Should I do a degree? - teachers page

Secondary activity

Should I do a degree?

Curriculum links

NCEA Mathematics Achievement Standard AS90645

• select and analyse continuous bi-variate data.

Mathematics: Statistics – level 8

• investigate relationships between two continuous variables using graphs and model-fitting methods including regression
• use graphs and correlation coefficients to assess the linearity of relationships and discuss the appropriateness of any regression line or correlation coefficient.

Background

The activity Should I do a degree? is a practice activity for AS90645. It asks students to investigate whether getting a degree helps to improve earning power. There is a lot of potential for discussion around the hidden variables which could affect the results, and to think about how valid these findings are.

Possible answers

Students could mix and match qualifications in various ways. However, to meet the context, ‘degree’ has to be one of them.

1. Justification depends on the choice made. Comparison of degree and vocational, for example, could compare a degree with getting a work or trade-orientated qualification where you get paid while training. We will use this in the answers. Graphs and formulae for other options are given below.

2. Sample graphs:

2) Degree y = 18.656x + 137.84 R2 = 0.3515 r = 0.59 b) Vocational or trade qualification y = 16.086x + 67.675 R2 = 0.6067 r = 0.78

3. For a degree, the model shows average earnings of $18.66 per hour, with an initial base salary of $137.85. For trade and vocational qualifications earnings average $16.09 per hour with a base of $67.68 per week

4. There is a moderate linear relationship (r = 0.59) between hours worked and income for    people with degrees. However, the linear model based on hours explains only 35 percent of the variation in income.

For vocational and trade qualifications, the linear relationship is stronger (r = 0.78) and the linear model explains about 61 percent of the variation in income.

5. From 3 it seems that having a degree increases your earnings by about $2.50 an hour. The earnings of those with degrees also start off at a higher level. However, there is a lot more variation in the earnings of people with degrees and the model is not a good one.

6. The relationship between the variables is not as strong for people with degrees, so there may be other factors affecting the income. Attributes like age and gender also affect the salary you get paid. Also, a lot of people with trade qualifications seem, from this dataset, to be working part time, so this may affect the rate of pay. This may be a result of bias in the sample.

7. A better analysis might be to just use people working full time (maybe 35 to 45 hours a week), and compare their pay for different qualification groups. This will give a better idea of earnings. It would also be useful to look at the age of the workers. It could be that the differences are caused because people with degrees are older when they start work or that, in our sample, age was not evenly distributed.

Graphs for the other qualification groups