Quantitative Analysis
Level of Significance — Explained Intuitively
The level of significance represents how much risk we are willing to take when rejecting the null hypothesis.
In simple terms, it answers this question:
How strong must the evidence be before we say the result is unlikely to be due to chance?
It reflects a tolerance for making a mistake, not a measure of confidence.
What the Level of Significance Really Means
The level of significance sets the maximum acceptable probability of rejecting a true null hypothesis.
If the result falls beyond this threshold, we reject the null hypothesis. If not, we do not.
This decision rule is chosen before looking at the data, which is a key exam point.
Why It Matters in Hypothesis Testing
Every statistical test involves uncertainty.
The level of significance controls the risk of a false positive—concluding that an effect exists when it actually does not.
In finance, false positives can lead to:
- incorrect trading strategies
- faulty risk conclusions
- misleading performance attribution
That is why this concept is central in CFA and FRM.
Trade-Off Involved
A lower level of significance:
- reduces false positives
- makes rejection harder
A higher level of significance:
- increases false positives
- makes rejection easier
This trade-off is frequently tested conceptually.
Commonly Used Levels
In practice, commonly used significance levels include low, moderate, and relatively higher thresholds depending on the cost of error.
The exact number matters less than understanding why one level is chosen over another.
Level of Significance vs Power
The level of significance and power address different risks.
- Level of significance controls false positives
- Power controls false negatives
Lowering the significance level generally reduces power, which creates a balance examiners often test.
Common Student Misunderstandings
Many students think the level of significance measures confidence. It does not.
Others believe a result slightly above the threshold is meaningless. It is not.
Some forget that the level is set before observing data.
These misunderstandings often appear in exam traps.
Final Insight
The level of significance is a rule for decision-making under uncertainty. It does not prove or disprove a hypothesis. It defines how cautious we are when interpreting evidence. For CFA and FRM preparation, understanding what this level controls—and what it does not—makes hypothesis testing questions far more intuitive.
