Resources by Chris Wild - 91 Fri, 03 Jul 2026 02:57:51 +0000 en-US hourly 1 Teaching Time Series in the Covid-affected Era /resource/teaching-time-series-in-covid-era/ Sun, 28 Feb 2021 19:51:15 +0000 /?post_type=resource&p=11261 All time-series forecasting methods make their forecasts by taking patterns from the past and projecting them into the future. (And there are lots of different methods for doing this.) 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 […]

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]]> All time-series forecasting methods make their forecasts by taking patterns from the past and projecting them into the future. (And there are lots of different methods for doing this.)

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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]]> Adding spice to statistics with dynamic and interactive graphics /resource/adding-spice-to-statistics-with-dynamic-and-interactive-graphics/ Mon, 06 Jan 2020 23:09:28 +0000 /?post_type=resource&p=10830 Online presentations of statistical data, flat, static graphics are sliding out the back door of history. Online graphics do things. They are like living things, not unresponsive, dead things. Poke them and they react. In this workshop, presented by Daniel Barnett (University of Auckland), participants saw both types of graphs, and generated a range of […]

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]]> Online presentations of statistical data, flat, static graphics are sliding out the back door of history. Online graphics do things. They are like living things, not unresponsive, dead things. Poke them and they react.

In this workshop, presented by Daniel Barnett (University of Auckland), participants saw both types of graphs, and generated a range of interactive and dynamic graphs. Using iNZight Lite (online) where it all happens at the click of a button, participants transformed familiar graphs they already use in their teaching and also stepped beyond to many other types of graph – some familiar, some less so, including graphical displays on maps.

[Note: This is the NZAMT16 workshop by Prof Chris Wild]

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]]> Probability distributions for teachers /resource/probability-distributions-for-teachers/ Sun, 22 Sep 2019 05:00:13 +0000 /?post_type=resource&p=10582 This page is aimed at helping teachers educate themselves about probability distributions. If you master the materials here, you can be confident that you have enough content knowledge (in contrast to pedagogical knowledge) to teach probability up to Year 13. The probability strand of the 2007 NZ Curriculum; Key ideas 2007 expanded If you want […]

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]]> This page is aimed at helping teachers educate themselves about probability distributions.

If you master the materials here, you can be confident that you have enough content knowledge (in contrast to pedagogical knowledge) to teach probability up to Year 13.

If you want a very quick exposure to some key ideas about probability distributions and their applications before starting on something more comprehensive, see these three videos from Dr Nic’s playlist on her (contain adds)

  • – Probability Distributions 1
  • : Distributions 2

(pdf) by Chris Wild & George Seber

This comprehensive resource is a pre-publication draft of the probability chapter for the book “Chance Encounters“. All of the answers to the exercises in the published chapter are here. Associated Powerpoint slides are here.

Discrete distribution Lectures

This is compiled from Lectures from the Stats 10x team at Auckland, narrated here by by Rachel Cunliffe. You may prefer to view this video before attacking the chapter above.

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]]> Probability for teachers /resource/probability-for-teachers/ Sun, 22 Sep 2019 04:59:20 +0000 /?post_type=resource&p=10553 This page (in progress) is aimed at helping teachers educate themselves about probability. Call back from time to time as it will continually be improved. If you master the materials here you can be confident that you have enough content knowledge (in contrast to pedagogical knowledge) to teach probability up to year 13. The materials […]

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]]> This page (in progress) is aimed at helping teachers educate themselves about probability. Call back from time to time as it will continually be improved.

If you master the materials here you can be confident that you have enough content knowledge (in contrast to pedagogical knowledge) to teach probability up to year 13. The materials go a bit further than Year 13 but not much further.

Over view of probability in the NZ curriculum

If you want a very quick exposure to some probability ideas before starting on something more comprehensive, see these two videos from Dr Nic’s playlist on her (contain adds)

(pdf) by Chris Wild & George Seber

This comprehensive resource is a pre-publication draft of the probability chapter for the book “Chance Encounters“. It goes a bit further than you need for Year 13 but it fills in a lot of the gaps and the motivations for what is done in the resources below. All of the answers to the exercises in the published chapter are here. Associated Powerpoint slides are here.

It does not explicitly contrast the notion of a true (but unknown) probability with probabilities from models (like equally-likely event models) and probabilities for data (obtained by doing something over and over again) as ways of obtaining approximations to a true probability. See the paragraph on true probability below.
Additionally, it does its more complex calculations for conditional probabilities using tree diagrams instead of simpler methods based on 2-way tables. Replacement pages that use 2-way tables are provided here. (The answers to the Exercises also use 2-way tables.)

Probability Lectures from the Stats 10x at Auckland

These Lectures are from the Stats 10x team at Auckland. They cover much of what you need and the ideas are very carefully explained by Matt Regan. You may prefer to view these videos before attacking the chapter above.

  • Video on “Apply probability concepts in solving problems” by Marion Steele with associated resources


    •   
    Understanding true probability, model estimates, and experimental estimates

    Probability Resources

    • From

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    ]]> Events occurring in time, the Poisson distribution, and Scampy /resource/events-occurring-in-time-the-poisson-distribution-and-scampy/ Sat, 21 Sep 2019 05:34:50 +0000 /?post_type=resource&p=10738 The post Events occurring in time, the Poisson distribution, and Scampy appeared first on 91.

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    ]]>         SCAMPY /resource/scampy/ Thu, 12 Sep 2019 00:12:12 +0000 /?post_type=resource&p=10722 The post SCAMPY appeared first on 91.

