Affect	0.102	0.125	0.029	3.581	<0.001
Effect↔Difficulty	0.034	0.075	0.016	2.111	0.035
Effect↔Affect	0.076	0.129	0.026	2.878	0.004
Age*Gender ↔Effect	–0.068	–0.011	0.183	–0.370	0.711
Gender↔Effect	–0.016	–0.059	0.009	–1.750	0.080
Age↔Effect	0.173	0.147	0.059	2.946	0.003
Age*Gender Affect	0.268	0.024	0.371	0.721	0.471
Gender↔Affect	–0.003	–0.006	0.017	–0.172	0.864
Age↔Affect	0.189	0.089	0.070	2.681	0.007
Age*Gender↔Difficulty	–0.957	–0.111	0.288	–3.318	<0.001
Gender↔Difficulty	–0.037	–0.094	0.013	–2.820	0.005
Age↔Difficulty	–0.084	–0.051	0.055	–1.543	0.123
Age*Gender↔Interest	–0.677	–0.071	0.317	–2.135	0.033
Gender↔Interest	–0.024	–0.056	0.014	–1.701	0.089
Age↔Interest	–0.107	–0.059	0.060	–1.766	0.077
Age*Gender↔Cognitive	2.039	0.226	0.312	6.543	<0.001
Gender↔Cognitive	0.087	0.215	0.014	6.251	<0.001
Age↔Cognitive	0.051	0.030	0.057	0.903	0.366
Age*Gender↔Value	1.614	0.156	0.353	4.570	<0.001
Gender↔Value	0.064	0.136	0.016	4.002	<0.001
Age↔Value	0.092	0.047	0.066	1.394	0.163
Age*Gender↔Age	4.201	0.187	0.722	5.816	<0.001
Gender↔Age	–0.101	–0.100	0.032	–3.143	0.002
Age*Gender↔Gender	5.070	0.954	0.232	21.819	<0.001

Table 6: Correlation among SATS constructs without age and gender.

Variable	Cov (X, Y)	(X,Y)	S.E	CrtR	p-value
Value↔Cognitive	0.422	0.531	0.035	12.066	<0.001
Value↔Interest	–0.132	–0.157	0.030	–4.422	<0.001
Value↔Difficulty	0.088	0.116	0.027	3.261	0.001
Value↔Affect	0.482	0.487	0.039	12.396	<0.001
Cognitive↔Interest	–0.110	–0.149	0.026	–4.257	<0.001
Cognitive↔Difficulty	–0.078	–0.118	0.023	–3.360	<0.001
Cognitive↔Affect	0.158	0.183	0.030	5.188	<0.001
Interest↔Difficulty	–0.061	–0.087	0.024	–2.502	0.012
Interest↔Affect	–0.065	–0.071	0.032	–2.055	0.040
Difficulty↔Affect	0.103	0.125	0.029	3.587	<0.001
Effect↔Difficulty	0.025	0.064	0.016	1.547	0.122
Effect↔Affect	0.055	0.107	0.032	1.720	0.085
Effect↔Interest	–0.030	–0.069	0.017	–1.817	0.069
Effect↔Cognitive	0.025	0.061	0.015	1.688	0.091
Effect↔Value	0.055	0.116	0.031	1.754	0.079

Note: CrtR refers to critical ratio.

Table 4: Summary of model fit indices.

Measure	Without Gender & Age	With Gender & Age	Threshold	Interpretation
Chi-square (χ^2)	325.034	385.391
df	137	137		–
Chi-square /df	2.373	2.813	Between 1 & 3	–
Comparative-Fit Index (CFI)	0.976	0.983	>0.95	Excellent
Standardized Root Mean Square Residual (SRMR)	0.040	0.035	<0.08	Excellent
Root Mean Square Error of Approximation (RMSEA)	0.048	0.043	<0.06	Excellent
Normed Fit Index (NFI)	0.967	0.975	>0.95	Excellent
Incremental Fit Index (IFI)	0.967	0.984	>0.95	Excellent
Goodness of Fit Index (GFI)	0.908	0.921	>0.95	Excellent
p of Close Fit (PClose)	0.679	0.992	>0.05	Excellent
Akaike Information Criterion (AIC)	571.391	478.607		Excellent

PClose: This measure is a one-sided test of the null hypothesis that the RMSEA equals .05, what is called a close-fitting model.

