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# Activity: I am just not fast enough

## Purpose

This activity is designed to lead to the conducting of an experiment using good experimental design principles. The experiment will look at the reaction times of a group of students who drink no coke and a group of students who drink sugar free coke or ‘normal’ coke. The students who do not drink coke are the control group and those who do drink it are the experimental group. The treatment is the drinking of the coke. It follows a discussion/evaluation of a statistically based report on New Zealand Youth Health Status (Ministry of Health NZ).

There are ethical issues that the teacher might consider in using coke as the treatment. Alternatives could be to have the treatment as “listening to music through headphones” or other possible attention distractors.

## Content knowledge

The content knowledge for this unit of work is likely to be unfamiliar to many teachers of statistics at this level (NZC level 8). Teachers should refer to the document provided on Census at School, which originate from the presentations for statistics teachers at the Auckland Statistics Day 2011. This provides links to the documentation and a download for iNZight, the software created for randomisation and bootstrapping processes.

## Achievement objectives

• S 8-1 Carry out investigations of phenomena, using the statistical inquiry cycle:
• A – Conducting experiments using experimental design principles.
• S 8-2 Make inferences from surveys and experiments:
• B – Using methods such as resampling or randomisation to assess the strength of evidence.
• S 8-3 Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies.

## Indicators

• Uses the statistical inquiry cycle.
• Conducts experiments using experimental design principles to find solutions to problems:
• Poses investigative questions using the statistical inquiry cycle.
• Defines and identifies variables that need to be accounted for in the experiment.
• Designs experiments, taking variability into account.
• Conducts experiments to generate data.
• Makes statistical inferences.
• Communicates findings:
• Support (or otherwise) for original hypothesis or conjecture.
• Appropriate graphs that relate to findings discussed in conclusion.
• Quantifies summary statistics to support (or otherwise) the conjecture.
• Population to which the findings can be generalised.
• Constraints of the experiment or survey within which the findings are valid.
• Alternative explanations.
• Evaluates all stages of the cycle:
• Specifies, justifies, and relates improvements (contextual or statistical) to the problem.

## Specific learning outcomes

Students will be able to:

• ask an investigative question that requires an experiment to be conducted
• plan an experiment using good experimental design principles
• categorise explanatory and response variables
• identify and act where appropriate on sources of variation
• conduct the experiment and record the data so that it may be used for future interpretation
• display the results of the experiment using appropriate methods and visual displays
• conduct any reanalysis of the data that might be appropriate.

## Diagnostic snapshot(s)

The report suggested as the starting point (Ministry of Health NZ) is a long study from the Ministry of Health (145 pages). There is a multitude of statistically based claims. Some focus on the effect on Maori youth. A selection of a few pages could be made that could lead to diagnostic activity where students discuss and interpret the claims made. It would be hoped that comments such as, “this section of the report contains evidence that the consumption of alcohol amongst NZ Youth has ….. the sample size of xyz means that we can be confident the claims are valid. However, the report is only valid for …” are made.

## Planned learning experiences

There are references in the report to slowing down of reaction time after intake of certain substances. The website below allows for testing of reaction times in a controlled, consistent manner between individuals and groups of students.

As an example, a possible question that could arise from the starting point is “will students who drink non-caffeine drinks have a different reaction time to those who do?” The drink here could be coke (treatment) and compared with no coke (control). Upon reflection of the results a further factor could be identified as sugar. Thus testing could be repeated comparing a drink with no sugar (for example coke zero) and no drink.

A suggested ‘order’ for the experiment to maintain as much as possible the element of good experimental design could be:

• Start of lesson every student does the chosen reaction time game to ascertain baseline data.
• The class is then randomly ‘split’ into two groups with one group conducting the reaction time game again having drunk nothing. The other group members drink a set amount of coke and then do the reaction time website activity again. The difference in each person’s results from the baseline data is then recorded. The distribution of differences for each group, treated and non-treated is displayed, probably through a box and whisker plot. (The effect of practice may have an impact but is negated since everyone in the class contributed to the baseline data and therefore had some practice).
• Students could be encouraged to reflect on the results discuss whether there is evidence for a difference between the two groups. They could also be prompted to discuss other factors which may have an impact on reaction time. Sugar but no caffeine could be identified and then the experiment could be repeated with the two groups’ reaction times tested. The members of each group here could be the same as before or randomised.

Coke consumption_data

• Randomisation can then be used (using iNZight) to ascertain the likelihood of the observed difference between the mean of the two groups occurring through chance alone. On the basis of this analysis a causal inference may, or may not, be made about the effect of the treatment.
• If students are unfamiliar with iNZight then the thinking behind this process could either be done using the material from Census at School or by manually doing the randomisation process using data cards identifying, for each person, their group and their difference in times.

### Possible adaptations to the activity

• The set up and order of the experiment could be altered. Coffee instead of coke or other could be used as the base caffeine VS non-caffeine drink. A more ethical approach could be taken by looking at the effect of distractors on reaction times: for example, vigorous exercise before the second test or listening to music on headphones whilst taking the second test.

• Many opportunities to link with physical education (for example, 3.1 Evaluate prior physical activity experiences to devise strategies for lifelong well-being) and health (for example, 3.1 Analyse a New Zealand health issue).

## Extension/enrichment ideas

• Students can have more ownership of the experiment to be conducted. Students should be encouraged to analyse their data at a much more complex level including the idea of randomisation.

## Planned assessment

This teaching and learning activity could lead towards assessment in the following achievement standards:

## Spotlight on

### Pedagogy

• E-learning and pedagogy:
• Using technology to explore concepts.
• Using tools such as software packages (for example GenStat and Fathom allow for resampling).
• Encouraging reflective thought and action:
• Engaging students in evaluating different methods and strategies.
• Encouraging students to fine-tune statistical thinking.

### Key competencies

• Thinking:
• Students hypothesise, investigate, analyse and evaluate.
• Students design investigations, explore and use patterns and relationships in data and they predict and envision outcomes.
• Using language, symbols and text:
• Students use statistical language to pose questions and communicate findings.
• Students use ICT appropriately. They capture their thought processes, recording and communicating mathematical ideas.

### Values

Students will be encouraged to value:

• innovation, inquiry, and curiosity, by thinking critically, creatively, and reflectively
• integrity, which involves being honest, responsible, and accountable and acting ethically.