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Group Statistics
Gender N Mean Std. Deviation Std. Error Mean
LS_Mean 1 180 3.4222 .73626 .05488
2 218 3.6908 .70679 .04787
Independent Samples Test
Levene's Test for Equality of t-test for Equality of
Variances Means
[…]
Run MATRIX procedure:
Written by Andrew F. Hayes, Ph.D. www.afhayes.com
Documentation available in Hayes (2022). www.guilford.com/p/hayes3
Model : 4
Y : LS_Mean
X : IQ_Mean
M : TU_Mean
Sample
Size: 400
OUTCOME VARIABLE:
TU_Mean
Model Summary
R R-sq MSE F df1 df2
p
.2603 .0677 .5153 28.9156 1.0000 398.0000 .00
00
Model
coeff se t p LLCI ULCI
constant 2.4815 .1891 13.1212 .0000 2.1097 2.8533
IQ_Mean .2748 .0511 5.3773 .0000 .1743 .3752
Standardized coefficients
coeff
IQ_Mean .2603
OUTCOME VARIABLE:
LS_Mean
Model Summary
Page 26
R R-sq MSE F df1 df2
p
.5519 .3046 .3725 86.9548 2.0000 397.0000 .00
00
Model
coeff se t p LLCI ULCI
constant 1.0707 .1924 5.5638 .0000 .6924 1.4491
IQ_Mean .4201 .0450 9.3370 .0000 .3316 .5085
TU_Mean .2796 .0426 6.5620 .0000 .1959 .3634
Standardized coefficients
coeff
IQ_Mean .4047
TU_Mean .2844
OUTCOME VARIABLE:
LS_Mean
Model Summary
R R-sq MSE F df1 df2
p
.4787 .2292 .4118 118.3430 1.0000 398.0000 .00
00
Model
coeff se t p LLCI ULCI
constant 1.7647 .1691 10.4376 .0000 1.4323 2.0971
IQ_Mean .4969 .0457 10.8786 .0000 .4071 .5867
Standardized coefficients
coeff
IQ_Mean .4787
Total effect of X on Y
Effect se t p LLCI ULCI c_
cs
.4969 .0457 10.8786 .0000 .4071 .5867 .47
87
Direct effect of X on Y
Page 27
Effect se t p LLCI ULCI c'_
cs
.4201 .0450 9.3370 .0000 .3316 .5085 .40
47
Indirect effect(s) of X on Y:
Effect BootSE BootLLCI BootULCI
TU_Mean .0768 .0180 .0442 .1142
Completely standardized indirect effect(s) of X on Y:
Effect BootSE BootLLCI BootULCI
TU_Mean .0740 .0167 .0431 .1081
Level of confidence for all confidence intervals in output:
95.0000
Number of bootstrap samples for percentile bootstrap confidence intervals:
5000
------- H1: Independent Samples t-Test (LS_Mean by Gender)
- H1: Levene's Test for Equality of Variances
- H8: Mediation Analysis — PROCESS Model 4 (IQ_Mean → TU_Mean → LS_Mean; 5,000 bootstrap samples)
H1
An independent samples t-test was conducted to examine whether LS_Mean differed between Gender group 1 and Gender group 2 (Gender group 3, n = 2, was excluded per syntax specification; analysis N = 398). Levene's test for equality of variances was non-significant, F(1, 396) = 0.31, p = .578, so equal variances were assumed. The test revealed a statistically significant difference, t(396) = −3.703, p < .001, 95% CI [−0.41, −0.13], with Gender group 1 (M = 3.42, SD = 0.74) scoring lower than Gender group 2 (M = 3.69, SD = 0.71). Cohen's d = 0.37, indicating a small effect size (Cohen, 1988). The hypothesis was supported.
