Curriculum links
NCEA Mathematics Achievement Standard AS90645
- Select and analyse continuous bi-variate data.
Mathematics and Statistics: Statistics strand – level 8
– Carry out investigations of phenomena, using the statistical enquiry cycle:
- conducting surveys, and using existing data sets;
- finding, using, and assessing appropriate models (including linear regression for bi-variate data and additive models for time-series data), seeking explanations, and making predictions;
o using informed contextual knowledge, exploratory data analysis, and statistical inference;
- communicating findings and evaluating all stages of the cycle.
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.
NB: Hours worked is not a variable for the current SURF. Age could be used as an alternate explanatory variable. It would be necessary to reword the activity page accordingly.
Possible answers
Students could mix and match qualifications in various ways. However, to meet the context, ‘degree’ has to be one of them.
- Students should be able to justify what two groups they choose to compare.
- Sample graphs.
- The base for degree is a high negative value (-37797) compared with all other qualifications. However wages and salaries increase by a higher rate as age increases ($1802.2 / year). The fitted regression line for degree appears to be the highest line of the four.
- There is a high linear relationship (r = 0.89) between age and income from wages and salaries for people with degrees.
- From 3 it seems that having a degree increases your earnings with age. The earnings of those with degrees also start off at a higher level. Additionally, the model provides a good prediction of wages and salary income based on age.
- The relationship between the variables is strong for people with degrees. However, there may be other factors affecting the income. Attributes such as sex also affect the salary you will receive.
- A better analysis might be to only use people who are employed and compare their pay for different qualification groups. It may also be the case that income from wages and salaries differ depending on other categorical variables such as sex and ethnicity. No information about whether people work part- or full-time has been included and this