if you have an ordinal scale consist of 4 categories and each category was given a score from 0 to 3, can we calculate the Mean and SD for this type of data? some studies present the data of this as a mean and SD, while others do not.
0 = no adhesive left on the tooth.
1 = less than half of the adhesive left on the tooth.
2 = more than half of the adhesive left on the tooth.
3 = all adhesive left on the tooth.
The ordinal scale does not assume that the distances from 0 to 1 and 1 to 2 (and so on) are equal. In addition, numbers other than what is stated in the category do not have any meaning (e.g. 1.5 does not mean anything). The most suitable measure for central tendency should be median or mode. When the mean is used, the assumption that the distances from 0 to 1 and 1 to 2 is applied.
In my opinion, it depends on how strict you are but I would use median and IQR.
Nattawut Leelakanok Thanks .. what is your opinion when dealing with a meta-analysis of ordinal data, what is your method? it can be meta-analyzed as continuous data if the authors expressed the results as a mean and SD?
Baraa Daraqel I have never done meta using ordinal data before. I also only use RevMan and Meta-analyst so I do not know if there are options for analyzing ordinal data out there. But if I were in the situation that you asked for, I would analyze the data as continuous. The hard part is the interpretation. For your example, if the mean score is 2.5 +/- 0.2, I do not know if this means more than 75% of the adhesive left. I would still say more than 50% left. However, if the data were pain scores or Likert scale (like to dislike etc), I would just assume that the data were continuous.
I'm waiting to see other opinion :)
Technically for ordinal data you cannot calculate the mean or sd. However, some people might convert the values to ranks and then calculate the mean and sd of the ranks. That is, if you classify your example data as 0, 1, 2, 3, then, yes, you could do these calculations on these rank classes. This may make sense in some cases.
Ordinal categories, even if labeled with numbers (e.g. 0, 1, 2, 3, etc.) cannot be meaningfully analyzed through descriptive statistics (such as mean, standard deviation and their transformations) unless there is some evidence that the categories represented are somewhat equally spaced along an implicit measurement scale. I too often encounter such mistakes made, even when it is evident that the categories are not equally spaced in a meaningful sense. I suggest resorting to alternative ways of summarizing data, using for example the median, the mode, or a bar chart.
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