Introduction to Communicating, Evaluating and Refining Findings
You have reached the final stage of the Statistical Enquiry Cycle! You have planned your investigation, collected your data, and processed your results into charts and averages. Now, it is time to wrap everything up. This stage is about two main things: telling your "story" to an audience and looking back to see if your methods were actually any good. In the exam, this is often where you earn AO3 marks by being critical of a statistical process.
1. Communicating Your Findings
Statistics is not just about numbers; it is about explaining what those numbers mean in the real world. When you communicate your findings, you need to be clear, concise, and aware of who is reading your report.
Audience Awareness
Who are you talking to? A scientific report for a group of experts will look very different from a poster for a primary school.
• Non-experts: Avoid heavy technical jargon and use clear, simple visualisations.
• Experts: Use precise statistical terms and include detailed measures like Standard Deviation (Higher Tier) or Interquartile Range.
Linking Back to the Hypothesis
Every investigation starts with a hypothesis (a statement you are testing). Your conclusion must explicitly state whether your results support or reject that hypothesis.
Example: If your hypothesis was "Students who eat breakfast have higher test scores," your conclusion should say, "The data supports this hypothesis because the mean score for the breakfast group was \(15\%\) higher than the non-breakfast group."
Key Takeaway:
Good communication should be evidence-based. Never just give an opinion; always point to a specific diagram or calculation you have made.
2. Evaluating the Investigation
This is the "detective" part of the cycle. You need to identify weaknesses in your investigation. No statistical study is perfect! To evaluate effectively, ask yourself these questions:
Is the Sample Reliable?
• Size: Was the sample size \(n\) large enough? A small sample might not represent the whole population.
• Bias: Did you use opportunity sampling? If you only asked your friends, your results are likely biased and don't represent everyone.
• Sampling Frame: Was everyone in the population actually available to be picked? If you did a phone survey but some people don't have phones, you have a problem!
Was the Data "Clean"?
Think back to when you collected the data. Were there outliers?
• Did you investigate if that extreme value was a recording error or a genuine piece of data?
• If you ignored missing data, did that change your results?
Are the Diagrams Appropriate?
Sometimes, we choose the wrong way to show data.
Example: Using a pie chart with \(20\) different categories makes it impossible to read. A bar chart would have been a better choice. Evaluating means admitting when a different diagram would have been clearer.
Quick Review: Common Weaknesses
• Leading Questions: "Don't you agree that..." (This forces a specific answer).
• Small Samples: Not enough data to spot a real trend.
• Extraneous Variables: Other things that might have affected the results (e.g., weather, time of day).
3. Refining the Process
Once you have found the weaknesses, you must suggest improvements. This is called "refining" the process. If you were to do the whole investigation again, what would you change?
Common Refinements include:
• Increasing Sample Size: "To improve reliability, I would collect data from \(200\) people instead of \(20\)."
• Changing Sampling Technique: "Instead of convenience sampling, I would use stratified random sampling to ensure all age groups are represented fairly."
• Redesigning Questionnaires: "I would use closed questions with tick boxes to make the data easier to group and analyse."
• Higher Tier - Controlling Variables: "I would use a matched pairs design to ensure the control group and experimental group are as similar as possible."
4. Comparing Results (Higher Tier Focus)
At the Higher Tier, you are expected to evaluate more complex measures. You might need to comment on:
• Skewness: If your data is positively skewed, is the mean still the best average to use? (Usually, the median is better if there is a heavy skew).
• Standard Deviation: If you have a large standard deviation \(\sigma\), your data is very spread out. This might mean your findings are less "consistent" than a set of data with a small standard deviation.
• Extrapolation: If you used a line of best fit to predict a value far outside your data range, you should evaluate this as a "danger" because the trend might not continue.
Key Takeaway:
Refining isn't just about saying "get more data." It's about explaining how that change would make your conclusion more valid or reliable.
Summary Checklist for the Exam
When you see a question asking you to "evaluate" or "critique" a statistical enquiry, check for these five things:
1. Hypothesis: Did they actually answer the question they started with?
2. Bias: Is the sample fair?
3. Reliability: Is the sample size big enough?
4. Accuracy: Were the calculations and diagrams done correctly (e.g., no distorted scales)?
5. Improvements: Give a specific, practical suggestion to fix a problem you found.