Descriptive statistics can be thought of as summary statistics that describe data that has been collected. Descriptive statistics are almost always part of qualitative, quantitative, and mixed-methods research; you are probably familiar with common descriptive statistics such as the mean, the median, and the mode. Research that uses descriptive statistics alone with no inferential statistics, is not considered quantitative.
While descriptive statistics can be useful for summarizing data or providing context for collected data, they are different from inferential statistics, whose purpose allows inferences to be made by a researcher. Inferential statistical methods include the t-test, multiple regression, analysis of variance (ANOVA), etc.
"Statistics [are] divided into two categories: descriptive and inferential. The objective of descriptive statistics is to describe or summarize the properties of data that a researcher has collected. Inferential statistics [are] for inferring from a sample to a population."*
Remember: All quantitative studies must contain statistical analysis but not all studies that include statistics are quantitative by nature. It depends on the amount of data collected, the statistical analysis performed, and whether the author is describing/providing context versus making inferences based on data.
*Schreiber, J. B. (2008). Statistics. In L. M. Given, The SAGE Encyclopedia of Qualitative Research Methods. Sage Publications. Credo Reference.
