The effect size in this hypothetical trial (2.7 fewer infections per 1000 vaccinated) is slightly smaller than the effect size found in the real 2009 HIV vaccine trial (2.8 fewer infections per 1000 vaccinated); so why is the p-value smaller?
The hypothetical trial has less variability. The sample size of the hypothetical trial is larger. . The real trial did not follow a normal distribution. The real trial used an intention to treat analysis
To understand why the p-value is smaller in the hypothetical trial despite a slightly smaller effect size compared to the real trial, we need to consider several factors that can affect the p-value calculation.
1. Variability: The p-value calculation takes into account the variability or spread of the data. A smaller variability generally leads to a smaller p-value. In this case, you mentioned that the hypothetical trial has less variability, which means the data points are closer to the mean. This reduced variability can result in a smaller p-value, even if the effect size is slightly smaller.
2. Sample Size: The p-value calculation is also affected by the sample size. The larger the sample size, the more precise the estimate of the effect size and the more power the study has to detect a significant difference. In this case, you mentioned that the sample size of the hypothetical trial is larger. A larger sample size can increase the power of the statistical tests, resulting in a smaller p-value.
3. Distribution of Data: The assumption of a normal distribution is often necessary for some statistical tests. If the real trial did not follow a normal distribution, it could affect the calculation of the p-value. Different statistical tests may be needed to analyze data that deviates from normality. If the test used in the real trial was not appropriate for the data distribution, it could result in a larger p-value.
4. Intention to Treat Analysis: The analysis method used can also affect the p-value. In the case of the real trial, if it used an "intention to treat" analysis, it means that all participants were included in the analysis according to their assigned treatment regardless of whether they completed the treatment or not. This analysis approach can sometimes result in larger p-values compared to other analysis methods.
In summary, the smaller p-value in the hypothetical trial is likely due to factors like reduced variability, a larger sample size, and differences in the data distribution or analysis method used in the real trial. However, without more specific information, it's challenging to make a definitive conclusion.
The p-value is a measure of the strength of evidence against the null hypothesis in a statistical hypothesis test. A smaller p-value indicates stronger evidence against the null hypothesis, suggesting that the observed effect is unlikely to occur by chance.
In this case, if the effect size in the hypothetical trial is slightly smaller but the p-value is smaller, there could be several reasons for this:
1. Less Variability: The hypothetical trial may have less variability in the data compared to the real trial. When there is less variability in the data, it becomes easier to detect even small differences, leading to a smaller p-value.
2. Larger Sample Size: The hypothetical trial may have a larger sample size compared to the real trial. A larger sample size increases the statistical power of the test, making it more likely to detect even small effects and leading to a smaller p-value.
3. Distribution Assumptions: It is possible that the real trial did not meet the assumptions of a normal distribution. Most statistical tests assume that the data come from a normal distribution. If this assumption is violated, it can affect the p-value. The hypothetical trial may have met the assumption of a normal distribution, leading to a more accurate p-value.
4. Intention to Treat Analysis: The real trial may have used an intention to treat analysis, where participants are analyzed according to the treatment group they were assigned to, regardless of whether they actually received the treatment or not. This approach can introduce some variability and dilute the effect size. The hypothetical trial may have used a different analysis approach, such as per protocol analysis, which only includes participants who strictly followed the protocol. This could explain the difference in effect size and p-value.
It is important to consider these factors when interpreting the effect size and p-value differences between two trials.