Testing for a Significant Correlation

Applies to: Pearson correlation test. It is also a good approximation for the non-parametric

Spearman correlation test.

Effect size: The correlation coefficient (r) you want to be able to detect.

Rule: You need

participants (pairs of values).

Imagine that you’re studying the association between weight and blood pressure, and you want the

correlation test to come out statistically significant if these two variables have a true correlation

coefficient of at least 0.2. Then you need to study

, or 200 participants.

Comparing Survival between Two Groups

Applies to: Log-rank test or Cox proportional-hazard regression.

Effect size: The hazard ratio (HR) you want to be able to detect.

Rule: The required total number of observed deaths/events

.

Here’s how the formula works out for several values of HR greater than 1:

Hazard Ratio Total Number of Events

1.1

3,523

1.2

963

1.3

465

1.4

283

1.5

195

1.75

102

2.0

67

2.5

38

3.0

27

Your enrollment must be large enough and your follow-up must be long enough to ensure that

the required number of events take place during the observation period. This may be difficult to

estimate beforehand as it involves considering recruitment rates, censoring rates, the shape of the

survival curve, and other factors difficult to forecast. Some research protocols provide only a

tentative estimate of the expected enrollment for planning, budgeting, and ethical purposes. Many

state that enrollment and/or follow-up will continue until the required number of events has been

observed. Even with ambiguity, it is important to follow conventions described in this book when

designing to avoid criticism for departing from good general principles.