 # Confidence Intervals: The basics

## Confidence intervals and statistical significance

Confidence intervals consist of lower bounds (the lower value) and upper bounds (the larger value).

In Null Hypothesis Significance Testing (NHST), the usual null hypothesis states that there is no difference between two entities (people, groups, etc.).

H0: A = B

In biostatistics, this is usually expressed as a difference between A and B:

A – B = 0

Therefore, if the confidence interval includes zero, there is no statistically significant difference between the two. However, if both the lower and upper bounds of a confidence interval are on the same side of zero, the difference is statistically significant (Both lower and upper bounds must either be less than zero, or greater than zero).

Examples:

95% CI: -1 to +1 (Zero falls within bounds of the confidence interval, so this is not statistically significant)

95% CI: -2.3 to -1.4 (Both bounds are less than zero, so this is statistically significant)

95% CI: 1.5 to 3.2 (Both bounds are greater than zero, so this is statistically significant)

In epidemiology, the expression of H0: A = B is usually in the form of a ratio of A and B:

A/B = 1

Therefore, if the confidence interval includes one, there is no statistically significant difference between the two. However, if both the lower and upper bounds of a confidence interval are on the same side of one, the difference is statistically significant (Both lower and upper bounds must either be less than one, or greater than one).

Examples:

95% CI: 0.1 to 1.0 (The confidence interval includes one, so this is not statistically significant)

95% CI: 0.23 to 0.4 (Both bounds are less than one, so this is statistically significant)

95% CI: 1.5 to 3.2 (Both bounds are greater than one, so this is statistically significant)

You may have noticed that all values are non-negative. This is because the range of values for epidemiological measures of risk (like Risk Ratio, Rate Ratio, and Odds Ratio) lies between zero and (plus) infinity.

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