The minimum number of units in an experimental design, there are mainly nine factors that are responsible for determining the number of replications.

- The extent of precision required
- Heterogeneity of experimental material
- Availability of resources
- Size of experimental units
- Required degrees of freedom of experimental error
- The relative cost of experimental units
- The number and nature of the treatments
- The fraction to be sampled
- The extent and nature of competition among experimental units

Precision means, if the differences between treatment means are expected to be large, then a low degree of precision is required.

Hence a small number of replications is required otherwise large number of replications is required.

If the experimental units are heterogeneous, a greater number of replications are required.

Even if many resources or experimental units are at the disposal of the investigator, one cannot take too many replications unnecessarily.

When the cost per unit is high, one would like to take a minimum number of replications and if low, a large number of replications prefer.

The reduction in experimental error provides a smaller standard error for a treatment.

As a general rule, the more is the number of replications, the better it is. But the problem is to decide the minimum number of units in an experimental design.

## Formula

According to R A Fischer amount of information available from the experimental data is given by the formula,

[(n+1)/(n+3)]*(1/s2)

s2 is estimate of the error variance based on n degrees of freedom.

Whereas, if the error variance sigma square is known, the information is equal to 1/sigma square.

The coefficient of 1/s2 increases rapidly as the value of n increases from 1 to 11 but stabilizes to a great extent when n reaches 12 or more.

## Conclusion

To have stable information to get from experimental design minimum **12 number of** **degrees of freedom** is required. Based on which statistical method you are applying according to n will change.

Sample Size Calculation Formula