Item analysis
We started by analyzing the distribution response for each dichotomous item (coded as 0 or 1). Results are presented in Table 1.
Prevalence rates ranged between 1.6 and 74.5 % and, as expected, serious infractions displayed lower prevalence rates than minor infractions. Seven items had prevalence rates <10 %, three of which <5 %, 10 items had prevalence rates ranging between 10 and 50 % and only 2 items had prevalence rates >50 %. This wide range of prevalence rates reflects the different severity level of the behaviors included in the scale.
Construct validity
Factor validity
Two models were tested using CFA. The first model was a one-factor structure, commonly used in delinquency research, especially when using variety scales (e.g. Bendixen and Olweus 1999; Trinkner et al. 2012; Weerman 2011). The second alternative model tested was based on the seriousness of the behaviors and it was a two-factor structure, composed by serious and minor infractions (see Table 1 for information on the items’ composing each of the factors), which is also commonly used (e.g. Bendixen and Olweus 1999; Peck 2013; Weerman, and Bijleveld 2007). The results of the CFA showed adequate goodness-of-fit indices for both models, with the two-factor structure showing a slightly better fit to the observed data in all the indices considered (χ
2/df = 2.437, p <0.001; CFI = 0.951; TLI = 0.944; RMSEA = 0.041, I.C.]0.036–0.047[; WRMR = 1.290) than the one-factor structure (χ
2/df = 2.591, p <0.001; CFI = 0.945; TLI = 0.938; RMSEA = 0.043, I.C.]0.038–0.049[; WRMR = 1.345). Despite these results, the correlation between serious and minor infractions in the two-factor model was very strong (r = 0.895, p <0.001), suggesting the absence of discriminant validity.
Convergent and discriminant validity
Convergent and discriminant factor validity were evaluated using the Average Variance Extracted (AVE, see Marôco 2014; Fornell and Larcker 1981). The AVE for the total score was 0.49, for serious infractions 0.54 and for minor infractions 0.48. These results indicate that both the total score and the two factors have appropriate convergent validity. However, as we suspected, the squared correlation between serious infractions and minor infractions was 0.80, which is larger than their individual AVE, and therefore indicates the absence of discriminant validity between these two factors in the present sample. Given these results, the one-factor structure is the most parsimonious and the one that more adequately fits the data. The standardized factor weights, as well as the items’ squared multiple correlations for the one-factor solution are presented in Fig. 1.
Reliability
The internal consistency of the DBVS was assessed using Cronbach α and Composite Reliability (CR). Cronbach α for the 19 items composing the scale was 0.829 and no significant improvements were found excluding any item. Following the indications of Fornell and Larcker (1981), the internal consistency of the scale was also examined using CR, which in the present sample was 0.90. Finally, the item/domain discriminating power was assessed through the corrected item-total correlations. All the items were significantly (p ≤ 0.001) and positively related with the total score, with correlation coefficients ranging between 0.20 and 0.52, although more than 2/3 of the items presented coefficients ≥0.40. These results strongly support the adequacy and reliability of the single-factor solution of the DBVS in the present sample.
Group differences and associations with related variables
Criterion validity was assessed through the scale’s ability to identify group differences, as well as its association with variables that have been consistently related in the literature with deviance and delinquency involvement, such as age and gender (e.g. Emler and Reicher 1995; Farrington et al. 2013; Gottfredson and Hirschi 1990; Hansen 2003; Junger-Tas, et al. 2003; Junger-Tas et al. 2004; Smith and McVie 2003), or school failure (e.g. Defoe et al. 2013; Emler and Reicher 1995; Farrington 2005; Hansen 2003) Starting with gender differences, the results of the Welch’s t test showed a statistically significant difference in deviant involvement (t
(675,10) = 6.824, p < 0.001), with boys reporting having engaged in a higher number of deviant acts (M = 4.59; SD = 3.84) than girls (M = 3.05; SD = 2.58). The results of the Welch’s t test also revealed a significant difference regarding school failure (t
(725,32) = 11.431, p < 0.001), with those who had been retained at school at least once reporting having engaged in a higher number of deviant acts (M = 4.92; SD = 3.72) than those who had never been retained (M = 2.54; SD = 2.24). In the same line, Pearson correlation coefficients showed that the deviance variety scores were significantly and positively related with the number of school retentions (r = 0.18; p < 0.001). Also as expected, age was positively associated with deviance (r = 0.23; p < 0.001). According to the literature (e.g. Emler and Reicher 1995; Farrington et al. 2013; Gottfredson and Hirschi 1990; Hansen 2003; Junger-Tas, et al. 2003), the engagement in deviant and delinquent activities escalates from pre-adolescence to mid-adolescence, when it reaches its peak (generally around 16 years old), and then starts to stabilize and decrease in the subsequent years. To see if we were able to find this developmental pattern using the DBVS, the average deviance variety score was calculated for each age cohort, separated by gender, and is graphically represented in Fig. 2. Results clearly show that the developmental pattern found with the DBVS is similar to the one found in previous research, except that girl’s involvement in deviance after 16 years old kept more or less stable instead of decreasing.
Finally, we wanted to examine the DBVS’s ability for detecting significant differences between the convicted and the non-convicted adolescents regarding their involvement in deviant activities and again the results of the Welch’s t test showed a statistically significant difference between the two groups (t
(91,11) = 5.84, p ≤ 0.001). Those who had already been convicted reported having been engaged in a higher number of deviant acts during last year (M = 6.43; SD = 4.53) than those who had never been convicted (M = 3.47; SD = 3.01). Since the composition of these two groups was significantly different in what concerns age and gender, and given the association between these variables and delinquency, it was important to control for their effect, including them in the analyses as covariates. So, although there was no homogeneity of variances between the two groups, given the robustness of the F statistic and the impossibility of including covariates in a non-parametric test, we performed an ANCOVA, with age and gender as covariates. The results showed that the difference between the two groups was still statistically significant (F
(3856) = 40.89, p < 0.001, η
2
p
= 0.05), even after controlling for age (F
(3856) = 58.72, p < 0.001, η
2
p
= 0.06) and gender (F
(3856) = 47.80, p < 0.001, η
2
p
= 0.05).