Figure 1: Adopted six-factor model of the SATS 36 items with and without demographic profile.

Table 7: Predictive relationship (standardised regression weights) of age and gender with SATS.

Variable	B	β	S.E.	CrtR.	p-value
Age * Gender→Value	0.084	0.601	0.030	2.794	0.005
Gender→Value	–1.565	–0.504	0.658	–2.378	0.017
Age * Gender→Cognitive	0.052	0.531	0.026	1.988	0.047
Age→Value	–0.099	–0.134	0.047	–2.078	0.038
Gender→Cognitive	–0.765	–0.349	0.577	–1.326	0.185
Age→Effect	0.001	0.003	0.032	0.036	0.971
Age→Affect	–0.020	–0.036	0.050	–0.389	0.697
Age→Difficulty	0.024	0.054	0.040	0.589	0.556
Age→Interest	–0.045	–0.103	0.045	–1.015	0.310
Gender→Effect	–0.770	–0.466	0.454	–1.696	0.090
Gender→Affect	–0.923	–0.397	0.710	–1.301	0.193
Gender→Difficulty	0.523	0.286	0.555	0.941	0.347
Gender→Interest	–0.368	–0.198	0.619	–0.595	0.552
Age * Gender→Interest	0.012	0.139	0.028	0.414	0.679
Age * Gender→Difficulty	–0.031	–0.381	0.025	–1.238	0.216
Age * Gender→Affect	0.041	0.395	0.033	1.253	0.210
Age * Gender→Effect	0.032	0.434	0.021	1.574	0.115
Age→Cognitive	–0.059	–0.114	0.042	–1.422	0.155

Note: B is unstandardized regression estimates; β is standardized regression estimates; p < 0.05 indicates significance level; CrtR refers to critical ratio.

Table 8: Multigroup analysis among the SATS constructs.

Variable	Male (β)	Female (β)	Male (t)	Female (t)	Difference in (t)
Gender Effect
Value↔Cognitive	0.535	0.499	9.717	6.608	3.109
Cognitive↔ Interest	–0.184	–0.064	–4.019	–1.198	–2.821
Cognitive↔ Difficulty	–0.191	0.045	–4.122	0.827	–4.949
Cognitive↔ Affect	0.086	0.400	1.925	5.877	–3.952
Effect↔ Cognitive	0.008	0.196	0.186	2.419	–2.233
Interest↔ Difficulty	–0.014	–0.196	–0.311	–3.527	3.216
Value↔ Difficulty	0.032	0.278	0.696	4.724	–4.028
Value↔ Interest	–0.142	–0.172	–3.110	–3.024	–0.086
Value↔ Affect	0.451	0.577	9.058	8.327	0.731
Effect↔ Value	0.045	0.274	0.956	2.393	–1.437
Interest↔ Affect	–0.042	–0.101	–0.926	–1.775	0.849
Effect↔ Interest	–0.106	–0.057	–1.764	–1.295	–0.469
Difficulty↔ Affect	0.101	0.157	2.250	2.711	–0.461
Effect↔ Difficulty	0.103	0.042	1.619	0.946	0.673
Effect↔ Affect	0.061	0.226	1.109	2.429	–1.320
Age group Effect	<23 years(β)	>23 years(β)	<23 years(t)	>23 years(t)	Difference in (t)
Value↔ Cognitive	0.509	0.499	9.838	6.608	3.230
Value↔ Affect	0.541	0.577	10.911	8.328	2.583
Cognitive↔ Interest	–0.160	–0.064	–3.736	–1.198	–2.538
Cognitive↔ Difficulty	–0.159	0.045	–3.677	0.827	–4.504
Value↔ Interest	–0.168	–0.172	–3.827	–3.024	–0.803
Value↔ Difficulty	0.125	0.278	2.849	4.724	–1.875
Effect↔ Value	0.213	0.274	3.101	2.393	0.708
Cognitive↔ Affect	0.195	0.400	4.489	5.878	–1.389
Effect↔ Cognitive	0.066	0.196	1.452	2.419	–0.967
Interest↔ Difficulty	–0.077	–0.196	–1.793	–3.527	1.734
Interest↔ Affect	–0.021	–0.101	–0.489	–1.775	1.286
Effect↔ Interest	–0.001	–0.057	–0.014	–1.295	1.281
Difficulty↔ Affect	0.121	0.157	2.812	2.711	0.101
Effect↔ Difficulty	0.025	0.042	0.521	0.946	–0.425
Effect↔ Affect	0.132	0.226	2.410	2.430	–0.020

