Moderator's Newsletter
November 2011
Contents
- AS 91035 Investigate a given multivariate data set using the statistical enquiry cycle
91035 Investigate a given multivariate data set using the statistical enquiry cycle
This newsletter looks at some issues that have arisen to date in relation to the interpretation of this standard.
Important understandings for this standard are the ideas around sampling, sampling variability and population.
An understanding relating to the difference between sample and population is required at all levels and needs to be evident somewhere in the report.
Posing an investigative question
- Students are required to pose their own investigative question for this standard.
- It must be a comparison investigative question and needs to reference the population.
- Teachers need to check students’ investigative questions to ensure they are suitable and allow time for students to correct or improve their question. There is information relating to the investigative question in the Conditions of Assessment document and there are guidelines relating to what should be in the investigative question given in the tasks on TKI.
- The data set that is provided needs to allow for choice of both the category variable and the numerical variable (there is a reference to this in the 6th paragraph in the Conditions of Assessment document).
- The investigative question needs to be one that can be answered using the survey data. That means the variables must be available.
Features
- The standard refers to discussing features of distributions comparatively … so students need to be looking at the sample distributions and discuss distinctive features of the distributions, for example shape, middle 50%, shift, overlap, spread, unusual or interesting features.
- At Merit and Excellence levels it is essential that students discuss features in context. For example identifying the two groups that are being compared and referring to a numerical value with its unit.
- At Merit and Excellence level there must be an understanding of the feature that is discussed.
The conclusion
- At Achieved level it is sufficient to answer the posed investigative question or make an informal inference about the population. At Merit and above, both are required.
- The answer to the investigative question needs to be consistent with the analysis that has occurred. At Merit and above there needs to be evidence to justify the conclusion that has been made. It is expected that the conclusion is consistent with the approach of looking at the medians and the relative location of the ‘boxes’ (middle 50% of the data).
- If there is no overlap in the middle 50% of the data then it is possible to conclude that one group tends to have bigger values than the other group.
- If the median of one sample lies outside of the middle 50% of the other sample then it is possible to conclude that one group tends to have bigger values than the other group.
- If the medians are ‘within’ the overlap of the middle 50% then it is too close to call.
- Students need to be making their conclusions using ideas about both medians and spread (either looking at the medians relative to the overlap in the boxes or the distance between the medians relative to the overall visual spread). Considering the medians only is not sufficient at this level as the students are dealing with samples and the difference in the medians may have been due to sampling variability and they need to have this understanding.
Some students may consider refining this further by looking at the distance between the medians in relation to the overall visual spread and as a result of this deeper analysis may conclude that one group tends to have bigger values than the other group.
A small difference between the medians relative to the overall visual spread might not enable a call to be made and this would need to be identified. In this case the consistent conclusion would be that it is not possible to make a call and this is the conclusion that would be expected at all levels.