A state health department is designing a campaign to increase vaccination rates for a new flu strain. They want to test the effectiveness of different message framing strategies. They create two versions of a public service announcement (PSA):
PSA A (Gain-framed): “By getting vaccinated, you have a 95% chance of avoiding this new flu strain.”
PSA B (Loss-framed): “If you don’t get vaccinated, you have a 5% chance of contracting this new flu strain.”
The department conducts a randomized controlled trial with 1000 participants, evenly split between the two PSAs. After viewing the PSA, participants are asked about their intention to get vaccinated on a scale of 1-10 (1 being “Definitely will not” and 10 being “Definitely will”).
Results:
PSA A (n=500): Mean intention score = 7.2, Standard deviation = 1.8
PSA B (n=500): Mean intention score = 7.8, Standard deviation = 1.5
Additionally, they collect data on actual vaccination rates 3 months later:
PSA A group: 380 vaccinated
PSA B group: 410 vaccinated
1. Conduct a t-test to determine if there’s a statistically significant difference in intention scores between the two PSAs. Use a significance level of 0.05.
2. Calculate the 95% confidence interval for the difference in mean intention scores.
3. Compute the effect size (Cohen’s d) for the difference in intention scores.
4. Calculate the relative risk reduction in contracting the flu for those who viewed PSA B compared to PSA A, based on the actual vaccination rates.
5. Perform a chi-square test to determine if there’s a significant association between the PSA viewed and vaccination status.
6. Discuss potential explanations for any discrepancies between intention scores and actual vaccination rates.
7. Considering both the statistical results and ethical implications, which PSA would you recommend for a wider campaign? Justify your answer.
1. T-test for intention scores:
H₀: μA = μB
H₁: μA ≠ μB
t = (x̄A – x̄B) / √(s²A/nA + s²B/nB)
t = (7.2 – 7.8) / √((1.8²/500) + (1.5²/500))
t ≈ -5.77
Degrees of freedom: 998
Critical t-value (two-tailed, α=0.05) ≈ ±1.96
|t| > critical value, so we reject H₀. There is a statistically significant difference in intention scores.
2. 95% Confidence Interval:
CI = (x̄A – x̄B) ± t₀.₀₂₅ * √(s²A/nA + s²B/nB)
CI = (-0.6) ± 1.96 * √((1.8²/500) + (1.5²/500))
CI ≈ (-0.6) ± 0.204
CI ≈ (-0.804, -0.396)
3. Effect size (Cohen’s d):
d = (x̄A – x̄B) / √((s²A + s²B) / 2)
d = (7.2 – 7.8) / √((1.8² + 1.5²) / 2)
d ≈ -0.36 (small to medium effect)
4. Relative Risk Reduction:
Risk A = (500 – 380) / 500 = 0.24
Risk B = (500 – 410) / 500 = 0.18
RRR = (Risk A – Risk B) / Risk A = (0.24 – 0.18) / 0.24 ≈ 0.25 or 25%
5. Chi-square test:
Observed: [380, 120]
[410, 90]
Expected: [395, 105]
[395, 105]
χ² = Σ((O-E)²/E) ≈ 5.67
Degrees of freedom = 1
Critical value (α=0.05) ≈ 3.84
χ² > critical value, so we reject H₀. There is a significant association between PSA viewed and vaccination status.
6. Discrepancies explanation:
– Social desirability bias in self-reported intentions
– Intention-behavior gap
– External factors influencing actual vaccination behavior
– Potential differences in message recall over time
7. Recommendation:
Statistically, PSA B (loss-framed) appears more effective in both increasing intention and actual vaccination rates. However, ethical considerations include:
– Potential anxiety or fear induced by loss-framed messages
– Long-term effects of negative framing on public health communication
– Balancing effectiveness with transparency and trust
Recommendation: Use PSA B for the wider campaign, but monitor for any negative psychological impacts. Consider A/B testing in the wider campaign to confirm results in a larger, more diverse population.
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