To determine which factor would tend to increase the likelihood of achieving statistical significance, let's analyze each option provided:
1. Weaker correlations (closer to 0):
- Weaker correlations imply that the relationship between two variables is less strong. When correlations are weaker, it is harder to distinguish any effect from random noise. This generally reduces the likelihood of finding statistically significant results.
- Conclusion: This factor tends to decrease the likelihood of statistical significance.
2. Larger sample size:
- A larger sample size increases the power of a statistical test. The power of a test is the likelihood that it will detect an effect if there is one to be found. With larger sample sizes, estimates of the population parameters become more precise, thus increasing the chances of detecting a true effect and achieving statistical significance.
- Conclusion: This factor tends to increase the likelihood of statistical significance.
3. If you had a more conservative threshold for significance (lower alpha level):
- A more conservative threshold for significance means a lower alpha level, such as moving from 0.05 to 0.01. This decreases the probability of committing a Type I error (false positive), making it harder to achieve statistical significance.
- Conclusion: This factor tends to decrease the likelihood of statistical significance.
4. All of the above would decrease statistical significance:
- This statement suggests that all the mentioned factors would reduce the likelihood of statistical significance. As discussed, both weaker correlations and a lower alpha level decrease the likelihood of statistical significance. However, a larger sample size increases the likelihood.
- Conclusion: This statement is not entirely correct since not all the factors listed would decrease the likelihood.
After analyzing all the options, we determine that the factor that would tend to increase the likelihood of statistical significance is:
Larger sample size
Thus, the correct choice is:
```2```
