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In order to compare the outcome for different clustering approaches and identify a number of clusters that is optimal in terms of cluster compactness and separation between the clusters, five validity indices are computed and aggregated by computing the sum of validity score ranks across all methods and numbers of clusters.
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The average sum of the content validity index for each item was of the MDHAQ-S was 0.94.
The MDHAQ-S was considered to be relevant since the average of the sum of the content validity index for each item was 0.94.
The items were considered to be relevant if the item-level CVI was >0.78 per item and the MDHAQ-S was considered to be relevant if the average of the sum of the content validity index for each item was > 0.90 [ 28, 33].
For a protocol to be considered valid, the sum of the responses on the Validity Scale must be less than or equal to 12, corresponding to all of the three items being scored as at most as four on the seven-point Osgood scale.
Unlike the work in [26] for two sum terms, the maximal regions of validity for our estimate of the unknown function are decided by boundaries of more than two planar regions.
ns P > 0.05, * P ≤ 0.05 and ** P ≤ 0.01 Both tests for validity (sum of square deviations, SSD, and raggedness index, RI) suggested that the mismatch distribution curves fitted significantly to the distribution under a model of population expansion (Table 2, see [additional file 3] for figures); however, there were clear differences in curve shape.
Although the Spanish version of the LTPAI and the PAWHI showed poor test retest reliability and poor construct validity, the sum of the two questionnaires showed much better associations.
In sum, Habermas's discourse theory aligns different types of validity claim with different types of justificatory discourse.
Each criteria had the same value or weighting, the sum of which was used as a validity score, calculated as a percentage of the maximum obtainable score.
We acknowledge that normally a diagnosis is made on the basis of a sum of observations with varying reliability and validity.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com