School leavers’ progression to bachelors-level study

5. Results

Logistic regression was used to analyse the relationship between a student’s likelihood of studying at bachelors level (or higher¹⁰) given the decile of their final school, their ethnic group and how well they did at school compared to other students. In addition, whether or not a student gained UE, and whether or not a student progressed directly to tertiary study after leaving school, were also included. Whether a student had achieved a NCEA level 3 qualification or not was found not to be important in understanding the results.

Different models were formulated for each of the ethnic groups. The variables and their interactions in the logistic regression models were found to explain a significant amount of variance in the data for each of the ethnic group models. Table 8 shows the goodness of fit statistics for each of the four ethnic group models, and the model used to produce the results for all ethnic groups combined. In all five models, the R² value is above 0.52, indicating considerable power – more than in most models in education¹¹. The C statistic also indicates strong predictive power. Of the students who actually progressed to bachelors-level study, the model correctly predicts bachelors study as the outcome for 88% of them.

Tests were conducted for the presence of multicolinearity between the independent variables in the models¹². No evidence of multicolinearity was found.

In all models, ethnic group, achievement score, school decile, time off and UE were found to be significant. That is, one needs to consider all five variables together to understand the relationship between the propensity to study at bachelors level and these other variables.

As noted previously, the time-off variable was included in the model as a binary variable; students either went directly to some type of tertiary study, or they did not. This latter group includes students who did study at tertiary level after a break, and those who, in the time frame chosen to delineate the study population, had not (yet) started tertiary study. Because the latter group contains these two quite different outcomes, they are not considered further in this report.

Additionally, the study focuses on those students who gained UE, since this is the usual pre-requisite for study at this level.

The results of the logistic regressions are converted to probabilities (the expected likelihood of studying at bachelors level) using the model equations derived from the regressions.

Sample sizes for the four ethnic group regression models are given in appendix A.

5.1 Overall results

The majority of students in the study population (82 per cent) attended formal tertiary study with a tertiary provider, with 2 per cent enrolled in industry training, and less than 0.5 per cent in various targeted training courses. A total of 16 per cent were not involved in tertiary education activities of any kind.

In the study population, on average (combining students who progressed directly to tertiary study, or took some time off) 71 per cent of students were studying at bachelors level, 5 per cent at diploma level, 4 per cent at certificate level 4, and a further 4 per cent were studying at certificate levels 1 to 3. As mentioned, a total of 16 per cent of the study population were not enrolled in any form of tertiary study. This last group of students were overseas (possibly to study at bachelors level elsewhere), found work, or were involved in some other activity. There is a chance that some of them will eventually go on to some type of tertiary study in New Zealand in the coming years.

For students who progressed directly to formal provider-based tertiary study after leaving school, 86 per cent were studying at bachelors level. For those in this group with UE, and who progressed directly to tertiary study, the figure is 90 per cent.

In table 7, it can be seen that the proportion of students studying at bachelors level varies by ethnic group category. It can be seen that overall, lower proportions of students who identify solely with the Māori or Pasifika ethnic groups study at bachelors level. Seventy-two per cent of students who were ever-Māori went on to study at bachelors-level after leaving school, compared with 40 per cent who were sole-Māori. Asian students show the highest proportions studying at bachelors level.

5.2 Achievement score and school decile

Figure 1 shows the expected probability of studying at bachelors level by achievement score and school decile for students with UE who progressed directly to tertiary study. The results are averaged over all ethnic groups. Results are only shown for achievement scores in the range 20 to 90 since very few students with these characteristics had achievement scores outside this range.

It can be seen that achievement score has a large effect on the likelihood of studying at bachelors level once UE status and the timing of the progression to tertiary study are controlled. Students with higher achievement scores are far more likely to go on to study a bachelors degree, and this occurs across all school decile categories.

At the lower end of the achievement score range (below 30), the likelihood of studying at bachelors-level for most students is between 70 and 80 per cent.

At achievement scores above 30, students from higher-decile schools have a statistically significantly higher likelihood of studying at bachelors level than other students. Students from lower-decile schools have a statistically significantly lower likelihood of studying at bachelors level than other students at achievement scores of 35 and higher. Students from mid-decile schools are significantly different from both other groups, with likelihoods falling between these other two groups. While at the highest achievement scores students from lower-decile schools have quite high likelihoods of studying at bachelors level, at around 95 per cent, this is still significantly lower than other students.

Higher-decile school students with an achievement score of 55 have a 95 per cent likelihood of studying at bachelors level. Lower-decile school students, on the other hand, have an achievement score of 85 for the same likelihood. For students from mid-decile schools, the equivalent achievement score is 65.

Figure 1: Expected probability (and 90 per cent confidence limits) of studying at bachelors level by school decile and achievement score

For students who gained University Entrance, and progressed directly to tertiary study after leaving school.
Where confidence limits do not overlap, there is at least a 95 per cent certainty that the means in question are statistically different.
Note the vertical axis starts at 0.5.

5.3 Achievement score, school decile and ethnic group category

The graphs in figure 2 (page 23) show the expected probability of studying at bachelors-level by achievement score and school decile, controlling for ethnic group category, for students who gained UE and progressed directly to tertiary study after leaving school. Each row of graphs (never-, ever- and sole-European for example) is the output from a single model run. Ninety per cent confidence limits are shown¹³. Confidence limits are wider when there are fewer students in the study population for the given combination of variables.

