Higher Applications of Mathematics

z-tests for two proportions

Comparing proportions using a z-test.

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 comparing proportions from two groups. In Higher Applications, RStudio is used as a practical tool to calculate, graph and test ideas from data.
A strong answer shows what command was used, what output was produced, and what that output means in context. Use careful language such as 'This suggests...' or 'There is evidence to suggest...'.

Key commands and skills

prop.test(c(success1, success2), c(total1, total2))
names(data)
summary(data)
Use comments in scripts with # to explain your steps.

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

Hypothesis test output

A paired test compares typing speeds in words per minute for 18 volunteers before and after a short training session. There is no control group. Differences are after minus before, with sample mean 4.82 and standard error 2.00 words per minute.

Simulated output

> t.test(after, before, paired = TRUE)
t = 2.41, df = 17, p-value = 0.028
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
  0.6004  9.0396
sample estimates:
mean difference
  4.82

At the 5% level, what should you decide from p = 0.028?

Choose an option, then check the feedback.

Worked examples

Walkthrough 1

Run the command

A pupil is using RStudio for comparing proportions from two groups with a small school-friendly data set.

Load or identify the data frame.
Check the exact column names with names(data).
Run the key command: prop.test(c(success1, success2), c(total1, total2))

The output should be checked against the variables and the original question.

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.

The output tests whether there is evidence that the two proportions differ.

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

Misspelling a data frame or column name.
Forgetting brackets or quotation marks in a command.
Copying output without explaining what it means.
Claiming causation from correlation.
Using strong language such as 'proves' when the data only suggests evidence.

Statistics connection

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