Statistical Experiments and Design

A look at some experiments that address Achievement Standard AS91583 (3.11) Conduct an experiment to investigate a situation using experimental design principles.

DEREK SMITH

Te Tapuae o Rehua Consortium 

Mā te huruhuru ka rere te manu.

It is the feathers which enable the bird to fly.

Conduct an experiment to investigate a situation using experimental design principles

Achievement Achievement with Merit

Achievement with Excellence

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

Conduct an experiment to investigate a situation using experimental design principles, with justification.

Conduct an experiment to investigate a situation using experimental design principles, with statistical insight.

Explanatory Notes

This achievement standard is derived from Level 8 of The New Zealand Curriculum, Learning Media, Ministry of Education, 2007; and is related to the achievement objectives:

• 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

• Make inferences from surveys and experiments:– using methods such as randomisation to assess the strength of the

evidence

The process of investigating a situation by experiment using experimental design principles involves:

• posing an investigative question about a given experimental situation

• planning the experiment using experimental design principles– selecting experimental units– determining treatment and response variables– determining allocation of treatments to experimental units– determining data collection and recording methods– considering other sources of variation

• conducting the experiment– collecting data– recording any issues that arise

• selecting and using appropriate displays and summary statistics

• making an appropriate formal statistical inference• communicating findings in a conclusion.

Conditions of Assessment• Assessment of this standard involves an investigation which requires at

least two separate sessions: the first session for planning, then subsequent session(s) for data collection, analysis, and conclusions.

• Teachers need to allow time between the planning phase and the data collection and analysis/conclusion phases, so they can review student’s plans and to allow time for students to make minor adjustments to their plan in consultation with the teacher.

• Students can be provided with an experimental situation or may negotiate a suitable experimental situation with the teacher.

• Background information related to the experimental situation is to be provided to the student and the context should be familiar to students. This information should be provided in advance to allow student time to research the context.

• If the student has negotiated an experimental situation with the teacher the student needs to source background information for that situation.

• A further assessment opportunity needs to involve a new experimental situation.

Aspirin

THE FIRST RANDOMIZED TRIAL OF ASPIRIN FOR HEART ATTACK

Around 1969, Peter Elwood proposed a randomized controlled trial of aspirin in patients after heart attack (myocardial infarction).

When the trial had run its course there had been 47 deaths among patients taking aspirin and 61 among those taking placebo, but this difference was not statistically significant at conventional levels of significance.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1633560/

Findings

• The trial led us and others to set up and report further randomised controlled trials. In all of these, mortality was lower in the aspirin groups than in the placebo groups, but in none were these differences statistically significant. We found the consistency of the results of the six trials that were available impressive, and believed that they were virtually conclusive in support of aspirin.

• As a result of all this work, the beneficial effects of aspirin have probably been more conclusively established than those of any other drug.

Aspirin now used as a Therapeutic Agent in Cardiovascular Disease.

Experiment 1

Can you estimate 5 seconds

Experiment 2

Can you calculate efficiently

Concepts

• Question and Hypothesis • Experiment Design• Control and Subject groups (units)• Treatment-Response• Randomisation• Minimising other factors • Blocking and replication• Collecting, Recording, Calculating and Displaying• Statistical Inference• Conclusion and Findings

Investigative question

Asking a what if question ....

Or

Investigating a phenomenon...

Is it to investigate or a a comparison?

Comparison – treatment applied and observations made before and after between control and treatment groups to see the effect on the dependent variable.

This gives you an hypothesis.

Experimental Design

• What are the variables? Cause and effect (independent /explanatory and dependent/response)

• What is the treatment? Controlling the conditions

• Subjects/participants – experimental units• Confounding and lurking variables – may

influence the relationship between independent and dependent variables

• Rule out alternative explanations to the variable being investigated

• Minimising the variability of the treatment conditions

Control and Subject groups (experimental units)

• Control and comparison

- some influencing factors:

placebo and Hawthorne effects

use of single and double blind testing

• Random assigning units to groups and the order treatments are given – minimise other sources of variation affecting the experiment.

• Blocking

Confounding and lurking variables could interfere with the experiment and the outcome. Some of these maybe known and others known. For example soil variability when testing a new strain of strawberry plant.

Blocking is the process of placing the units into groups (blocks) which are similar in nature. Then the block can be randomised to receive the treatment.

• Replication

Taking repeated measurements from the experimental units

Recording collection and display of results

Paired dot plots

Stem and leaf

Box and whisker graphs

Bar graphs and histograms

Scattergraphs

Recording sheets for the participants to complete

Observational sheets for the observer to complete

Tables to record and collate the results

Summary statistics:

Mean, 5-point summary set, standard deviation

Causal inference

Paired dot plots

Stem and leaf

Box and whisker graphs

Bar graphs and histograms

Scattergraphs

Recording sheets for the participants to complete

Observational sheets for the observer to complete

Tables to record and collate the results

Summary statistics:

Mean, 5-point summary set, standard deviation

Causal inference is the process of drawing a conclusion about a causal connection based on the conditions of the occurrence of an effect applied in an experiment.

Causal inference

• A may be the cause of B.• B may be the cause of A.• some unknown third factor C may actually be the cause of both A

and B.• there may be a combination of the above three relationships. For

example, B may be the cause of A at the same time as A is the cause of B (contradicting that the only relationship between A and B is that A causes B).

• the "relationship" is a coincidence or so complex or indirect that it is more effectively called a coincidence (i.e. two events occurring at the same time that have no direct relationship to each other besides the fact that they are occurring at the same time).

Is it chance alone that could be a factor in the results and there is no difference?

• Use iNZight to illustrate this.

Randomisation Tests

Causal inference is the process of drawing a conclusion about a causal connection based on the conditions of the occurrence of an effect applied in an experiment.

Statistical inference

• Number of participants

• Shapes of distributions

• Confidence intervals: 2-S

Conclusion and findings

• What was the question again?

• Is there evidence to ...