Least Size of Simple Random Samplings (respondents management)

Here you may calculate the minimum number of needed respondents that should be selected by simple random sampling. The calculation corresponds to absolute errors of the means that arised from the frequently used rating scales.

An orthogonal main-effect plan (OMEP) enables a judgement sampling that selects seperate combinations from a great multitude of possible combinations of factor values in a multi-factorial survey design.
While a research object with, for example, four relevant factors and each with four imaginable values has 4x4x4x4=256 combinations, only 16 combinations that would be selected by using an OMEP could be sufficient for a survey including the calculation of statistical measures.

Both of the following conditions must be met at a respective sampling: all pairs that can be set up with the values of every two different factors have to be present at least once; and every factor value of the selected combinations may not be correlated with any other factor value (so-called orthogonal condition).
The foremost named condition also determines the minimum number of combinations to be selected (= number of all pairs that can be set up with those two factors having most of the values). Within large survey designs it might be necessary to select more combinations to meet the orthogonal condition too.

The algorithm used in the following OMEP calculation not only accounts for the two above named conditions, but also makes sure that no combination appears twice. Therefore, there is no guarantee that always the minimum number of combinations will be selected. Furthermore, the calculation is limited to survey designs with a maximum of 5 factors and a maximum of 5 values per each factor.