Note: t refers to the t-test statistic for the gender (male and female) and age group (<23 years and >23 years)

Table

SN	Statement	M	SD	Skewness	Kurtosis
	Affect: students’ feelings concerning statistics
AF1	I will like statistics.	3.71	0.86	–0.74	−0.07
AF2	I will feel insecure when I must do statistics problems.	3.90	0.77	–0.82	0.80
AF3	I will get frustrated going over statistics tests in class.	3.87	0.94	–0.78	−0.11
AF4	I will be under stress during statistics class.	3.90	0.92	–0.93	0.46
AF5	I will enjoy taking statistics courses.	3.75	0.92	–0.82	0.27
AF6	I am scared by statistics	3.75	0.96	–0.91	0.43
	Cognitive Competence—students’ attitudes about their intellectual knowledge & skills when applied to statistics
CO1	I will have trouble understanding statistics because of how I think	3.95	0.92	–0.99	0.60
CO2	I will have no idea of what’s going on in this statistics course	3.99	0.95	–1.07	0.88
CO3	I will make a lot of math errors in statistics	3.81	0.94	–0.86	0.44
CO4	I can learn statistics.	3.69	0.91	–0.67	−0.09
CO5	I will understand statistics equations.	3.79	0.92	–0.87	0.38
CO6	I will find it difficult to understand statistical concepts	3.76	0.93	–0.64	−0.19
	Value—students’ attitudes about the usefulness, relevance, & worth of statistics in personal and professional life
VA1	Statistics is worthless.	3.66	0.94	–0.54	−0.41
VA2	Statistics should be a required part of my professional training.	3.83	1.00	–0.86	0.15
VA3	Statistical skills will make me more employable	3.77	0.91	–0.70	0.07
VA4	Statistics is not useful to the typical professional.	3.71	0.97	–0.74	−0.04
VA5	Statistical thinking is not applicable in my life outside my job.	3.80	0.89	–0.66	0.01
VA6	I use statistics in my everyday life.	3.73	0.86	–0.57	−0.03
VA7	Statistics conclusions are rarely presented in everyday life.	3.86	0.83	–0.58	0.13
VA8	I will have no application for statistics in my profession.	3.91	0.93	–0.75	0.15
VA9	Statistics is irrelevant in my life.	3.57	0.93	–0.53	−0.22
	Difficulty—students’ attitudes about the difficulty of statistics as a subject
DI1	Statistics formulas are easy to understand.	3.70	0.83	–0.55	0.09
DI2	Statistics is a complicated subject.	3.31	1.09	–0.61	−0.48
DI3	Statistics is a subject quickly learned by most people.	3.56	0.96	–0.55	−0.31
DI4	Learning statistics requires a great deal of discipline.	3.94	0.87	–0.77	0.22
DI5	Statistics involves massive computations.	3.36	0.91	–0.22	−0.99
DI6	Statistics is highly technical.	3.80	0.86	–0.76	0.43
DI7	Most people have to learn a new way of thinking to do statistics.	3.48	1.06	–0.87	0.08
	Interest—students’ level of individual interest in statistics
IN1	I am interested in being able to communicate statistical information to others.	3.72	0.93	–0.86	0.26
IN2	I am interested in using statistics.	4.02	0.77	–0.79	0.82
IN3	I am interested in understanding statistical information.	3.73	1.05	–1.17	0.87
IN4	I am interested in learning statistics.	3.85	0.84	–0.94	0.96
	Effort—amount of work the student expends to learn statistics
EF1	I plan to complete all my statistics assignments.	3.93	0.75	–0.66	0.84
EF2	I plan to work hard in my statistics course.	3.92	0.83	–0.86	1.15
EF3	I plan to study hard for every statistics test.	3.88	0.76	–0.67	0.75
EF4	I plan to attend every statistics class session.	3.62	0.96	–0.81	0.34