GROWING UP IN SCOTLAND: THE CIRCUMSTANCES AND EXPERIENCES OF 3 YEAR OLD CHILDREN LIVING IN SCOTLAND IN 2007/08 AND 2013

Appendix B: Notes on interpreting the data

Interpreting the cohort comparison tables

Many of the results in the report are presented as nested cross-tabulations. These are cross-tabulations of two variables (e.g. whether child has a longstanding illness by equivalised household income) nested by a third variable: cohort. This approach allows that all of the information of interest is produced as a single table and also permits a statistical test to explore whether the relationship between the two variables has changed between the cohorts.

Statistical significance is reported as a p-value of either <.05, <.01, <.001 or NS. These indicate statistical significance at the 95%, 99% and 99.9% levels or non-significance. For each table, three p-values are given, as shown in the example below.

Table 4.8 Child's longstanding illnesses or disabilities, by equivalised household income (quintiles) and cohort

Tested on 'yes': differences by income - p < .01; differences by cohort - p < .01; cohort*income - NS.

In this example, the first p-value indicates whether differences by income are statistically significant. This test is based on combined values for both cohorts (not shown in the table) and not on the individual cohort figures. As such, it does not tell us whether differences by income are statistically significant within each cohort. Furthermore, the test is run across all categories and does not test for differences between each individual category and the next, e.g. between the 4th quintile and highest quintile. Separate p values for each cohort are not reported. These would not provide an insight into any statistically significant differences between the cohorts. The third p-value - described below - is used for this purpose.

The second p-value indicates whether the outcome being measured differs by cohort in a way that is statistically significant. In the example, this indicates whether there was any statistically significant difference in longstanding illness/disability across BC1 and BC2. This test is based on overall values of the row variable for the cohort (not shown in the table). It does not compare the individual values on the row variable for each income subgroup by cohort. For example, the p-value does not indicate that the difference between the 17% of children in the lowest income quintile of BC1 with a longstanding illness is statistically significantly different from the 19% of children in the same group in BC2.

The third p-value indicates whether the relationship between the two variables is statistically significantly different between the two cohorts. In this example, using interaction analyses, the test assesses the association between household income and longstanding illness in BC1 and then BC2 and compares the association found in each cohort. A p-value of <.05 indicates the association is statistically significantly different. Where this p-value is <.05, the figures in the table can be used to interpret the change. For example, it may indicate a strengthening of the association, a weakening of the association or some other change - such as moving from a positive relationship (as income increases likelihood of having a longstanding illness also increase) to a negative relationship (as income increases likelihood of having a longstanding illness decreases). In the example above, the interaction p-value is NS. This indicates that there is no statistically significant change in the relationship between income and longstanding illness between the two cohorts. Looking at the results, it can be seen that in both cohorts lower income is associated with a higher likelihood of longstanding illness. Whilst prevalence has changed in some individual income sub-groups (e.g. increasing from 14% to 18% in the 2nd income quintile) these changes have not been sufficient to alter the overall relationship between the two variables.

Multivariable regression analysis

Multivariable regression analysis was used where further investigation was required of whether a change had occurred between BC1 and BC2.

This type of analysis allows the examination of the relationships between an outcome variable (e.g. frequent parent-child reading or language ability score) and multiple explanatory variables (e.g. parental education, parental employment status, child gender, cohort) whilst controlling for the inter-relationships between each of the explanatory variables. This means it is possible to identify an independent relationship between any single explanatory variable and the outcome variable.

'Interactions' were included in the multivariable models to consider whether the relationship between, for example household income and longstanding illness was different in each cohort. In this example, where longstanding illness is the outcome variable, the interaction would be fitted between household income and cohort. Where an interaction is statistically significant this indicates that the relationship between the explanatory variable (e.g. household income) and the outcome variable (e.g. longstanding illness) is different in each cohort.

Binary logistic regression analysis was used. The results are presented (appendix C) as odds ratios, all of which have a significance value attached. Logistic regression compares the odds of a reference category (shown in the tables) with that of the other categories. An odds ratio of greater than one indicates that the group in question is more likely to demonstrate this characteristic than is the chosen reference category, an odds ratio of less than one means they are less likely. For example, Table C.2 contains the results of the regression model seeking to identify factors related to the child having had accidents. In the 'OR' column, the category of BC2 returns an odds ratio of 2.25. This indicates that the odds of children in BC2 having had an accident are 2.25 times greater than they are for children in BC1 (the reference category).

Note that an odds ratio cannot be interpreted in the same way as a co-efficient. An odds ratio of 2 does not mean 'two times as likely' but instead means 'the odds are two times higher'. To understand an odds ratio we first need to describe the meaning of odds. The definition of odds is similar but significantly different to that of probability. This is best explained in the form of an example. If 200 individuals out of a population of 1000 experienced persistent poverty, the probability (p) of experiencing persistent poverty is 200/1000, thus p=0.2. The probability of not experiencing persistent poverty is therefore 1-p = 0.8. The odds of experiencing persistent poverty are calculated as the quotient of these two mutually exclusive events. So, the odds in favour of experiencing persistent poverty to not experiencing persistent poverty, is therefore 0.2/0.8=0.25. Suppose that 150 out of 300 people living in social rented housing experience persistent poverty compared to 50 out of 150 who live in owner occupied housing. The odds of a person living in social rented housing of experiencing persistent poverty are 0.5/0.5=1.0. The odds of a person living in owner occupied housing of experiencing persistent poverty is 0.33/0.66=0.5. The odds ratio of experiencing persistent poverty is the ratio of these odds, 1.0/0.5=2.0. Thus the odds of experiencing persistent poverty are twice as high among people who live in social rented housing (compared to people who live in owner occupied housing - the 'reference category'). Note that this is not the same as being 'twice as likely' to experience the outcome.

Categories which have a p value of greater than 0.05 are not considered to be statistically significant.