Advantages of interval over point estimation

A point estimate gives a single value (for example x̄ = 52) for an unknown parameter. An interval estimate gives a range (L, U) that contains the parameter with a stated confidence level, for example 95%.

Advantages of interval estimation

1. Shows the precision. The width of the interval tells how accurate the estimate is. A single number gives no idea of its error.
2. Includes the sampling error. A point estimate from a sample is almost never exactly equal to the parameter, since it changes from sample to sample. The interval allows for this variation through the standard error.
3. Gives a probability statement. The confidence level (90%, 95%, 99%) states how often such intervals will contain the true value. For a point estimate, the chance of being exactly right is nearly zero for a continuous variable.
4. Reliability can be chosen. The user may fix the confidence level and, by changing the sample size, control the width.
5. Helps decision making. One can check whether a claimed value lies inside the interval, which links directly to hypothesis testing.
6. Allows sample-size planning. The margin of error E = z·σ/√n can be used to find the n needed for a required accuracy.

Example

Take a sample of 16 with x̄ = 52 and a known σ = 4:

Point estimate:    x̄ = 52
Interval estimate: 52 ± 1.96 × (4/√16) = (50.04, 53.96)

The interval states the likely range of μ; the single value 52 does not.