Do positive activities work? Effects and publication bias

Step 1 Warm-up recall

From M3.L2: what does a meta-analysis do, and what does a 95% confidence interval show?

Your answer

Private: nothing you type here is sent or stored.

Step 2 Learning goal

By the end of this lesson you can:

• state what Sin and Lyubomirsky (2009) pooled and found (Foundation);
• convert a correlation r to Cohen’s d (Core);
• explain publication bias and small-study effects, and why a later reanalysis found smaller effects (Core).

Step 3 A familiar example

Imagine fifty small baking contests. Winners boast; losers stay quiet. Someone who reads only the boasts will think recipes always win. Research has a quieter version of the same problem.

Step 4 Clear explanation

Positive activities are short, deliberate practices such as writing down things you are grateful for or doing kind acts. Sin and Lyubomirsky (2009) pooled 51 interventions with 4,266 individuals. They reported that these interventions significantly enhanced well-being (mean r = .29) and decreased depressive symptoms (mean r = .31).

Studies report effects in different units, so analysts convert them. The conversion from r to Cohen’s d is d = 2r ÷ √(1 − r²). For r = .29: 1 − 0.0841 = 0.9159, √0.9159 = 0.957, and d = 0.58 ÷ 0.957 ≈ 0.61, a medium-to-large effect on Cohen’s anchors.

Later work questioned the size. Publication bias means studies with striking results are more likely to be published, and small-study effects mean small studies can show bigger effects partly by chance and selection. White and colleagues (2019) reanalysed earlier meta-analyses of positive psychology interventions and concluded that the effects are much smaller than previously reported (the title of their paper).

Step 5 Worked example (4 marks)

A meta-analysis reports a mean correlation of r = 0.30 for a positive activity.

1. r² = 0.09 (1 mark).
2. 1 − r² = 0.91, and √0.91 ≈ 0.954. (1 mark)
3. d = 2 × 0.30 ÷ 0.954 = 0.60 ÷ 0.954 ≈ 0.63. (1 mark)
4. Before trusting it, ask whether small or unpublished studies are missing; a bias-corrected value could be much smaller. (1 mark)

Step 6 Learner practice (instant-marked)

Step 7 Recap

• Sin and Lyubomirsky (2009): 51 interventions, 4,266 individuals; mean r = .29 for well-being and .31 for depressive symptoms.
• d = 2r ÷ √(1 − r²).
• Publication bias and small-study effects can inflate pooled results.
• A later reanalysis (White and colleagues, 2019) found the effects much smaller than earlier reports.

Step 8 Exit ticket (ungraded)

Write one sentence you could responsibly say about the size of the effect of positive activities, given both the pooled result and the later reanalysis.

Your sentence

Private: nothing you type here is sent or stored.

Step 9 Go further (Extension)

Read the abstract of White, Uttl and Holder (2019) in PLoS ONE. Note which earlier meta-analyses they reanalysed and what corrected effect sizes they report.