To address the study’s aims, statistical analyses were conducted using Statistical Package for the Social Sciences (SPSS). Data was obtained from measures described in this study to address racial malleability, authenticity, identity experiences, and psychological well-being. This chapter describes analyses in two steps: preliminary analyses and hypothesis-testing analyses to address the aims of this study. Statistical Power and Missing Data An apriori power analysis was conducted to determine the minimum sample size (nmin) required to determine a medium effect size (f2 = .15) for the regression analyses needed for Aims 1 and 2 of the study. Preliminary power analysis for multiple regression analyses was performed using a free online statistics calculator (GPower 3.1; Faul, Erdfelder, Buchner, & Lang, 2009). In order to conduct the power analysis the following information was required: desired effect size, power anticipated (1-β), number of predictors, and alpha level (α= .05). The power analysis was set to have a minimum of 80% power (1-β) (Faul et al., 2009) to detect the desired effect size, with nine independent variables (e.g., Malleable Racial Identification, the three subscales Authenticity Scale, the four subscales of the Multiracial Challenges and Resilience Scale, and Survey of Recent Life Experiences). The statistical calculator generated an nmin=114. In order to account for missing data due to individuals not completing the survey (Eysenbach, 2004; Gosling, Vazire, Srivastava & John, 2004) the population was oversampled such that 149 individuals participated in this study to ensure enough power to run the proposed analyses.

In order to conduct preliminary analyses the data was cleaned and checked for missing data. To address missing data, the procedures outlined by Baraldi and Enders (2009) were utilized as they take into account characteristics inherent in the population being studied and how those characteristics may impact how they respond to the outcome measures. A missing data analysis revealed that data was missing at random. Missing data ranged from 0% to 16.1%. Multiple imputation was used and 20 datasets with possible imputed values were generated based on the recommendations from Baraldi and Enders (2009). The pooled parameter estimates were used during hypothesis testing. The Role of Identity Experiences in Multiracial Well-Being The first aim of this study was to examine the relationship between racial malleability and psychological well-being, defined by perceived stress and life satisfaction, as moderated by identity experiences. The first hypothesis was that the relationship between racial malleability and perceived stress would be moderated by identity experiences. The second hypothesis was that the relationship between racial malleability and life satisfaction would be moderated by identity experiences. In order to assess these hypotheses hierarchical linear regression was conducted, as this is the first study to provide an initial exploration of these relationships. Prior to conducting the regression analyses to test the hypotheses, the factors of the Multiracial Challenges and Resilience Scale (MCRS; Salahuddin & O’Brian, 2011) needed to be confirmed in order to determine what identity experience moderators were appropriate for this sample. Confirming Challenges and Resilience Factors In order to assess the first aim of this study, confirmatory and exploratory factor analyses were utilized to assess the factor structure of the MCRS, which is utilized to determine the identity experiences that may moderate the relationship between racial malleability and psychological well-being. A confirmatory factor analysis based on the proposed six-factor structure of the 30-item MCRS revealed a poor fit for the data (RMSEA = .108, 90% CI [.106, .110]; SRMR = .08; CFI = .67). Given the poor fit of the proposed factor structure, a principal component factor analysis using varimax rotation suggested a four-factor model using an eigenvalue cutoff of 1.00, which explained 60% of the variance. The retained items loaded on the factors with components > .5. One of the four factors that emerged mapped onto the items and factors identified by Salahuddin and O’Brian (2011): the Appreciation of Human Differences subscale (Items 19, 21, 23, 25, 27). A second factor retained three of the five items originally on the subscale of Lack of Family Acceptance, however, one item that was originally conceptualized as multiracial discrimination loaded onto this factor as well (Items 3, 4, 6, 8). Three items were retained from the Others’ Surprise and Disbelief Regarding Racial Heritage subscale (Items 2, 7, and 15). A new factor emerged from this measure, which combined items from the scale of Multiracial Pride (Items 16, 22, 26) and having items reverse scored from the subscale of Challenges with Racial Identity (Items 17 and 30). Given the review of the literature presented in Chapter 2 of this dissertation, these items seem to be related to racial regard as they describe affective or evaluative views of being multiracial such as item 16, I love being multiracial. In light of the factor analysis of this sample and recent literature about the role of the family and racial regard, this study would be remiss not to include lack of family acceptance (Nadal et al., 2013) and racial regard (Sanchez, Shih, & Garcia, 2009) as identity experiences that may moderate the relationship between racial malleability and psychological well-being.