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    ]]>         91 to Insight: An Introduction to 91 Analysis and Visualisation /resource/data-to-insight/ Wed, 03 Jul 2019 02:54:51 +0000 /?post_type=resource&p=15164 The post 91 to Insight: An Introduction to 91 Analysis and Visualisation appeared first on 91.

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    ]]>         Interactive Visualizations for Conditional Probability: Eikosograms and Pachinkograms /resource/interactive-visualizations-for-conditional-probability/ Wed, 17 Apr 2019 04:42:32 +0000 /?post_type=resource&p=10417 For an excellent description of Eikosograms and Pachinkograms and their use in teaching conditional probability, see the article by Marie Fitch and Stephanie Budget (“Conditional Probability: Friend or foe?” in the Proceedings of the Tenth International Conference on Teaching Statistics (2018). Eikosograms: An Eikosogram is a graphical representation of a two-way table of counts (or […]

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    ]]>     For an excellent description of Eikosograms and Pachinkograms and their use in teaching conditional probability, see the (“Conditional Probability: Friend or foe?” in the Proceedings of the Tenth International Conference on Teaching Statistics (2018).

    Eikosograms:

    An Eikosogram is a graphical representation of a two-way table of counts (or joint probabilities) which makes the relative sizes of the counts in each table clearly visible by making the area of each cell proportional to the count.

     

     

    They are useful for seeing relative sizes and conditional proportions/probabilities in the vertical direction. In this example that corresponds to proportions of eye-colour for each each of the sexes (or equivalently, “given Sex=female“, or “given Sex=male“)

    Our produces these graphics for data read in by the user.

    If you want constitutionality the other way around the other way around a “Swap factors” button reverses it.

    which helps for seeing the relative sizes of conditional proportions/probabilities of Sex givenEye colour.

    Resources for teaching using Eikosgrams:

    From Malia Puloka’s 2017 Teachers Day workshop exploring how to teach the concepts of conditional and joint probability using the Eikosogram. Equally important is the interpretation and verbalisation of proportion and probability statements and the posing of questions, which Malia also looked at. The workshop was based on Malia’s master’s research with Year 13 students.

     

    Pachinkograms:

    A Pachinkogram can be thought of as interactive and dynamic tree-diagram.

     

     

     

    They are particularly useful for conveying issues in “reversing the order of conditionality”, i.e. converting from pr(A | B) to pr (B | A). They expose the sizes of the probabilities through the widths of the flow-paths, and expose the “proportion of a proportion” idea as you move down the path.

    Seeing is believing! In her 2017 Teachers’ Day workshop Stephanie Budgett (University of Auckland) cast a light on common and widespread probability misconceptions. Teaching probability is difficult. Learning probability is difficult. We all have misconceptions that are remarkably resistant to change. This workshop Stephanie presented common probability misconceptions from a variety of disciplinary areas. Participants used software and the following activities designed to address these common misconceptions and explore these issues.

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    ]]>         Pachinkogram /resource/pachinkogram/ Mon, 15 Apr 2019 04:50:18 +0000 http://new.censusatschool.org.nz/?post_type=resource&p=9983 The post Pachinkogram appeared first on 91.

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    ]]>         Videos: numeric-variables /resource/numeric-variables/ /resource/numeric-variables/#comments Tue, 07 Nov 2017 22:01:43 +0000 http://new.censusatschool.org.nz/?post_type=resource&p=8983 We explore single numeric variables and learn how to plot and interpret them. We discover how to describe the shape, centre and spread of dot plots and look for oddities This resource contains: Numeric variables (video, 6 min) Features of numeric variables (summarizing explanatory document) Feature spotting (video, 5 min) Numeric Variables Plotting numeric variables […]

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    ]]>     We explore single numeric variables and learn how to plot and interpret them. We discover how to describe the shape, centre and spread of dot plots and look for oddities This resource contains:

    1. Numeric variables (video, 6 min)
    2. Features of numeric variables (summarizing explanatory document)
    3. Feature spotting (video, 5 min)

    Numeric Variables

    Plotting numeric variables shows us interesting characteristics of our data. In this video we’ll explore pulse rates and household incomes and learn how to describe what we see.

    []

    After you’ve watched these videos, you should be able to answer these questions:

    • How is a stacked dot plot constructed?
    • What are the four types of things we look for in dot plots?
    • What is the common name for the mean?
    • How does the mean relate to the dot plot?
    • What property defines the median?
    • When do the mean and median tend to be very similar, and when can they be quite different?
    • Why might we prefer the median to the mean for personal incomes?

    Features of numeric variables

    Learn to identify and interpret the features of numeric variables that are evident on dot plots, box plots and summary tables.

    The linked pdf is both a reading and reference document. It lays out the main ideas relating to Centre, Spread, Shape and Oddities for a numeric variable. It is done in a landscape tabular form designed to make it easier to see the inter-relationships between ideas. It is a core part of the teaching about these issues. The video that follows assumes that the viewer has already read the pdf.

    Feature spotting

    n this video we’ll introduce you to box plots and measures of spread, and to shape and oddities. We’ll use our knowledge to look at our data, to draw insights from it, and possibly ask more questions about the data. Why are weights bimodal and heights not?

    []

    After you’ve watched these videos, you should be able to answer these questions:

    • What sort of “oddities” should we look for and what sort of questions should we ask when we see them?
    • What is the defining property of a median? the first quartile? and third quartile?
    • What information does the box plot add to the dot plot?
    • What is the interquartile range and how does it relate to the box plot?
    • What is an “outlier”?
    • What does “positively skewed” mean?
    • What does “bimodal” mean?

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