Planning an Enquiry (Edexcel GCSE Statistics)
Revision Note
Statistical Enquiry Cycle
What is the statistical enquiry cycle?
The process for statistical investigations in the real world is a cycle, known as the statistical enquiry cycle
Being a cycle means there is no simple ‘beginning’ and ‘end’
Instead the steps are repeated with improvements made each time
An ‘improve-repeat’ process like this is known as an iterative process
The statistical enquiry cycle is divided into five stages:
Hypothesis and Planning
Specify a hypothesis to be investigated
Plan what data to collect (and how it will be recorded)
Plan how you will process the data
Plan how the data will be represented (graphs, tables, diagrams, etc.)
Reasons should be given for each choice made in a plan
Collecting Data
Design data collection to minimise bias
Be aware of possible issues of sensitivity
Collect primary data using an appropriate method
Consider using secondary data (but only if it is reliable)
Processing and Representing Data
Organise the data and process it according to the plan
Clean the data if necessary
Create diagrams, etc., to represent the data
Calculate summary statistics to allow the data to be compared
Consider your target audience when presenting the data
Acknowledge any sources used (e.g. sources of secondary data)
Use technology where appropriate to save time and avoid errors
Interpreting Results
Interpret your summary statistics, and your diagrams, etc., in the context of the investigation
Draw conclusions that are related to the hypothesis
Make any appropriate inferences and predictions
Be sure to comment on the reliability of the results
Evaluating
Identify any possible issues with how the data was collected, processed and represented
Suggest improvements to deal with those issues
Reflect on how appropriate the data representation(s) were for the target audience
Repeat the process with improvements to investigate the hypothesis further
An exam question may directly mention one or more stages of the statistical enquiry cycle
But you should keep the statistical enquiry cycle process in mind when answering any exam question
Hypotheses & Constraints
What is a hypothesis and how can it be tested?
A hypothesis is a statement that you would like to test using statistics
For example, ‘As cars get older their annual maintenance cost is likely to go up’
A hypothesis should always be stated at the start of a statistical enquiry
Before any data is collected
Testing a hypothesis requires
Collecting valid and relevant data
Appropriate analysis of the data collected
What sort of constraints might affect a statistical investigation?
Constraints are practical limits that affect how an investigation may be conducted
You should try to anticipate these at the start of an investigation
And include them in your planning
‘Anticipate’ means try to think of what they might be ahead of time
Time
You may only have a limited amount of time for conducting the investigation
So you must plan an investigation that can be completed with the time available
Cost
The ‘best’ investigation might cost more than is available
You need to plan for the ‘best investigation you can afford’
Ethical Issues
You must always look out for the well-being of any participants in the investigation
Confidentiality
People may not be willing to reveal confidential (‘secret’) information
Any confidential information collected must be kept confidential
Sensitivity
People may be uncomfortable discussing sensitive topics
Who the data collector is, or how the data is collected, may affect this
Convenience
Some pieces or types of data might be hard to find or collect
What other issues might affect an investigation?
You should also try to anticipate issues that might arise during the statistical enquiry process
And think of proactive ways to deal with these
Being proactive means acting ahead of time, instead of only reacting once a problem has appeared
Some examples might be:
Difficulties identifying the population you want to study
People may not answer some or all of the questions asked
Some responses or outcomes of an experiment may be unexpected
Worked Example
Guillaume wants to investigate the amount of time students and teachers in his school spend listening to music.
He is going to write a plan for this investigation.
His hypothesis is
“The amount of time that students spend listening to music is greater
than the amount of time that teachers spend listening to music”.
Write down three other things he should include in his plan.
Explain why each of these things is appropriate.
You must refer to more than one stage of the statistical enquiry cycle.
A question like this doesn’t have a single ‘standard’ answer
To get full marks, the important things are to follow the directions in the question:
Make sure to write down three valid things that should be in his plan
Make sure to give an explanation for each of those things
Make sure to refer to more than one stage of the statistical enquiry cycle
An example from the ‘Collecting Data’ stage could be:
Guillaume should use random sampling to choose the students and teachers to include in his study. This will help reduce bias, because if he only chooses students and teachers he knows well they may have similar listening habits to him.
‘Collecting Data’ answers could also involve: what data to collect; how to collect and record the data; a strategy for processing the data; the importance of acknowledging sources for secondary data; identifying possible issues of sensitivity in collecting data
An example from the ‘Processing and Representing Data’ stage could be:
Guillaume should use box plots to represent the data. This allows easy visual comparison of the data for teachers and students, and also allows medians and interquartile ranges to be compared easily.
‘Processing and Representing Data’ answers could also involve: how to organise and/or process the data; what statistical measures will be calculated to compare the data
An example from the ‘Interpreting Results’ stage could be:
Guillaume should compare the medians and interquartile ranges for the students and teachers. The medians will show which group spends the higher average amount of time, and the interquartile ranges will show how spread out the results for the two groups are.
‘Interpreting Results’ answers could also involve: planning to make a prediction or an inference based on the results of the investigation
Possible answers from the ‘Evaluating’ stage could involve: planning to identify any weaknesses in the approach used or in the representations chosen; planning to improve the process in order to get a better sense of how valid the hypothesis is
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