It was wonderful seeing so many teachers at last year’s Statistics Teachers’ Day in Auckland. Planning is already underway for this year’s event!

Later this year, we’ll let you know the overarching theme and put out a call for workshops and talks.

In the meantime, save the date:

Statistics Teachers’ Day 2026
Friday November 27

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A teaching plan covering statistics and probability achievement objectives

• Introduction to if the world were 100 people concept
• Understanding about percentages
• Explore making data visualisations using a 100 people chart for given percentages

• Understanding what a census is, in particular, what is the census of population and dwellings in New Zealand.
• Exploring migration and birthplace statistics from the 2018 census – connecting to from Aotearoa New Zealand histories curriculum

• Deciding the region of New Zealand to explore
• Deciding on topics of interest
• Sourcing secondary data (existing information) to use to create a “If _____ were 100 people” presentation

• Exploring and interrogating data visualisations
• Deciding on visualisations to use for their�� “If ______�� were 100 people” presentation

• Creating visualisations to use in the “If ________ were 100 people” presentation
• Use a variety of data visualisations
• Making summary statements about the data
• Starting to use technology and statistical software to create their data visualisations

• Students make their videos, check them, and share them with their teacher
• Students prepare their own evidence of undertaking a statistical enquiry to share with others

• Introduction to time series graphs

• Exploring Gapminder trends graphs
• Reading and describing time series graphs

• Exploring Figure.NZ graphs
• Attributing the charts used
• Writing descriptions of time series graphs including seasonal variation

• Introduction to Common Online 91���� Analysis Platform – CODAP, a free browser-based statistical analysis tool

• Using CODAP to explore time series datasets

• Record results of a simple probability experiment
• Interpret results and decide if a game is fair

• Record results of a probability experiment on a tally chart
• Discuss experimental and theoretical probabilities
• Use technology to do a large number of trials

Additional probability activities could include:

• The rest of the lessons
  • Determine an experimental estimate of the probability of simple events using frequency tables.
  • Determine the theoretical probability of simple events using percentages, fractions, and decimals.
  • Systematically find all possible outcomes of an event using tree diagrams and organised lists.
• • Make predictions based on data collected.
  • Identify all possible outcomes of an event.
  • Assign probabilities to simple events using fractions (1/2, 1/6, etc).
• • Take samples and use them to make predictions.
  • Compare theoretical and experimental probabilities.

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Because all we can do is project from the patterns we already have seen, when unprecedented patterns emerge (i.e., patterns we have never seen before), our forecasting methods fail. This is an unavoidable reality. Short of clairvoyance, it couldn’t be any other way. It is impossible for the projected trends and confidence limits our tools produce to make reasoned allowances for types of changes we have never before experienced or thought about. In the context of our experience they are unexpected outliers.

Some series, especially tourism related, have reacted to covid-19 by producing patterns we have never seen before. For those situations the forecasts from our simple Year-13 tools fail. All the assumptions that have been used in making their forecasts have been violated by emerging real-world events. Currently (January 2021) , for example, even the professionals have no idea of how to reliably forecast what will happen to visitor arrivals in New Zealand over the next year or two. They have no real idea what the pattern of recovery will look like over what period.

There are a lot of other data series for which covid has had next to no effect (e.g., climate series), or little effect (e.g., fruit and vegetable prices as in Figure 5 below). Our current tools work fine for those.

At year 13 our students learn to work with time series that show a particular, visually-obvious, type of pattern that is quite common, a trend plus a regularly repeating seasonal component (cf. Figure 2 below).

It is important for students to see series that do look like this (and for which our tools are appropriate), and others that do not (and for which our tools are not appropriate). We recommend that formal NCEA assessments use the former type of series, but that students are shown examples of both and can distinguish between them. We give some illustrative examples after the following set of links. We conclude with descriptions of some methods that .

If you are unfamiliar with these ways of thinking and working, or if you want a reminder, see the following short videos [mins: secs]:

• [4:38]
• [6:01]
• [5:12]
• A simple but interesting extension: [5:16]

These are also on /resources/3-8/ under “Teacher Preparation” together with pdfs that contain illustrated transcripts of what the movies say.

