In research papers, the number of outliers is not typically included in the total sample size (n=x) unless specifically mentioned in the methodology or analysis. The sample size n usually refers to the number of valid observations in your dataset, excluding outliers. However, the handling of outliers (such as identifying, excluding, or reporting them) is usually described separately.
Here are some common practices regarding outliers in research papers:
Outliers Excluded from n: If outliers are excluded from analysis, the sample size presented (n=x) would generally refer to the number of observations after excluding the outliers. You would mention the number of outliers separately in the results or methodology section, and explain how they were determined and treated.
Outliers Included in n: In some cases, outliers may be included in the total sample size (n=x) if they are not removed or if their inclusion is part of the research focus. If outliers are included, it’s important to justify this choice in the methodology or discussion section.
Reporting Outliers Separately: If outliers are identified but not excluded, researchers often report how many outliers were found. For example, "Outliers were identified using the IQR method, and X number of outliers were found."
Statistical Treatment of Outliers: If statistical methods (e.g., robust statistics or transformations) are applied to account for outliers, these methods should also be discussed in the paper.
Example:
"The initial sample consisted of 100 participants, but 5 were identified as outliers using the Z-score method and were excluded from the analysis. Thus, the final sample size was 95 participants."
So, unless the outliers are part of the dataset's analysis, they are not typically included in the main n figure for the research paper.