Table 1: Group Statistics and Independent Samples t-Test Results for LS_Mean by Gender
| Group | n | M | SD | Mean Difference | SE | t | df | p | Cohen's d |
|---|---|---|---|---|---|---|---|---|---|
| Gender 1 | 180 | 3.42 | 0.74 | −0.27 | 0.07 | −3.703 | 396 | < .001 | 0.37 |
| Gender 2 | 218 | 3.69 | 0.71 |
Note. Equal variances assumed; Levene's F(1, 396) = 0.31, p = .578. Gender group 3 (n = 2) was excluded from the analysis. The 95% CI for the mean difference was [−0.41, −0.13]. Cohen's d reflects a small effect size (Cohen, 1988).
H8
PROCESS Model 4 mediation analysis (Hayes, 2022) was conducted to examine whether TU_Mean mediated the relationship between IQ_Mean and LS_Mean (N = 400), using 5,000 bootstrap samples and 95% bias-corrected confidence intervals. Path coefficients and effect estimates are presented in Table 9. The a-path (IQ_Mean → TU_Mean) was significant (B = 0.27, SE = 0.05, t = 5.377, p < .001, 95% CI [0.17, 0.38]), indicating that higher IQ_Mean was associated with higher TU_Mean. The b-path (TU_Mean → LS_Mean, controlling for IQ_Mean) was also significant (B = 0.28, SE = 0.04, t = 6.562, p < .001, 95% CI [0.20, 0.36]). The indirect effect of IQ_Mean on LS_Mean through TU_Mean was significant (B = 0.08, BootSE = 0.02, 95% Boot CI [0.04, 0.11]), as the confidence interval excluded zero; the completely standardized indirect effect was .074. The direct effect of IQ_Mean on LS_Mean remained significant after controlling for TU_Mean (B = 0.42, SE = 0.05, t = 9.337, p < .001, 95% CI [0.33, 0.51]), and the total effect was also significant (B = 0.50, SE = 0.05, t = 10.879, p < .001, 95% CI [0.41, 0.59]). Because both the indirect effect and the direct effect were significant, the results indicate partial mediation of the IQ_Mean → LS_Mean relationship by TU_Mean. The hypothesis was supported.
Table 9: Direct, Indirect, and Total Effects for the Mediation of LS_Mean by TU_Mean (IQ_Mean as Predictor)
| Effect | B | SE / BootSE | t | p | 95% CI |
|---|---|---|---|---|---|
| a-path: IQ_Mean → TU_Mean | 0.27 | 0.05 | 5.377 | < .001 | [0.17, 0.38] |
| b-path: TU_Mean → LS_Mean | 0.28 | 0.04 | 6.562 | < .001 | [0.20, 0.36] |
| Direct effect: IQ_Mean → LS_Mean | 0.42 | 0.05 | 9.337 | < .001 | [0.33, 0.51] |
| Indirect effect: IQ_Mean → TU_Mean → LS_Mean | 0.08 | 0.02 | — | — | [0.04, 0.11] |
| Total effect: IQ_Mean → LS_Mean | 0.50 | 0.05 | 10.879 | < .001 | [0.41, 0.59] |
Note. N = 400. Bootstrap samples = 5,000; 95% bias-corrected confidence intervals. SE for the indirect effect is BootSE. The 95% Boot CI for the indirect effect excludes zero, indicating a significant indirect effect. Completely standardized indirect effect = .074. Partial mediation was concluded because both the direct and indirect effects were significant (Hayes, 2022).
References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
Hayes, A. F. (2022). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach (3rd ed.). The Guilford Press.
An independent samples t-test was conducted to examine whether LS_Mean differed between Gender group 1 and Gender group 2 (Gender group 3, n = 2, was excluded per syntax specification; analysis N = 398). Levene's test for equality of variances was non-significant, F(1, 396) = 0.31, p = .578, so equal variances were assumed. The test revealed a statistically significant difference, t(396) = −3.703, p < .001, 95% CI [−…
An independent samples t-test was conducted to examine whether learning satisfaction differed between gender group 1 and gender group 2 (gender group 3, n = 2, was excluded per syntax specification; analysis N = 398). Levene's test for equality of variances was non-significant, F(1, 396) = 0.31, p = .578, so equal variances were assumed. The test revealed a statistically significant difference, t(396) = −3.703, p < .001, 95% CI [−…
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