Higher Applications of Mathematics

Writing up the statistical project

Structuring method, analysis and conclusion.

RStudio reference Project support Mixed quiz

Project support

Plan reports, conclusions and limitations.

Before you start

Know the statistical question you are trying to answer.
Check that variables are named clearly and measured in suitable units.
Be ready to write an interpretation, not just copy RStudio output.

Method chooser

Which RStudio method do I use?

Do you need to load a data file?

Use read.csv() and check the data frame.

Do you need averages or spread?

Use mean(), median(), sd() and summary().

Do you need to compare distributions?

Use boxplot() or hist().

Do you need to check a relationship between two variables?

Use plot() and cor().

Do you need a straight-line model?

Use lm() and interpret the gradient.

Are you estimating a population mean?

Use a confidence interval from t.test().

Are you testing a mean or paired data?

Use t.test(), with paired = TRUE for matched pairs.

Are you testing two proportions?

Use prop.test().

Are you writing the project conclusion?

State evidence, context and limitations clearly.

RStudio lesson

Key idea

This topic focuses on turning analysis into a clear report with evidence and limitations. A statistical report should connect the research question, data, displays, descriptive statistics, additional analysis and conclusion in a clear evidence trail.
Report structure is not an R command. Refer to genuine software commands only when explaining how a result or graph was produced, then interpret that output in context.

Report structure and skills

Report checklist: introduction, subjective impression, analysis and interpretation, conclusion, presentation and sources.
Link every graph, descriptive statistic and additional test to the research question.
Use headings and refer to the evidence in the body of the report.
Keep genuine R commands in code formatting only when documenting the analysis performed.

Technology output practice

Output interpretation preview

Read the simulated output, pick out the key value, then turn it into a written conclusion. This is a learning preview, not a real RStudio environment.

Context

Summary statistics output

A class compares journey times to a sports venue, measured in minutes.

Simulated output

> summary(travel$minutes)
Min.   1st Qu.   Median   Mean   3rd Qu.   Max.
18.0     26.0      30.5    31.4     36.0    48.0

> sd(travel$minutes)
[1] 6.8

Mean31.4

Median30.5

Standarddeviation 6.8

Mean

31.4 min

The average journey time in the sample.

Median

30.5 min

Half the journeys were shorter than this and half were longer.

Standard deviation

6.8 min

A typical spread from the mean; smaller would mean more consistent times.

What it means

The typical journey took just over 30 minutes. The standard deviation shows there was some variation, so one journey time should not be treated as exact for everyone.

What to write

The mean journey time was 31.4 minutes and the median was 30.5 minutes, so a typical journey was about 31 minutes. The standard deviation of 6.8 minutes shows the journey times varied by several minutes.

Weak answer: The standard deviation is 6.8, so the average is 6.8.

Watch out

Remember that standard deviation is not the average. It describes spread, not centre.

Which value would you quote to describe consistency?

Choose an option, then check the feedback.

Worked examples

Walkthrough 1

Plan the report structure

A pupil has completed their analysis and needs to organise an original statistical report.

State the research question and explain the data source and its robustness.
Organise graphical evidence, descriptive statistics and the chosen additional analysis.
Build a conclusion that connects all three forms of evidence and acknowledges limitations.

The report should read as one connected investigation, not as a list of commands or disconnected output.

Walkthrough 2

Read the output

RStudio has produced numerical or graphical output.

Find the key value, graph feature or p-value.
Check the unit and variable name.
Avoid copying every line of output into the conclusion.

A good project conclusion uses cautious evidence-based language.

Walkthrough 3

Write the interpretation

The result must be used in a project conclusion.

Start with a cautious phrase such as 'This suggests...'.
Refer to the context and variables.
Mention a limitation if the data set is small, biased or observational.

The conclusion should be clear, cautious and linked to evidence.

Watch out

Treating the report as a list of commands or pasted output.
Using a graph or statistic without explaining what it contributes to the research question.
Omitting the data source, sample size or discussion of robustness and bias.
Claiming causation from correlation.
Using strong language such as 'proves' when the data only suggests evidence.

Next step

Move into practice

Use the learning notes to read output tables carefully, then try varied summary, correlation, regression and test-output interpretation.

RStudio mixed quiz