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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.

Please pay attention to the remarks on formula and boundary conditions.
 GENERAL SPECIFICATIONS Population Size N: Sample Confidence Level: 80% (corresponds to k = 1.28) 90% (corresponds to k = 1.65) 95% (corresponds to k = 1.96) 98% (corresponds to k = 2.33) 99% (corresponds to k = 2.58) SPECIFICATIONS ON RATINGS Largest Dispersion About the Means: σ = 0.5 (2-step rating scale) σ = 1.0 (3-step rating scale) σ = 1.5 (4-step rating scale) σ = 2.0 (5-step rating scale) σ = 2.5 (6-step rating scale) σ = 3.0 (7-step rating scale) σ = 3.5 (8-step rating scale) σ = 4.0 (9-step rating scale) σ = 4.5 (10-step rating scale) Absolute Error of Means: e = ±0.05 e = ±0.10 e = ±0.15 e = ±0.20 e = ±0.25 CALCULATION Least Sample Size n: Creating an OMEP (=Orthoplan) (conjoint analysis)

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.

CALCULATING ORTHOGONAL MAIN-EFFECT PLANS
 Number of Values (factor 1): Number of Values (factor 2): Number of Values (factor 3): Number of Values (factor 4): Number of Values (factor 5):

 1st Combination of Factor Values: 2nd Combination of Factor Values: 3rd Combination of Factor Values: 4th Combination of Factor Values: 5th Combination of Factor Values: 6th Combination of Factor Values: 7th Combination of Factor Values: 8th Combination of Factor Values: 9th Combination of Factor Values: 10th Combination of Factor Values: 11th Combination of Factor Values: 12th Combination of Factor Values: 13th Combination of Factor Values: 14th Combination of Factor Values: 15th Combination of Factor Values: 16th Combination of Factor Values: 17th Combination of Factor Values: 18th Combination of Factor Values: 19th Combination of Factor Values: 20th Combination of Factor Values: 21st Combination of Factor Values: 22nd Combination of Factor Values: 23rd Combination of Factor Values: 24th Combination of Factor Values: 25th Combination of Factor Values: ColorPicker2400 (Individual Layout)

The "ColorPicker2400", that can be used for individual layouting your questionnaire, may be downloaded here as open source freeware (ZIP file, 7KB). Please note that the "ColorPicker2400" only functions within the Internet Explorer by Microsoft. 