Calculating Probable Error with a Correlation Coefficient of 0.8
Calculating the probable error involves determining the range within which the true value of a statistic is likely to lie. In the case of a correlation coefficient, the probable error provides an estimate of the reliability of the correlation.

Formula for Probable Error
The formula for calculating the probable error of a correlation coefficient is:
Probable Error = 0.6745 * (1 - r^2) / sqrt(n)
Where:
- r is the correlation coefficient
- n is the number of pairs of items in the sample

Given Values
In this scenario, the correlation coefficient is 0.8, and the sample consists of 25 pairs of items.

Calculation
Substitute the given values into the formula:
Probable Error = 0.6745 * (1 - 0.8^2) / sqrt(25)
Probable Error = 0.6745 * (1 - 0.64) / 5
Probable Error = 0.6745 * 0.36 / 5
Probable Error = 0.24282 / 5
Probable Error ≈ 0.0486
Therefore, the probable error for a correlation coefficient of 0.8 from a sample of 25 pairs of items is approximately 0.0486. This means that the true correlation coefficient is likely to fall within ±0.0486 of the observed value.