difficult as the term 'validation' is extremely vague. In general the mean, sd and sample size are reasonable for reproduction and replication as mean (expected value) is statistically favorable. The median and mean combined, both provided as a way to asses the skew of the data. The 'correct' way is different based on the question. The together mean and media are a neutral choice. The 'correct' way would be to provide the data with the text. If someone would have wanted something else then he/she is freely capable of doing so.

Measure of central tendency to be used depends upon the type of data. Some measures of central tendency have already been developed each of which is suitable or valid for particular type(s) of data. Each of them has own domain of applicability and each of them has limitations.

If the type of data is made clear, it may be possible for obtaining a solution.

The best measure of central tendency to compare in a validating tool depends on the type of data,

1. Use mean if the data is symmetrical and continuous.

2• Use median if the data has outliers or is skewed.

3. Use mode for categorical or bimodal distributions.

In a validating tool, combining measures (e.g., reporting both the mean and median) often provides a more comprehensive understanding of central tendency, especially when distributions are not uniform. Pairing these with measures of spread (like standard deviation or interquartile range) is also critical for accurate comparisons.

The mean

I propose to compute mean, median and mode to measure the central tendency, then you should compare them:

- if they are equal, then you got the best case

- else you describe it by explaining each term and I think in this case the median has more meaningful

I like to mention again that measure of central tendency to be used depends upon the type of data. For a set of data of a particular type, only one measure is a suitable one. However, this may be one of the already discovered measures or may not be among these discovered measures. Note that number of type of data are not limited. Accordingly, number of measures of central tendency may not be limited. Only some measures have been discovered. Therefore, that measure is to be selected which is the most suitable among the available ones. Of course, this selected one may not be a perfect one.

In statistics mean, median, and mode are all used to have some idea about the distribution of data values. Hence, they are called "central tendency" measures. "Description of the validation of statistical tools" does not sound a very valid expression. The central tendency measures as some contributors also noted, are used to obtain some idea about the symmetry or skewness of the distribution of the data values. One can talk about the validation of the data, i.e. to check for extreme or incorrect values in the data set. But it's not correct to say validation of statistical tools. Maybe you can open up your question as to what you mean by validation, then it will be easier to contribute towards your difficulty.

I am validating a primary care assessment tool theoratically and statistically

After EFA , when adding the descriptive statistics of the dara set in which the tool was validating, i faced the confusion of having the mean or median

For validating tools, ensure the choice aligns with the goals of your analysis and the data characteristics.

Mean (Arithmetic Average), its best for Symmetric, continuous data with no extreme outliers because the mean provides a comprehensive summary of the data but is sensitive to outliers and skewed distributions. Example: Comparing average scores in a normally distributed dataset.

Median, its best for Skewed data or datasets with outliers since the median represents the middle value, making it more robust to extreme values. Example: Analyzing income data, where outliers (e.g., very high incomes) are common.

Mode, its best for Categorical or discrete data because the mode identifies the most frequent value, which can be more meaningful in non-numeric or categorical datasets. Example: Determining the most common product category in a dataset.

Recommendation:

Use mean for normally distributed, continuous data.

Use median for skewed data or when outliers are present.

Use mode for categorical data or to identify the most frequent value.

For ordinal data like Likert scales or Numeric Rating scales, addition of item scores is not meaningful and thus Mean (X) and Mean(Y) are not comparable. (Jamieson, 2004).

Suggestion: transform item scores to normally distributed data by method given by Chakrabartty and go ahed with mean.

References:

Jamieson, S.(2004). Likert scales: how to (ab) use them. Medical Education; 38, 1212-1218

Chakrabartty SN.(2022). Disability and Quality of Life. Health Science Journal, Vol. 16. No.12, 1 - 6 DOI: 10.36648/1791- 809X.16.12.989

Prof. Satyendra Nath Chakrabartty

Its the median. The mean is affected by outliers usually: the lowest value tends to make the mean smaller than usual while the largest outlier pulls the mean towards it.