The quantitative research method(s) that you set in your dissertation will depend on (a) the goals of your research, (b) the research design that you have set, (c) the route you are following, and the approach within that route, and (d) the relative advantages and disadvantages of the different research methods available to you. There are a number of research methods available when taking on a quantitative dissertation, including survey methods (i.e., questionnaires), structured interviews, structured observation, laboratory data and data sets. Unless you already understand the differences between these different quantitative research methods, we would recommend that you learn more about them now, including their advantages and disadvantages, in the Research Methods section of the Fundamentals part of Lærd Dissertation.
Even though you are likely to use just a single quantitative research method in your dissertation, it is important to understand the other research methods that could have been available to you. This is an important difference between dissertations and the main journal article you are interested in because of the way that dissertations are marked. After all, the main journal article is unlikely to discuss the different research methods that could have been used, and in some cases, even fully justify the choice of research methods that were used. By contrast, whilst this is not always the case, the marking scheme for the research strategy section of your dissertation tends to require you to (a) discuss the different research methods available to you, and (b) justify your choice of research method, taking into account the goals of your research, and the relative advantages and disadvantages of each research method (NOTE: In some cases, you will also be expected to take into account the different research methods used within the area of the literature that you are studying, since sometimes there is research to show that particular research methods are more effective within a given area than others, but this is more common at the doctoral level than the undergraduate or master's level). Before moving on, it is worth checking your dissertation guidelines to see if you are required to explain the different research methods available to you, including their relative advantages and disadvantages, in addition to justifying your chosen research method.
In order to select the most appropriate research method for your dissertation, start by thinking about the route you have chosen, and the approach within that route:
If you are pursuing Route A: Duplication, it is most likely that you will adopt the same research methods as those used in the main journal article for the same reason that you would adopt the same research design (i.e., the purpose of your dissertation is to duplicate the research strategy set in main journal article).
This is because one of the principals of replication-based dissertations (i.e., any Route #1: Replication-based dissertation) is the desire to compare the findings from your dissertation to those of the main journal article. Such comparisons are easiest and clearer when you can compare like-for-like results, which also requires you to collect like-for-like data. For example, if you were interested in examining the relationship between study time and exam performance, the differences in the scores on the dependent variable (i.e., exam performance), in relation to the independent variable (i.e., study time) would be clearest if the measures used to examine exam performance and study time were the same in your dissertation and the main journal article (e.g., if both your dissertation and the main journal article measured exam performance using a multi-choice questionnaire with the same questions, where students could score between 0-100 marks). That way, if the results from your dissertation and the main journal article are significantly different (e.g., the marks from your study were 15 points lower out of 100, and the results were statistically significant), you could be more confident in concluding that the findings from the main journal article could not be confirmed (i.e., could not be duplicated). As a result, the dependent variable (e.g., exam performance) may be explained by more than the independent variable (e.g., study time). Therefore, in terms of research methods, it would make sense that your dissertation and the main journal article used the same research methods (e.g., a multi-choice questionnaire with the same questions, where students could score between 0-100 marks).
If the reasons why these research methods were chosen are explained in the main journal article, this will help when it comes to the write up. However, if this is not the case, you still need to think about why such research methods were used in the main journal article and the appropriateness of such research methods.