University learnersModel and challengeExample · 4 steps · 9 min

Regression or Illusion?

Read five weeks of quiz data, weigh wide against narrow intervals, separate association from cause and choose a study that could test the cause.

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Your example

Weekly quiz scores (mean of 40 students)

Week	Mean	95% interval
Week 1	51%	46–56%
Week 2	52%	47–57%
Week 3	54%	48–60%
Week 4	53%	48–58%
Week 5	57%	50–64%

Five weeks of mean quiz scores from 40 students: 51, 52, 54, 53 and 57 percent. The 95% intervals run from 46–56% in week 1 to 50–64% in week 5.

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What do the five weekly means show?

They rise every single week, without exception.They rise overall by about 6 points, with a dip in week 4.They stay flat, because the intervals overlap.

About this activity

What you practise: Reading a trend together with its uncertainty, telling association from causation and choosing a design that can test a cause.

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What do the five weekly means show? Five weeks of mean quiz scores from 40 students: 51, 52, 54, 53 and 57 percent. The 95% intervals run from 46–56% in week 1 to 50–64% in week 5. From 51% to 57% is a rise of 6 points. Week 4 dips slightly, so the rise is not perfectly steady.