The distribution of literacy

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We begin with a simple description of the distribution of Document literacy based on the IALSS 2003. In Chart 1, we present a kernel density plot for Document literacy for our sample. The density is slightly negatively skewed with a mean of 280, a median of 287 and a standard deviation of 50. The fact that the distribution is negatively skewed when ability is typically thought of as distributed according to a positively skewed distribution such as the log normal may be a reflection of a lack of sufficient questions to differentiate among highly literate respondents. The minimum Document score in the sample is 84, representing extremely low proficiency at the Document test tasks, while the highest is 436.¹ Inequality in the distribution is reflected in an associated Gini coefficient value of 0.107 and a value for the log of the ratio of the 90th percentile to the 10^th percentile of 0.513. To put this in perspective, the Gini for pre-tax and transfer family income from the 2001 Canadian Census is 0.438 and the log of the 90 : 10 ratio is 3.48 (Frenette et al, 2006). Thus, the distribution of literacy is much less unequal than that of market income. This is not surprising since literacy skills are only one of the components playing a role in earnings generation.

The other comparison we can make with this data is with the extent of inequality in the 1994 literacy distribution. The Gini for that distribution is 0.151 and the log of the 90 : 10 ratio is 0.76. Thus, the Document literacy distribution became substantially less unequal in the nine years between the surveys. In part, this occurred because of an improvement at the low end of the literacy distribution. The 10^th percentile of the 1994 literacy distribution was 160, compared to a value of 197 in 2003. The news is not unambiguously good, however, since the 95^th percentile of the distribution actually fell from a value of 359 in 1994 to 351 in 2003. Thus, the decline in literacy inequality reflects both substantial improvements at the low end of the distribution and some deterioration at the top end. We will return to discussing these differences below, but for the moment we will focus on characterizing the 2003 distribution.

In Table 1, we present a depiction of the joint distribution of literacy and family income, showing the percentage of observations in each cell in a grid defined by the 5 quintiles of the Document literacy distribution and the five quintiles of the household (pre-tax and transfer) income distribution. The correlation between household income and literacy equals 0.31, indicating that the two variables are positively correlated, but not strongly so. This is seen in Table 1 from the fact that cells on the main diagonal are not overly large relative to the other entries. Perhaps the most interesting cell is the one corresponding to individuals in the bottom quintile of both the literacy and income distributions – a cell which contains just over 8% of the population. These individuals could be viewed as suffering from a double poverty – both in terms of literacy and income. Everyone in this cell is what Crompton (1996) describes as "marginally literate". In terms of document literacy, Crompton describes the marginally literate as unlikely to be able to complete tasks such as using a bus schedule to chart out what time the last bus leaves a particular stop on Saturday night (Crompton (1996)). Thus, they are severely disadvantaged in terms of their ability to function in society. Perhaps not surprisingly, these doubly poor individuals have extremely low education levels, with 80% of them being high school drop outs. The same pattern can be seen in their family background, with over 90% of them having fathers who were also drop outs. In contrast, the 7.4% of individuals who are in both the top quintile for literacy and the top quintile for income are very highly educated and come from high education backgrounds. Fully 30% of this group are university graduates and an additional 21% have post-graduate education. One-quarter of their fathers also completed university, which is much higher than for the population as a whole, in which just over 9% of fathers had a university degree.

To provide a further perspective on potential difficulties associated with low literacy, in Table 2 we present measures of societal participation and individual well-being for low and high literacy individuals. We define a low literacy group as a set of people who were recorded as level 1 when we use all five plausible Document test scores. In terms of literacy skills, this is an extremely disadvantaged group of individuals who are unlikely to be able to do tasks such as process patterns in more than one chart (Crompton ,1996). Our high literacy group consists of individuals scoring in either of the top two literacy levels. The low literacy group claims to have been more likely to have voted in a municipal election than the high literacy group, though this is the only measure of participation in which they lead. Indeed, the high literacy group was more likely to have voted in a federal or provincial election, though the difference is not large. Differences are large, however, in participation in political organizations and in community and school groups, with the high literacy group being at least twice as likely to participate in either of these groups. We are not claiming that the link between literacy and participation is causal (i.e., that increasing a group's literacy would result in an increase in their participation) but the strong correlation does emphasize a point made by Sen (1999) that literacy bears an important relationship to full participation in society. This is evident as well in the fact that nearly 11% of low literacy individuals stated that having to make basic calculations such as calculating a tip makes them anxious. The strongest association, though, is in terms of self-assessed health. Approximately 76% of high literacy individuals rated themselves as being in either excellent or very good health compared to only 30% among the low literacy group. To make sure this is not just a reflection of poor health causing individuals to have trouble completing the tests, these percentages are calculated after dropping individuals who were listed as not completing the basic questionnaire for reasons related to health or disability. In part, the health-literacy differential reflects the fact that the low literacy group is much older, revealing generational differences in literacy to which we return below. However, even if we drop individuals over age 65 and estimate a linear probability regression of a dummy variable equalling one if an individual rated herself as in very good or excellent health on age, years of schooling, family income and a dummy variable corresponding to people in the low literacy category, the latter variable has a coefficient of -0.16 and is highly statistically significant (with an associated standard error of 0.041). Thus, low literacy individuals are approximately 16% less likely to claim they are in good health than everyone else, even after controlling for age, years of schooling and family income. Again, whether this is causal is not clear but it does raise serious concerns about the functioning of low literacy individuals in Canadian society.

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Note

1. We truncated the density plot at 96 to focus attention on the main part of the distribution. This eliminates only five observations but because of the smoothing inherent in the kernel density plots, their inclusion would result in a plot that is visually dominated by a thin, long left tail. The plot uses Strata 7's default values for the kernel and smoothing parameters.