Resources for teaching statistics (Last updated 24/03/17)

NZC Level 1

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NZC Level 2

NZC Level 3

NZC Level 4

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NZC Level 5

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NZC Level 6, NCEA Level 1: Statistics and Probability

1.10 Investigate a given multivariate data set using the statistical enquiry cycle

(91035)
Internal 4 credits

This standard is derived from Achievement Objective S6.1, plan and conduct surveys and experiments using the statistical enquiry cycle.  In particular,

  • determine and justify appropriate variables
  • cleaning data
  • using multiple data displays, and re-categorising data to find patterns, variations, in multivariate data sets.
  • comparing sample distributions visually, using measures of centre, spread, and proportion
  • presenting a report of findings.

It is important for students to consider the context of the data and make an informal inference about the population from the sample data.

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NZC Level 6, NCEA Level 1: Statistics and Probability

1.11 Investigate bivariate numerical data using the statistical enquiry cycle

(91036)
Internal 3 credits

This standard is derived from Achievement Objective S6.1, plan and conduct surveys and experiments using the statistical enquiry cycle.

In particular,

  • determine and justify appropriate variables and measures
  • consider sources of variation
  • gathering and cleaning data
  • using multiple displays, and re-categorising data to find patterns and relationships, in multivariate data sets
  • presenting a report of findings

The data must be numerical, with the explanatory variable (x variable) being either continuous or discrete, and the response variable (y variable) measured.  The context of the data should be considered throughout the process.

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NZC Level 6, NCEA Level 1: Statistics and Probability

1.12 Demonstrate understanding of chance and data

(91037)
External 4 credits

This standard is derived from Achievement Objective S6.2, Evaluate statistical reports in the media by relating the displays, statistics, processes and probabilities to the claims made and S6.3, Investigate situations that involve elements of chance

  • Calculating probabilities in discrete situations.

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NZC Level 6, NCEA Level 1: Statistics and Probability

1.13 Investigate a situation involving elements of chance

(91038)
Internal 3 credits

This standard is derived from Achievement Objective S6.3 Investigate situations that involve elements of chance.

This standard encourages students to undertake a probability experiment.  They will need to pose a question, plan and conduct an experiment, choose appropriate displays including experimental probability distributions, and identify and communicate patterns in the data.   Students need to understand the variation between theoretical and experimental probability distributions and realise the effect of the sample size.

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NZC Level 7, NCEA Level 2: Statistics and Probability

2.8 Design a questionnaire

(91263)
Internal 3 credits
NZC Level 7, NCEA Level 2: Statistics and Probability

2.9 Use statistical methods to make an inference

(91264)
Internal 4 credits

This internal Achievement Standard is derived from Achievement Objective S7.1, Carry out investigations using the statistical enquiry cycle.
In particular, using existing data sets,

  • evaluating the choice of sampling and data collection methods used
  • using relevant contextual knowledge, exploratory data analysis, and statistical inference,

and S7.2, Make inferences from surveys,

  • using sample statistics to make point estimates of population parameters
  • recognising the effect of sample size on the variability of an estimate.

Using an existing data set of population data, students will pose an investigative comparison question, select random samples, use appropriate displays and measures, discuss sampling distributions and variability including the variability of estimates.   They will use sample statistics to make point estimates of population parameters and make an inference.  Attention should be paid to the shape of sampling distributions and whether or not samples overlap.  It is important throughout the statistical enquiry cycle to consider the context of the data.

Note,

  • statistical inference – the process of drawing conclusions about population parameters based on a sample taken from the population.
  •  sampling error – the error caused because data are collected from part of population (even if a sample is unbiased), rather than the whole population.

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NZC Level 7, NCEA Level 2: Statistics and Probability

2.10 Conduct an experiment to investigate a situation using statistical methods

(91265)
Internal 3 credits

This standard is derived from Achievement Objectives S7.1, Carry out investigations of phenomena using the statistical enquiry cycle.
In particular,

  • conducting experiments
  • evaluating the choice of measures for variables and data collection methods used
  • using relevant contextual knowledge, exploratory data analysis, and statistical inference.

Evidence of each step of the statistical enquiry cycle should be documented. This process includes posing an investigative question, plan and conduct the experiment, select appropriate displays and measures, discuss findings in a conclusion, supporting findings with evidence gained from the experiment.  Note that an experiment requires an intervention and cannot be an observation study.
Experiments can be either,

  • Two independent group comparison, or
  • Paired comparisons.

