Social class / Appendix

Appendix

Below are the results of two factor analyses, on 1984 and 2012 data, on the attitudinal items used in the analysis in this chapter. Factor analysis is a statistical technique which aims to identify whether there are one or more apparent sources of commonality to the answers given by respondents to a set of questions. For further details on this kind of analysis see the Technical details chapter.

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  1. The reduction in the strength of the association between socio-economic group and party identification is clear from the Cramer's V score in each year. Cramer's V is a chi-square based measure of association. While a chi-square coefficient depends both on the strength of the relationship and on sample size, Cramer's V eliminates the effect of sample size by dividing chi-square by N, the sample size, (together with a further adjustment) and taking the square root. V may be interpreted as the association between two variables expressed as a percentage of their maximum possible variation. In 1984, the Cramer's V was 0.180 (Chi2 = 179.7 (20 df), p < 0.0001). In 2012, it was 0.125 (Chi2 = 181.4 (20 df), p < 0.0001).
  2. The seven classes identified by Savage et al. (2013) are the elite; the established middle class; new affluent workers; the technical middle class; the traditional working class; emergent service workers and the precariat.
  3. Our analysis of the responses to the items on the first and the second priority for government spending (cross-tabulating the two variables and inspecting the adjusted standardised residuals) indicated that the responses "health" and "education" were highly significantly associated, while the responses "defence" and "police and prisons" were also significantly associated. None of the other responses showed a distinctive pattern of association. In our analysis we have therefore constructed three categories: health and education; defence and police; other.
  4. Factor analysis (see Technical details for more information) confirms that the questions we selected do indeed belong (in both periods) to two distinct ideological dimensions, the structure remaining largely unchanged over time. See the appendix to this chapter for the results of the factor analysis. 
  5. Chi-square is very sensitive to the sample size, and sample sizes vary both between surveys and within surveys (since some items were asked only of randomly chosen subsets of respondents). We cannot therefore use chi-square to tell us about the strength of association, only about its statistical significance. As a measure of strength of association we use Cramer's V (explained in note 1). 
  6. We also explored alternative 'objective' measures of class and reached the same conclusion.
  7. Since the factor analyses indicated that attitudes towards tax and spending and towards premarital sex had the strongest loadings on the two ideological dimensions (both in 1984 and in 2012 - see the appendix to this chapter), we focus on these two issues in our more detailed cross-tabular and regression analysis.
  8. The 1984 and 2012 datasets were pooled and a loglinear model fitted to the data. The model was one which assumed that there were relationships between social cleavage and attitude, between social cleavage and year, and between year and attitude, but that there was no three-way inter-relationship. In effect this tested whether the relationship between cleavage and attitude was the same in both years (allowing for changes in the marginal frequencies over time). It is analogous to the 'constant social fluidity model' in social mobility research. If the model does not give a good fit to the data, as judged by the deviance, then the null hypothesis of a constant relationship has to be rejected.
  9. Deviance 14.0 with 8 df, p > 0.05.
  10. Null hypothesis that the relationship is unchanged is rejected: Deviance = 9.9 with 2 df, p < 0.01.
  11. Deviance 76.9 with 16 df, p > 0.001.
  12. The measure of education level is different in the two years, so we therefore hesitate to interpret the changing pattern.
  13. The only measure available in 1984 was age when education completed, namely 19 and over (plus "still at college or university", equated to degree), 18 (equated with A levels), 17 (equated with GCSE), 16 (equated with CSE) and 15 or less (equated with CSE). These are very crude equivalences but do capture the hierarchical nature of education.
  14. Deviance 76.9 with 16 df, p > 0.001.
  15. We used ordered logit modelling, which is the appropriate technique when we have dependent variables such as attitudes towards premarital sex which are ordered (responses ranging from strongly agree to strongly disagree).
  16. Variance explained, or R squared, is a statistical measure of "the proportion of the total variability of the outcome that is accounted for by the model". It is used in OLS regression, where continuous, normally-distributed variables are assumed. The OLS interpretation has no formal equivalent in logistic regression (which does not assume that variables are either continuous or normally distributed). However, if some heroic assumptions are made, a statistic that looks like R-squared, and which has the same range from - to 1, can be developed. (They are essentially counterfactuals - what might the variance explained have been if this were a continuous normally distributed variable?) Lots of different pseudo R-squareds have been developed, and none has become standard. We use the Nagelkerke version. These measures should not be used to compare different datasets but only really to compare goodness of fit of different models within the same dataset. 
  17. See note 8.
  18. We also found some evidence, from the measures of variance explained (the pseudo R2 statistic) that the overall explanatory power of the predictors has declined somewhat between 1984 and 2012. We have to be a little cautious here, since the multivariate analyses reported in Table 7.16 only cover two of our nine attitude measures. To check our results we constructed composite measures of the two main ideological dimensions, using all the available attitude items. This composite analysis confirmed our individual analysis of government spending on the welfare state (R2 for the government spending dimension falling from 0.061 to 0.022) but it did not confirm a decline in explanatory power for the liberal dimension (R2 actually increasing when a composite measure was constructed from 0.264 to 0.301).