Examples

Figure 1 below shows monthly time-series data of average numbers of overseas visitors in NZ from January 2010 until December 2020.��

Figure 1: Monthly series of average overseas visitors in NZ from January 2010 until December 2020��

Figure 2 shows a seasonal decomposition of this series using just the data up until January 2020. The thin blue line shows an estimated trend plus a repeating seasonal effect. It almost perfectly reproduces the actual data (red line). (Note: few series are this perfectly modelled by a trend plus seasonal effect). But after January 2020 covid starts to affect things, borders get closed and visitor numbers begin to fall off a cliff. The simple analysis tools we give our students cannot cope with this radical change in behaviour.��

Figure 2: Decomposition of this series from January 2010 to January 2020����

Figure 3: Forecasting visitor numbers after January 2020 using the data from 2010-January 2020����

Figure 3 uses the data up to January 2020 to forecast average visitor numbers from February 2020 on. We see the forecast (red line) with its uncertainty bands in pink. The actual data is the black line. The forecast missed what really happened by miles. Our forecasts are made by projecting forwards the patterns we have seen in the past but, in 2020, covid and border closures changed everything and the real series departed from the patterns it had followed in the past and started behaving in a way that we had never seen before.��

��Figure 4: Forecasting visitor numbers in 2021 and beyond using the data up until December 2020����

Figure 4 tries to forecast 2021 and beyond using all the data up until December 2020. We cannot trust this forecast at all because the simple (monotone) trend plus season model the Holt-Winter method is assuming is no longer applicable. The pattern has been broken and we don’t know if, when, and over what period it might “go back to normal”. Students should see this and learn a very big lesson about forecasting from it — that the world doesn’t always play nice with us and sometimes something new and unexpected happens that makes our forecasts badly wrong.

����Figure 5: Forecasting average fruit and vegetable price index values using data up until December 2020����

Figure 5 is looking at the fruit and vegetable component of the NZ consumer price index (CPI) up until December 2020 and doing a Holt-Winters forecast for 2021 and 2022. Looking at the historical data (black line) and how it is approximated by the Holt-Winters modelled trend+seasonal-effect estimates (green line) you will see that there is nothing particularly unusual about 2020. We could use this series in an assessment.����

But as we have said professionals can do better at modelling and forecasting time series than we can because they have a wider range of tools. Professional times-series analysts have methods for making adjustments for all sorts of strange behaviours.

Modelling for disrupted time series

By Rachel Passmore

[Note: this is beyond the scope of NCEA Level 3]

Disruptions to time series are a relatively common event for time series modellers to contend with. Disruptions may be caused by price changes, policy changes, definition changes and environmental changes as well as pandemics. Recovery from such disruptions can be handled in a number of ways, depending on what information about the disruption is available. For example, if a time series has been disrupted by a price change, there may have�� been other price changes in the past, so an estimate of the impact of a price change can be made and the time taken for levels to recover can be made and projections adjusted accordingly. The four most common patterns for a disruption are:

• Permanent shift to the level of the time series, either up or down.
• A ‘blip’ , perhaps caused by a one-off event; time series resumes pre-blip level and patterns afterwards.
• Permanent shift to the level of the time series but it does not happen all at once.
• Sudden shift to the level of the time series which gradually over time reverts to its pre-sudden shift level

Each of these possibilities can be incorporated into a model of time series. This part of time series analysis is known as intervention analysis and is usually modelled using an ARIMA or Autoregressive Integrated Moving Average Model although other models are possible too. Some disruptions to time series are not easy to detect, and this is where change point detection can be employed. This technique can be used to detect sudden changes in live data streams for monitoring purposes, but can also be used to detect all historic changes in the time series, not just the most obvious one

Some Australian researchers have also been developing probabilistic forecasting. They were interested in forecasting international arrivals to Australia as there is strong interest from a number of parties in knowing when pre-COVID levels might resume, if ever. Their approach was to survey 433 tourism experts and ask their opinion on pessimistic, most-likely and optimistic rates of recovery in visitor arrivals. Scenario-based��

Probabilistic forecasts were produced and compared with forecasts generated as though COVID had never happened. This allowed tourism operators to estimate the difference between the scenario-based probabilistic forecasts and the projections generated as if the pandemic had never occurred.

Intervention analysis and scenario-based probabilistic forecasting iis beyond the scope of the NZ Secondary School curriculum, but given the number of time series data sets that could be impacted by the pandemic, here are some suggestions that could provide a way forward, admittedly they are a bit of a ‘fudge’ !