It is useful to comment briefly on the graphs as a whole. For any one row of graphs, each ethnic group category represents a distinct group of students, with no overlap between them. That is, when considering any one ethnic group (each row in the figure), each student is in one and only one of the three categories for that ethnic group. Each row considers the entire study population separately for each ethnic group. This means that a student who is in the sole-European category, will also be in the never-Asian, never-Māori and never-Pasifika categories in the other rows of the figure (see table 1). Given the size of the sole-European group (see table 2), it is not surprising that the graphs for these four cases are similar.

A similar situation occurs with the never-European category. This group will contain all those students who are sole-Māori, sole-Pasifika and sole-Asian, and any other combination of these groups that exclude the European ethnic group, and as a consequence, the results will be influenced by these other ethnic group categories. A similar situation occurs for the other never-ethnic results. These characteristics need to be kept in mind when interpreting the graphs.

The general pattern seen in the results is one where the likelihood of studying at bachelors level increases with increasing achievement score, although the rate of increase declines after an achievement score of about 50. This is the pattern seen in figure 1. This generally holds true across school decile categories, and generally across the ethnic group categories.

The most obvious aspect of the results is that, in general, there is consistency in the pattern of responses both within and between ethnic groups. However, there are some striking exceptions. The consistency in part results from the fact that the sole-European, never-Asian, never-Māori and never-Pasifika categories contain much the same group of students. In spite of this, in each row of results, and for the sole-ethnic column, the results for some groups of students are very similar.

The similar results generally occur for students from the mid- to higher-decile schools with higher achievement scores. For these students, when achievement scores are above 50, the likelihood of studying at bachelors level is, in the main, over 90 per cent. For Asian students, the likelihood is somewhat higher, while for sole-Māori students from mid-decile schools it is slightly lower, but still above 85 per cent.

Differences between ethnic groups are seen between European and Asian students on the one hand, and Māori and Pasifika on the other. European and Asian students all basically show the pattern just described, regardless of the decile of the school the student attended. For sole-Māori and sole-Pasifika students however, students from lower-decile schools with mid to high achievement scores show significantly lower likelihoods of studying at bachelors level compared to other students. This occurs in the middle range of achievement scores in the case of Māori, and for achievement scores above 35 in the case of Pasifika. For ever-Māori there is a similar situation, with students from lower-decile schools with achievement scores over 40 having a significantly lower likelihood of studying at bachelors level than similar students from other schools. Ever-Pasifika students do not show differences between students from schools of different decile ratings. Ever-Asian students from low-decile schools also show a difference in likelihood of studying at bachelors level for achievement scores in the 50 to 90 range, but the differences are small when compared to the differences seen for Māori and Pasifika.

Within ethnic group differences can also be seen. The ever- and sole-ethnic categories for each ethnic group show little difference for European and Asian students, but for Māori and Pasifika students there are some differences. For ever-Māori, lower-decile school students have a lower likelihood of studying at bachelors level than other students across nearly the whole range of achievement scores. For sole-Māori on the other hand, the difference between the lower-decile school students and others is greater than that seen for ever-Māori, but these are only statistically significantly different in the middle range of achievement scores. For Pasifika, the sole-Pasifika group are quite substantially different from the ever-Pasifika group.

For students with the lowest achievement scores there are also differences between ethnic groups, with Asian students showing the greatest difference. Asian and Pasifika students with lower achievement scores have higher likelihoods of studying at bachelors level.

In the sole- and ever-European, sole-Asian, and ever-Pasifika groups, school decile does not have a statistically significant association with the propensity to study at bachelors level.

It is worthwhile commenting on the results of the never-European group. As mentioned previously, this category contains all those combinations of ethnic identifications excluding Europeans. Specifically, it contains the Māori and Pasifika ethnic groups and the Asian group in nearly equal proportions (refer to table 2). While the individual ever- and sole-ethnic group categories for Māori and Pasifika show wide confidence limits because of their relatively smaller group sizes, the never-European group is substantial (at nearly 14,000 students), and has correspondingly narrower confidence limits. The never-European group shows significantly lower likelihoods of studying at bachelors level for students from lower-decile schools, across nearly the entire achievement score range. This reinforces the finding that the lower likelihood of studying at bachelors level for these lower-decile school students is a real effect. It is likely that in a few years time, when more data is available, the findings for these smaller ethnic group categories will become more certain.

Figure 3 shows the results for the sole-ethnic groups for the higher- and lower-school decile groups. This figure more clearly shows between-ethnic group differences, and the differences between the high and low school decile groups.

Figure 3: Expected probability (and 90 per cent confidence limits) of studying at bachelors level by achievement score, ethnic group category for low and high decile school students [click image to enlarge]

For students who gained University Entrance, and progressed directly to tertiary study after leaving school.
Where confidence limits do not overlap, there is at least a 95 per cent certainty that the means in question are statistically different.
Note the vertical axis starts at 0.5.

For students from higher-decile schools, sole-Asian students have a very high likelihood of studying at bachelors level across the entire achievement score range. For the other ethnic groups, there is no statistical difference between the students from higher-decile schools. At the highest achievement scores, all students have essentially the same very high likelihood of progressing to bachelors-level study.

For students from lower-decile schools however, the situation is somewhat different. As described above, the sole-Asian and sole-European students exhibit the same pattern as their higher-decile school counterparts – school decile is not a factor in determining the propensity to study at bachelors level. At the highest achievement scores, Asian and European lower-decile school students have much the same likelihood of studying at bachelors level, but for Māori and Pasifika students, the likelihood is significantly lower, and this occurs from achievement scores of around 50 and higher.

In summary, the higher the achievement score, the more likely a student is to study at bachelors level. For Asian and most European students, school decile has no bearing on this. However, for Māori students generally, and sole-Pasifika students, with higher achievement scores from lower-decile schools, there is a significantly lower likelihood of progressing to study at bachelors level.

Footnotes