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    1. The reduction in the strength of the association between socio-economic group and party identification is clear from the Cramer's V score in each year. Cramer's V is a chi-square based measure of association. While a chi-square coefficient depends both on the strength of the relationship and on sample size, Cramer's V eliminates the effect of sample size by dividing chi-square by N, the sample size, (together with a further adjustment) and taking the square root. V may be interpreted as the association between two variables expressed as a percentage of their maximum possible variation. In 1984, the Cramer's V was 0.180 (Chi2 = 179.7 (20 df), p < 0.0001). In 2012, it was 0.125 (Chi2 = 181.4 (20 df), p < 0.0001).
    2. The seven classes identified by Savage et al. (2013) are the elite; the established middle class; new affluent workers; the technical middle class; the traditional working class; emergent service workers and the precariat.
    3. Our analysis of the responses to the items on the first and the second priority for government spending (cross-tabulating the two variables and inspecting the adjusted standardised residuals) indicated that the responses "health" and "education" were highly significantly associated, while the responses "defence" and "police and prisons" were also significantly associated. None of the other responses showed a distinctive pattern of association. In our analysis we have therefore constructed three categories: health and education; defence and police; other.
    4. Factor analysis (see Technical details for more information) confirms that the questions we selected do indeed belong (in both periods) to two distinct ideological dimensions, the structure remaining largely unchanged over time. See the appendix to this chapter for the results of the factor analysis. 
    5. Chi-square is very sensitive to the sample size, and sample sizes vary both between surveys and within surveys (since some items were asked only of randomly chosen subsets of respondents). We cannot therefore use chi-square to tell us about the strength of association, only about its statistical significance. As a measure of strength of association we use Cramer's V (explained in note 1). 
    6. We also explored alternative 'objective' measures of class and reached the same conclusion.
    7. Since the factor analyses indicated that attitudes towards tax and spending and towards premarital sex had the strongest loadings on the two ideological dimensions (both in 1984 and in 2012 - see the appendix to this chapter), we focus on these two issues in our more detailed cross-tabular and regression analysis.
    8. The 1984 and 2012 datasets were pooled and a loglinear model fitted to the data. The model was one which assumed that there were relationships between social cleavage and attitude, between social cleavage and year, and between year and attitude, but that there was no three-way inter-relationship. In effect this tested whether the relationship between cleavage and attitude was the same in both years (allowing for changes in the marginal frequencies over time). It is analogous to the 'constant social fluidity model' in social mobility research. If the model does not give a good fit to the data, as judged by the deviance, then the null hypothesis of a constant relationship has to be rejected.
    9. Deviance 14.0 with 8 df, p > 0.05.
    10. Null hypothesis that the relationship is unchanged is rejected: Deviance = 9.9 with 2 df, p < 0.01.
    11. Deviance 76.9 with 16 df, p > 0.001.
    12. The measure of education level is different in the two years, so we therefore hesitate to interpret the changing pattern.
    13. The only measure available in 1984 was age when education completed, namely 19 and over (plus "still at college or university", equated to degree), 18 (equated with A levels), 17 (equated with GCSE), 16 (equated with CSE) and 15 or less (equated with CSE). These are very crude equivalences but do capture the hierarchical nature of education.
    14. Deviance 76.9 with 16 df, p > 0.001.
    15. We used ordered logit modelling, which is the appropriate technique when we have dependent variables such as attitudes towards premarital sex which are ordered (responses ranging from strongly agree to strongly disagree).
    16. Variance explained, or R squared, is a statistical measure of "the proportion of the total variability of the outcome that is accounted for by the model". It is used in OLS regression, where continuous, normally-distributed variables are assumed. The OLS interpretation has no formal equivalent in logistic regression (which does not assume that variables are either continuous or normally distributed). However, if some heroic assumptions are made, a statistic that looks like R-squared, and which has the same range from - to 1, can be developed. (They are essentially counterfactuals - what might the variance explained have been if this were a continuous normally distributed variable?) Lots of different pseudo R-squareds have been developed, and none has become standard. We use the Nagelkerke version. These measures should not be used to compare different datasets but only really to compare goodness of fit of different models within the same dataset. 
    17. See note 8.
    18. We also found some evidence, from the measures of variance explained (the pseudo R2 statistic) that the overall explanatory power of the predictors has declined somewhat between 1984 and 2012. We have to be a little cautious here, since the multivariate analyses reported in Table 7.16 only cover two of our nine attitude measures. To check our results we constructed composite measures of the two main ideological dimensions, using all the available attitude items. This composite analysis confirmed our individual analysis of government spending on the welfare state (R2 for the government spending dimension falling from 0.061 to 0.022) but it did not confirm a decline in explanatory power for the liberal dimension (R2 actually increasing when a composite measure was constructed from 0.264 to 0.301).
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