1. Permanent shift to level of time series. In this instance, remove data post shift and predict from the last pre-shift data point. Make an assumption about the size of the shift, and reduce/increase projections by that amount.
2. Blip – remove this value from the data set and replace with an interpolated value, then calculate projections in the usual manner
3. Permanent shift that happens over time, such as a gradual decline. This could be be modelled by adding an additional variable in the model that decreases over time.
4. Sudden shift that gradually recovers to pre-disruption levels. This could be modelled by adding an additional variable in the model that increases over time until pre-disruption levels are regained.

The first scenario can be handled by employing iNZight in the usual way, but then adjusting projections by the estimated size of the shift. At secondary school level, this does not have to be a sophisticated estimate; as long as some justification can be provided for the size of the estimate that should be sufficient.

The second scenario just requires substitution of the one unusual data value, then iNZight can be used in the usual way.

The third scenario requires two assumptions to be made; the size of the shift, and the length of time taken for the shift in mean level to occur. This is definitely outside the scope of secondary school students in terms of assessment, but might be a useful teaching activity to discuss how this could be done. Suggestions include taking projections produced by data up to but not including any COVID effect, and then adjusting projections by applying a linear or non-linear decay element.

The fourth scenario can be handled in a similar fashion to the third scenario, but this time adjust projections by applying a growth element for a limited period of time.

References

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The graphs are interactive – slide the dividers to highlight different time periods.

The catagories are comrehensive – Borrowing, Saving, Property, Insurance, Kiwisaver, Rural matters to name a few. Click on the blue catagory tabs along the top to browse.

For example: 15 years of prices, seperated by course, mid and fine micron.

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Lucy Edmonds�� & Heral Patel from Green Bay High School, covered their process of writing both internals and E-O-Y school assessments, from choosing interesting and engaging contexts, to developing an assessment at different levels of understanding. Lucy and Heral are reasonably confident they’ve already made every mistake possible when writing, moderating and administering assessments – and shared a system of writing assessments which make them interesting to both us and the students (acknowledgements to Sue Spencer, Epsom Girls’ Grammar School).��

Resources

• Writing Statistics or any internal assessments
• Writing Statistics (or any really) Internal assessments Powerpoint

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DS: The Evolution of��Daisy’s Career in Statistics: Statistics, why would someone even study that? What kind of job can I get with that?”��Daisy’s 16 year-old self used to protest. Flash forward a decade later, and��Daisy�� is working toward her doctorate in Statistics. So what changed over those years that made her mind set switch completely? In this session,��Daisy discussed her personal journey through a career in statistics that changed the former skeptic to a passionate statistician. Daisy talked about her research combining statistics with molecular evolution, attempting to explain the many exciting opportunities of statistics to her 16 year-old self. Link to resources:

LM: Louise��loves statistics because it allows her to dabble in several different fields. Her PhD is on statistical methods for animal population genetics, but she also separately collaborated with an ecologist who is studying the growth patterns of tree ferns. Her consulting work has mostly been investigating predictors of students’ tertiary outcomes.

OS: The wide world of stats: from crickets to cricket: Today data exists in almost every facet of life, and where there is data, is an opportunity for a statistician. The versatility of statistics has allowed��Ollie to contribute to a wide range of areas of interest , including projects in ecology, education, marketing and sports. Presently, I am a PhD candidate focussing on developing new statistical models and methods with applications to the sport of cricket, an opportunity��Ollie would never have thought was possible studying statistics at high school.

AH: Mapping species and communities: using statistics to improve ecosystem management.��Andrea’s career has been motivated by both a passion in ecology and a love for statistics.�� She enjoys applying her spatial reasoning skills to tackle questions related to species distributions, or the spatial patterns of animals found across a land or seascape.��Andrea’s PhD research focuses on developing statistical models to estimate and predict these patterns and relate them to environmental variables. Her PhD thesis lies at the forefront of this new area of research, looking into three different systems: a community of soil mites, a community of surf clam off the NZ coast, and the distribution of the marbled murrelet, a seabird found around the Pacific Northwest of the United States.

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Link to resources:

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In level 1, the Statistics team & PE teachers worked on Multivariate Analysis, in level 2, Questionnaire design with the Business department and in level 3 the department moved away from traditional reports to presentations and posters for assessment.

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Stats day 2019

Stats-day-2016-Improving students PPDAC responses

Templates-and-strategies-zipped��These templates and strategies are for 1.10, 2.9, 3.8, 3.9 & 3.10 standards

Sophie’s video demonstrates the PEEL writing technique.

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Overcoming the Blank Page

Poster Graphs

Socrative

Student Marking

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