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# 3.9 Achievement Objectives

### Excellence

• Investigate bivariate measurement data.

This involves showing evidence of using each component of the statistical enquiry cycle

• Investigate bivariate measurement data, with justification.

This involves linking components of the statistical enquiry cycle to the context, and referring to evidence such as statistics, data values, trends, or features of visual displays in support of statements made.

• Investigate bivariate measurement data, with statistical insight.

This involves integrating statistical and contextual knowledge throughout the investigation process, and may include reflecting about the process; considering other relevant variables; evaluating the adequacy of any models, or showing a deeper understanding of the models.

Achievement Standard 3.9 #91581 (link to NZQA)

Carry out investigations of phenomena, using the statistical enquiry cycle:
- posing an appropriate relationship question using a given multivariate data set (The investigative question needs to be an appropriate one it is expected that a purpose for the investigation is evident)
- selecting and using appropriate displays
- identifying features in data
- finding an appropriate model
- describing the nature and strength of the relationship and relating this to the context
- using the model to make predictions
- using informed contextual knowledge and statistical inference
- communicating findings and evaluating all stages of the cycle and in a conclusion.

Clarifications
Updated December 2014. This document has been updated to address issues that have arisen from moderation.

Students need to provide evidence of each component of the statistical enquiry cycle detailed in Explanatory Note 3 of the standard.
It is possible for a student to meet the criteria for all grades by considering an appropriate linear model.

Posing an appropriate relationship question using a given multivariate data set
Sufficient time needs to be allocated for students to research the context and acquire appropriate contextual knowledge. Students need to identify a purpose, and pose a relationship question which is informed by this contextual knowledge, for all grades.
Students may choose to split or re-categorise the data as part of the investigation. The initial data set should be sufficiently large to ensure that the subsets of data that may be investigated are large enough to allow a meaningful investigation.

Identifying features in the data
Students need to create a scatter graph, and need to use a visual inspection to describe features in the data, before fitting a model. Features need to include the strength and direction of the relationship and could include whether a linear model is appropriate, clusters and unusual values. Students need to take care to justify the existence of any unusual value/outlier with reference to the data set and the context.

Using the model to make a prediction
Students need to make a prediction, in context, for at least one value of the explanatory variable. The precision of the prediction could be discussed by reviewing the strength of the relationship and the scatter on the graph close to the relevant explanatory data value. It is not sufficient to produce a table of values for the prediction.

Required quality of student response
For Merit, students need to justify all findings with reference to evidence from the displays and statistics and link the purpose and findings to their research.
For Excellence, students need to integrate the statistical and contextual knowledge, gained from their research, throughout the response and also reflect on the process, which could be shown by considering other relevant variables, evaluating the adequacy of the model or showing a deeper understanding of the model.