Therefore, four moderators will be included in this study as a measure of identity experiences: appreciation of human differences (MCRS Appreciation of Human Differences, α = .90), racial regard (MCRS Racial Regard, α =.76), lack of family acceptance (MCRS Lack of Family Acceptance, α = .73), and identity questioning (MCRS Others’ Surprise and Disbelief Regarding Racial Heritage, α = .65). Preliminary Analyses for Identity Experiences Moderators Descriptive statistics of the demographics of this population and the reliability and psychometric properties of the measures were described in the previous chapter. In order to run the hierarchical regression analyses, the data was needed to fulfill the following assumptions: normality of the distribution, independence of observations, and homoscedasticity. Specifically, the data was analyzed for measures of central tendency, skewness, kurtosis, and Pearson correlations among the covariate, independent variable, moderator variables, and the outcome variables. The covariate, independent variable, and outcome variables were normally distributed based on heuristics for skewness. (See Table 3). Regarding the moderator variables, appreciation for human differences was slightly skewed, based on literature; the slight skewness seemed appropriate for this population (Salahuddin & O’Brian, 2011). It is important to note that racial malleability had a very low correlation with perceived stress (r = .01, p = .929), but was significantly correlated with life satisfaction (r = .19, p = .024). Therefore, it was deemed appropriate to proceed with hypothesis testing for moderators of the relationships because there could be enhancing effects of the interactions. Racial malleability was also significantly correlated with appreciation of human differences (r = .18, p = .029). The covariate, recent life experiences was correlated with racial regard (r = -.22, p = .008), lack of family acceptance (r = .31, p = .000), perceived stress (r = .56, p = .000), and life satisfaction (r = -.38, p = .000). (See Table 4). The outcome variables significantly, negatively correlated with each other (r = -.50, p = .000). Tests for multicollinearity indicated that a very low level of multicollinearity was present for the study variables in relation to perceived stress (VIF = 1.08 for racial malleability, 1.12 for appreciation of human differences, 1.19 for racial regard, 1.19 for lack of family acceptance and 1.12 for identity questioning). Given the significant correlations between life satisfaction and study variables, it was essential to assess for multicollinearity, which indicated that a very low level of multicollinearity was present (VIF = 1.10 for racial malleability, 1.15 for appreciation of human differences, 1.16 for racial regard, 1.21 for lack of family acceptance and 1.11 for identity questioning). Perceived Stress with Identity Experiences Hierarchical regression analyses, using the steps outlined by Frazier, Tix, and Barron (2004), was used to test the first hypothesis of the relationship of study variables with perceived stress. Given that the relationship between racial malleability and perceived stress was not significant, moderation was analyzed to determine whether experiences related to identity had an enhancing interaction on perceived stress. The interaction terms were created between racial malleability and each of the moderators: appreciation of human differences, racial regard, lack of family acceptance, and identity questioning. The covariate, recent life experiences, was entered into the first step of the regression model. The second step included the independent variable, racial malleability, and the moderators. The interaction terms, created by utilizing the product of racial malleability with each of the moderators (appreciation of human differences, racial regard, lack of family acceptance, and identity questioning) were entered into the third step. Results of the regression analysis provided partial confirmation for the research hypothesis. The results of a hierarchical linear regression suggest that a significant proportion of total variation in perceived stress was predicted by recent life experiences, R2 = .36, F(1, 114) = .17, p = .000. After controlling for recent life experiences, racial malleability, appreciation of human differences, racial regard, lack of family acceptance, and identity questioning did not account for a significant amount of the variance in perceived stress (R2 change = .03, F change = 1.22, p = .303). Therefore, identity experiences did not directly effect the variance in perceived stress in the second model. However, the addition of the interaction terms did account for a significant portion of the variance in perceived stress (R2 change = .06, F change = 2.788, p = .030). (See Table 6). In the third model, racial malleability did not significantly predict perceived stress, b = .06, t = .287, p = .775. In this third model, lack of family acceptance did have a significant main effect on perceived stress, b = .46, t = 2.310, p = .021. Identity questioning also had a significant main effect on perceived stress, b = -.60, t = – 2.370, p = .018. Further, identity questioning appeared to be a significant moderator between racial malleability and perceived stress b = .03, t = 2.124, p = .034. The third model supports the first hypothesis such that the relationship between racial malleability and perceived stress is moderated by experiences of identity questioning. The role of lack of family acceptance and identity questioning as directly impacting the variance in perceived stress must be explored further.