Family functioning and family life was compared between British Indian families (n = 26), British Pakistani families (n = 31) and non-immigrant White families (n = 33).
The statistical software package PASW version 18, (PASW, 2009)64, was used in the analyses of data. The analysis aimed to determine whether groups differed on an underlying construct (e.g. whether there was a difference between British Indian, British Pakistani and non-immigrant White families in child psychological adjustment). When outcome variables were multivariate, multivariate analyses of variance (MANOVAs) were conducted. This statistical technique allows for the simultaneous entry of more than one dependant variable into a particular analysis. The Wilks’ λ statistic was used because it is considered to be an accurate and robust test of significance (Field, 2009). Where MANOVAs could not be applied, (i.e. because outcome variables were univariate or they did not hang together in a construct), univariate analyses of variance (ANOVAs) were conducted. T-tests were used when a two-way group comparison was needed. Categorical data were analysed using Chi- square tests to conduct comparisons between groups.
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When the MANOVA was statistically significant, one way analyses of variance (ANOVAs) were carried out for each variable included in the MANOVA, in order to fully explore the dataset. The MANOVA-ANOVA technique has been justified by researchers as a means of controlling for the inflated Type I error rate (the probability of falsely rejecting the null hypothesis).
Before data analysis was carried out, the data were explored to examine whether the following assumptions were met:
1) Normal distribution: In order to check this assumption, histograms were examined and z-scores were calculated for kurtosis and skew for each variable in each group. Values greater than 1.96 were considered problematic (Field, 2009).
2) Homogeneity of variance: the variance in each group should be roughly equal for each dependant variable. In order to check this assumption the Levene’s Test was utilised.
The violation of the assumption of multivariate normality has been reported to have mild effects (Finch, 2005). Further, the Wilks’ λ statistic is considered to be robust to violations of normality (Field, 2009). Thus, MANOVAs were conducted where data violated the distribution assumption, but upheld the homogeneity assumption. Where univariate data was non-parametric (i.e. it violated both assumptions), the Kruskal-Wallis test was used to examine group differences. This procedure allows for the testing of differences between several independent groups using non-parametric data. When a significant group difference was found, follow up Mann-Whitney tests were applied using a Bonferroni correction, to control for the inflated Type I error rate (Field, 2009). The Mann-Whitney test allows for non-parametric data comparison by examining the differences in ranked positions of scores in different groups (Field, 2009)
When MANOVAs were significant, post-hoc tests were performed to determine where differences lay between groups. Post-hoc tests were applied rather than contrast analysis in accordance with the differing research hypotheses relating to different aspects of family functioning. The Gabriel or the Games-Howell post-hoc tests were used. Both of these tests are robust and can and used when group sizes are unequal as was the case in the present study (Field, 2009). The Gabriel post-hoc test was used where the data was parametric, while the
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Games-Howell post hoc test was used when data did not uphold the normal distribution assumption (Field, 2009). Post-hoc tests were carried out to address specific questions as follows: (1) British Indian mothers versus non-immigrant White mothers (BI vs. NIW), (2) British Pakistani mothers versus non-immigrant White mothers (BP vs. NIW), and (3) British Indian versus British Pakistani mothers (BI vs. BP).
British Indian, British Pakistani and non-immigrant White families were recruited with the intention of minimising differences between groups in demographic variables such as the educational levels of parents. Indeed, aside from small differences in three areas between groups (i.e. Father’s Age, Mother’s Working Status and Number of Other Adults in the Household), all key contextual factors (including Child’s Sex, Father’s Educational Level, Mother’s Educational Level, Number of Siblings and Current Marital Status) showed close matching between groups. For this reason, a decision was taken not to enter any contextual factors into the analyses as covariates when assessing group differences (see Methodology, Sample Characteristics).
In the following quantitative analyses, the inter-correlations between variables within each construct are reported as recommended by Huberty and Morris (1989) as well as the α- coefficients of the overall constructs, in order to demonstrate the internal consistency of the constructs. Significance values have been reported at the alpha values of .05 and .01.
There were a number of variables measuring religion in family life. In order to condense the religion variables into a more robust measure, a single Religion variable was created using Principle Components Analysis (PCA). This statistical method identifies groups or clusters of variables. In the case of religion, quantitative variables from the interview with the mother (Religiosity, Religious Beliefs, Religious Practices and Child’s Knowledge of Religion), were combined to form a Religion variable. Although it is unusual to conduct PCA in small samples, Field (2009) recommends that there are over 10 times as many subjects as variables for each index. This condition was met for the Religion construct used in the analysis.
Controlling for Type I and Type II Error
The rejection of a true null hypothesis is known as a Type I error, while a failure to reject a false null hypothesis is known as a Type II error. Type I error leads a researcher to conclude a
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finding exists when it actually does not, while Type II error leads a researcher to conclude no finding exists when it actually does, and thus represents a false negative (Field, 2009). In the present study every attempt was made to minimise the chances of error. Steps taken to minimise Type I error include:
1) Inter-correlations between variables within each group of measures were first examined. Where correlations were high, an aggregate (composite) score was created (by conducting PCA). Where correlations were low to medium, each variable was used as an independent predictor within a measurement construct and multivariate analysis was conducted (followed by ANOVA and post-hoc tests). ANOVA were conducted as the only form of analysis when the variables were univariate and did not hang together in a construct.
2) The Type I error rate is linked to the statistical power of a test and a trade-off exists between Type I and Type II error. Conservative tests have a lower probability of Type I error but are likely to lack statistical power and have a higher probability of Type II error rate (Field, 2009). Therefore, choosing the particular type of multiple comparison test to use is important. In the present study, great care was taken in the choice of multiple comparison tests, such that they would control the Type I error rate without a major loss in power. Importantly, MANOVA were followed up with ANOVAs (and post-hoc tests) only when the effect was significant. No further analysis was conducted on the data when it was not significant.
In this way the data was effectively analysed (while always keeping the risk of Type I error in mind) as the minimal number of effects were examined. Thus, there was a greater likelihood that the significant values found represented true effects as opposed to ‘accidental significants.’
The risk of Type II error (i.e. the chance of missing an effect and thus stating that there is no significant effect, when in reality there is) is increased with a small sample size. In the present study, the sample size of 90 mothers (distributed among the three ethnic groups) was fairly small, and this may mean that some effects could be found to be non-significant because of lack of power. Therefore, care was taken in the types of analyses performed on the data such that under-powered analyses were avoided. Also, caution was also taken in the interpretation of results.
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