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Difficulty: MediumStatistical Inference and Hypothesis Testing

A prospective cohort study is conducted to evaluate the association between a diet high in ultra-processed foods and the subsequent development of metabolic syndrome. Researchers follow 5,000 healthy adults over a 10-year period. At the conclusion of the study, they compare the incidence of metabolic syndrome between participants in the highest quartile of ultra-processed food consumption and those in the lowest quartile. The analysis yields a relative risk (RR) of 1.451.45 with a 95% confidence interval of [0.92,2.15][0.92, 2.15]. Which of the following is the most accurate statistical interpretation of these findings?

  1. The findings fail to reject the null hypothesis, indicating that the pp-value for this association is greater than 0.05.Answer
  2. B
    The results demonstrate a statistically significant increased risk of metabolic syndrome because the confidence interval does not cross zero.
  3. C
    There is a 95% probability that the true population relative risk falls precisely between 0.92 and 2.15.
  4. D
    The width of the confidence interval indicates that the association is primarily driven by effect modification.
  5. E
    An independent two-sample t-test is the most appropriate method to calculate this specific confidence interval.

Answer

The findings fail to reject the null hypothesis, indicating that the pp-value for this association is greater than 0.05.
The study reports a 95% confidence interval (CI) for a Relative Risk (RR). Because a relative risk is a ratio, the null hypothesis (indicating no difference in risk between groups) is a value of 1.0. The reported 95% CI is [0.92,2.15][0.92, 2.15], which encompasses 1.0. Therefore, the results are not statistically significant at an alpha level of 0.05. This directly implies that the researchers fail to reject the null hypothesis, and the corresponding pp-value is greater than 0.05.

Step-by-Step Solution

1
Identify the reported statistical measure.
The study reports a Relative Risk (RR) of 1.45.
Recognizing the measure type is essential to identify the correct null value.
2
Determine the null hypothesis value for this measure.
For any ratio measure (RR, Odds Ratio, Hazard Ratio), the null value representing no association is 1.0.
A ratio of 1.0 means the risk in the exposed group equals the risk in the unexposed group.
3
Evaluate the 95% Confidence Interval (CI) against the null value.
The reported 95% CI is [0.92, 2.15]. This interval includes the null value of 1.0.
If a 95% CI includes the null value, the observed result could plausibly be due to chance.
4
Interpret the statistical significance and pp-value.
Because the CI includes 1.0, the association is not statistically significant at α=0.05\alpha = 0.05, meaning the null hypothesis cannot be rejected and the pp-value must be >0.05> 0.05.
Confidence intervals and pp-values are mathematically related; a 95% CI crossing the null corresponds to p>0.05p > 0.05.

Key Concept

Interpreting Confidence Intervals for Ratio Measures
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Topics

Statistical Inference and Hypothesis Testing

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