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NZC Level 7, NCEA Level 2: Statistics and Probability

2.11 Evaluate a statistically based report

(91266)
Internal 2 credits

This standard is derived from Achievement Objectives S7.3, Evaluate statistically based reports.  In particular, identifying sampling and posisble non-sampling errors in surveys, including polls.

Students are required to evaluate a statistically based report using their knowledge of statistical concepts and exercising statistical literacy.  Sampling methods, population measures and variables, including polls and surveys, sampling variability, appropriate data displays and sampling and possible non-sampling errors and the effect of sample size need to be studied.  Students apply this knowledge to analytically dissect a report from the media within the context and intention of the report.  Teachers can use worry questions, writing frames and literacy strategies to encourage students to begin writing.   It is an opportunity for students to question what they are presented with from the media, and realise the pitfalls (or motivation) of misinterpreting results.

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NZC Level 7, NCEA Level 2: Statistics and Probability

2.12 Apply probability methods in solving problems

(91267)
External 4 credits

This standard is derived from Achievement Objectives S7.3, Evaluate statistically based reports,  in particular, interpreting risk and relative risk,
and S7.4 Investigate situations that involve elements of chance.
In particular,

  • comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions
  • calculating probabilities, using such tools as two-way tables and tree diagrams.

Using extended abstract thinking, students look at risk and probabilities in a wide range of contexts including statistics based reports or situations that involve elements of chance.

There are three parts to this standard,

Part A    Interpreting risk and relative risk:   They need to be able to calculate and interpret risk, select a baseline group, and calculate and interpret relative risk and absolute risk.  Students should consider what relevant information may be missing.

Part B    Compare theoretical distributions, such as the normal distribution, with experimental distributions.  Students will describe and compare distributions and recognise when they have similar and different characteristics.  Carry out an experimental investigation of probability situation and understand the ways a sample is likely to be representative of a population.  Use the mean and standard deviation as sample statistics or as population parameters.

Part C    Calculate probabilities, using tools such as two-way tables, probability trees.  Students should be able to draw a probability tree based on a concrete situation including sampling with and without replacement.  They can use probability trees to calculate simple conditional probabilities.

Where appropriate, use contextual knowledge to interpret and reflect on an answer generated by the above methods using appropriate statements.

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NZC Level 7, NCEA Level 2: Statistics and Probability

2.13 Investigate a situation involving elements of chance using a simulation

(91268)
Internal 2 credits

This standard is derived from Achievement Objective S7.4, Investigate situations that involve elements of chance, in particular, calculating probabilities using such tools as simulations and technology.

Students will show evidence of investigating the situation using each component of the simulation process, integrating statistical and contextual knowledge throughout the process.
Students will design the simulation for the given situation, identify the tools to be used, define what is a trial and the number of trials, determine the data recording methods; carry out the simulation and record the outcomes; select and use appropriate displays and measures; and communicate findings in a conclusion.

In their report the student should show evidence that they have:

  • Designed the simulation for the situation given. They have described in detail the tools to be used, what a trial is, the number of trials and the data recording method. They have identified at least two assumptions in designing their simulation
  • Conducted the initial simulation, recorded the results and repeated the simulation
  • Selected and used appropriate displays and measures.

Students need to communicate their findings clearly, and link their recommendations clearly to the results of the simulation. They have discussed more than one aspect of the recommendation with respect to the context of the simulation in depth.
Note that the simulation can be done using technology (calculator or computer random numbers generated), and a record of the simulation must be set out in table form with labeled headings including the random numbers generated or selected.

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NZC Level 8, NCEA Level 3: Statistics and Probability

3.8 Investigate time series data

(91580)
Internal 4 credits

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NZC Level 8, NCEA Level 3: Statistics and Probability

3.9 Investigate bivariate measurement data

(91581)
Internal 4 credits

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NZC Level 8, NCEA Level 3: Statistics and Probability

3.10 Use statistical methods to make a formal inference

(91582)
Internal 4 credits
NZC Level 8, NCEA Level 3: Statistics and Probability

3.11 Conduct an experiment to investigate a situation using experimental design principles

(91583)
Internal 4 credits

This standard is derived from Achievement Objective S8.1 Carry out investigations of phenomena, using the statistical enquiry cycle, and Achievement Objective S8.2b Make inferences from surveys or experiments and use methods such as randomisation.

