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Assessment Report
New Zealand Scholarship
Statistics 2016
Standard 93201
Part A: Commentary
Overall the standard of the candidates’ answers was similar to 2015. The best answered questions were Q3 and Q4 where 47% and 48% of candidates respectively achieved scholarship standard. In Q3, 27% of candidates achieved outstanding standard. The most difficult question was Q5 where only 22% achieved scholarship standard.
The percentage breakdown of candidates reaching both a scholarship standard (S) and an outstanding scholarship standard (O) per question is shown in Table 1 below:
Question  1  2  3  4  5  
Grade  S  31.7  19.6  19.6  36.3  17.4 
 O  8.1  5.6  27.0  11.3  4.3 
Table 1: Percentage Breakdown of Grade per Question (S: 5 or 6 marks, O: 7 or 8 marks)
Part B: Report on performance standard
Candidates who were awarded Scholarship with Outstanding performance commonly:
 identified the need for a representative sample in order to obtain statistics for effective estimation
 knew in detail how to establish the validity of a forecast
 described fully an experiment, in detail, through to the analysis stage
 accurately described an experiment with all its key elements
 understood the difference between a mean and a median, the value of percentages versus raw data and a sample versus a population census
 discussed confidence intervals, bootstrap distribution and rerandomisation clearly knowing what was appropriate to the question
 clearly identified appropriate probability distributions and their underlying assumptions
 selected probability distributions that fitted the data provided and built a model along with calculating and discussing the relative fit of these distributions
 used proportions, both in comparing time series graphs and in comparisons between countries
 computed interval predictions for time series values in the future
 suggested possible reasons for changes in time series graphs
 linked their answers with the purpose and themes of the questions
 showed a sound understanding of statistical terminology and the importance of backing their comments with evidence
 wrote fluently, succinctly and in context.
Candidates who were awarded Scholarship commonly:
 discussed trend and seasonality of a given data set and made comparisons with data but not necessarily with percentages
 compared bivariate graphs with respect to correlation and outliers
 provided evidence for the validity of a prediction
 interpreted correctly the output for a randomisation test
 knew about setting up an experiment
 in Question Three selected the appropriate distribution and calculated the required probability correctly
 correctly discussed the differences between a series of Time Series graphs
 recognised and considered the model for the normal and triangular distributions for fitting a set of data
 identified seasonal effects in context from Time Series data
 justified reasons for randomisation and also formed correct conclusions from the output
 showed a reasonable understanding of statistics but often failed to fully relate their answers to the question
 wrote in context and were successful in linking statistical concepts
 deduced a good range of observations from a series of graphs
 described some information contained in a graph in context but often omitted details like values and dates.
Other candidates commonly:
 did not use “linear” in their description of correlation
 did not know the characteristics of a sample
 did not understand how to justify validity in a regression prediction
 described the use of a “control group” and “treatment group” rather than pre and posttests results
 did not read the question carefully hence they went on to discuss two different teaching methods in Q2 rather than a single teaching method
 missed out referring to the mean when discussing differences in test scores and consequently did not make a correct inference about the size of the difference in mean scores. The confidence interval was interpreted incorrectly
 did not write a conclusion which captured all of the evidence given in the question
 were unable to calculate straightforward normal, binomial or triangular probabilities
 provided too much detail in describing time series where every up and down was described rather than the overall picture
 did not find and briefly discuss the salient features in a time series
 gave a year by year account of what happened and did not discuss the time series graph as a whole. The terminology used in their descriptions was poor. For example, “spikes” was freely used even though there were no spikes at all. Peaks and troughs were used even when there was no seasonality present. The actual values indicated by the graphs were frequently not mentioned at all. Vague statements of increases and decreases resulted
 thought that fluctuations meant there had to be seasonal or cyclic effects present
 did not provide dates, values and a description of the overall pattern including fluctuations for the threetime series graphs
 made vague descriptions of possible graphs in Q4. While some candidates could describe (in some way) a comparative bar graph they could not say why this would be a better graph
 did not make clear what they were doing in working out predictions for a time series. In many cases numbers came out of nowhere for calculations.
 gave only one generic vague comment about a prediction when other evidence was present in the paper
 named contributing factor(s) to obtaining representative data but were unable to provide an explanation. Candidates also used vague language describing things which were not factors, such as they should be “geographically representative” or that the weather stations “should be spread evenly across the country” and “should not be close together”.
 wrote long passages speculating why something might have happened rather than describing what information was actually in the graph
 mixed up features for different types of statistical investigations. For instance, they wrote about relationships in Time Series and trends in Bivariate.
 typically repeated their observations. Many didn’t compare gradients in Q5 which was a key concept in comparing between NZ/Antarctica/Global of the rate of temperature change.
 made statements that were generally vague with no supporting data and did not state where they were referring to
 confused terminology and lacked context
 often did not write totally clear concise statements backed up by evidence.
Further comments
There was evidence that some candidates failed to use their basic statistical knowledge and were not familiar with statistics at Levels 1 and 2 especially when working with graphs, tables and probability distributions.
Many candidates had difficulty writing clear and articulate answers.
There was a general lack of rigour in candidates’ writing. Students are advised to check read what they have written.
Many candidates did not start each question on a new page despite the instruction at the top of each page.
Several answers were devoid of context along with statistical concepts not being clearly articulated.