Assessment Report

New Zealand Scholarship
Statistics 2019

Standard 93201

Part A: Commentary

Successful candidates had a broad understanding of achievement objectives from across the Statistics strand of the curriculum up to and including Level 8. They were able to use this knowledge in solving problems set in both familiar and unfamiliar contexts and showed statistical insight by integrating statistical and contextual knowledge. Successful candidates supported their arguments with statistical reasoning and evidence and used precise and correct statistical language. They were careful to answer the questions that were actually asked, rather than providing rote learned responses that were not appropriate or adapted for the data, analysis or context given. It was evident that candidates who had carried out investigations using the range of data and methods expected for this subject, and had practised writing reports about these investigations, were able to confidently engage with concepts assessed in the examination.

It appeared that many candidates were unfamiliar with writing descriptive statements as part of exploratory data analysis e.g. Q1a and had limited experience with interpreting side-by-side bar charts of proportions. The word “compare” was used in questions but often ignored by candidates, which limited candidates’ ability to demonstrate the analytical thinking required for this standard. Many unsuccessful candidates did not understand the probabilistic nature of inference, which affected their interpretation of confidence intervals and randomisation test results. Areas of weakness for many candidates included the design of experiments, the randomisation test and critically evaluating statistical reports. Many candidates also struggled to demonstrate understanding that a time series model is formed from both trend and seasonality and could not link both of these components to forecasts and the Holt-Winters model.

Part B: Report on performance standard

Candidates who were awarded Scholarship with Outstanding Performance commonly:

  • considered information from several sources or displays and could integrate this information to communicate insightful statements
  • used appropriate methods to compare rates of increase
  • compared different models for time series data and discussed trend and seasonality
  • understand how a measure of the strength of linear association (r) may be affected by different features of the data
  • applied understanding of statistical inference and study design and the relationship between these concepts
  • demonstrated a strong conceptual understanding of statistical modelling and were able to use this to produce critiques of models
  • demonstrated familiarity with probability modelling and were able to complete full and correct probability calculations
  • applied statistical insight when working with unfamiliar contexts.

Candidates who were awarded Scholarship commonly:

  • showed a good understanding across the statistics curriculum, in particular design of experiments and evaluating statistical reports
  • interpreted a range of graphs and types of analysis
  • consistently backed up their statements with numerical evidence and succinctly linked to the context
  • used key statistical terminology to strengthen their discussion
  • referred to parameters in their interpretations of confidence intervals
  • used key features when comparing distributions, not just relatively frivolous ones such as a comparison of the size of the two largest outliers
  • succinctly described the shape of data distributions
  • were clear about possible (and impossible) effects of random variation on the features of a sample distribution
  • read the graph and familiarised themselves with the units before attempting to describe its features
  • responded to all questions by providing focused responses, rather than writing in-depth responses for only some questions.

Other candidates

Candidates who were not awarded Scholarship commonly:

  • had gaps in their understanding of statistics e.g. not communicating uncertainty when interpreting confidence intervals, not understanding key features of time series graphs
  • did not identify whether comments were about a sample or a population, especially evident in Q1 and Q3
  • struggled to identify and use information about samples (e.g. percentages, sample sizes) provided in a statistical report
  • wrote vague and general statements with little, no or irrelevant supporting evidence
  • wrote what they (thought they) knew about the displays, rather than answering the questions
  • had learned rote responses about randomisation tests and confidence intervals but applied them in the wrong contexts, showing they did not understand the concepts
  • failed to compare when this was prompted but instead stated two values without connecting them
  • incorrectly interpreted the large tail proportion from the randomisation test as “evidence that chance was acting alone”
  • incorrectly reasoned that a given model was invalid because a dot plot has several peaks
  • did not attempt every question or did not plan their time well and spent too long on some questions.

Performance standard specific comment

 

Subject page

 

Previous years' reports

2018 (PDF, 95KB)

2017 (PDF, 44KB)

2016 (PDF, 197KB)

 
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