Students should be able to:

    • Pose an investigative question about a given experimental situation
    • Conduct the experiment
    • Select and use appropriate displays and summary statistics
    • Make appropriate formal statistical inferences
    • Communicate findings in a conclusion

This standard requires students to use random allocation to treatment groups and randomisation tests to assess the strength of evidence for the causal inference. Computer use is essential.

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NZC Level 8, NCEA Level 3: Statistics and Probability

3.12 Evaluate statistically based reports

(91584)
External 4 credits

This standard is derived from Achievement Objective S8.3, Evaluate a wide range of statistically based reports, including surveys and polls, experiments and observational studies.

  • critiquing causal relationship claims
  • interpreting margins of error

Students also need to be familiar with the following AOs so that they have a good understanding of the Statistical enquiry process in a wide range of contexts:

Achievement Objective S8.1, Carry out investigations of phenomena, using the statistical enquiry cycle,

  • conducting experiments using experimental design principles
  • seeking explanations
  • using informed contextual knowledge, exploratory data analysis, and statistical inference
  • communicating findings and evaluating all stages of the cycle

Achievement Objective S8.2b, Make inferences from surveys or experiments

  •  determining estimates and confidence intervals for means, proportions & differences
  • use methods such as resampling or randomisation

Students should be able to:

  • Use the statistical enquiry cycle and elementary principles of experimental design, surveys and polls, including potential sources of bias
  • Interpret statistical inferences
  • Interpret a wide variety of statistical tables and graphs
  • Analyse a wide variety of statistical situations
  • Critique causal relationship claims and interpret margins of error

This standard requires a broad knowledge of a variety of statistical methods and situations.  The approach used in interpreting the margins of error is new and is based on making informed approximations or rules of thumb to interpret reported margins of error (linked to confidence intervals).

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NZC Level 8, NCEA Level 3: Statistics and Probability

3.13 Apply probability concepts in solving problems

(91585)
External 4 credits

This standard is derived from Achievement Objective S8.4, Investigate situations that involve elements of chance.

  • calculating probabilities of independent, combined and conditional events

Students should be able to:

  • Understand true probability vs model estimates vs experimental estimates
  • Randomness, independence mutually exclusive events, conditional probability
  • Probability distribution tables and graphs
  • Two way tables, probability tress, venn diagrams

This standard requires students to understand the relationship between true probability, model estimates, and experimental estimates.

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NZC Level 8, NCEA Level 3: Statistics and Probability

3.14 Apply probability distributions in solving problems

(91586)
External 4 credits

This standard is derived from Achievement Objective S8.4, Investigate situations that involve elements of chance.

  • calculating and interpreting expected values and standard deviations of discrete random variables
  • applying distributions such as the Poisson, binomial and normal

Methods are selected from those related to:

  • discrete and continuous probability distributions
  • mean and standard deviation of random variables
  • distribution of true probabilities versus distribution of model estimates of probabilities versus distribution of experimental estimates of probabilities.

Students should be able to calculate the mean and standard deviation from a plot of the distribution of a discrete random variable, linking probabilities and areas under density functions for continuous outcomes.

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NZC Level 8, NCEA Level 3: Statistics and Probability

Scholarship

(93201)
External

Scholarship Statistics candidates are expected to demonstrate high-level critical thinking, abstraction and generalisation, and to integrate, synthesise and apply knowledge, skills, understanding and ideas to complex situations.

The student will use knowledge of statistics to apply statistical and probability concepts and methods to complex problems in contexts which may be unfamiliar, interpret and, where appropriate, make inferences and clearly communicate concepts and findings.

     Applying and interpreting statistical and probability concepts and methods may involve:

  • exploring data
  • drawing on informed contextual knowledge
  • making inferences
  • dealing with sources and consequences of uncertainty
  • applying appropriate models
  • stating and evaluating assumptions of models used
  • explaining conceptions and processes (e.g. simulation-based processes)
  • critiquing based on the Problem-Plan-Data-Analysis-Conclusion (PPDAC) cycle
  • offering competing explanations and important follow-up questions
  • evaluating statistically based and / or probabilistically based reports

 * from the NZQA Statistics Performance Standard

Scholarship Statistics Specifications and Guides

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