The goal of the Certificate is to ensure that students have both a solid basis in Probability and Statistics as well as Inference and Quantitative Research Design, as well as some depth of experience in a more advanced topic area. As such, students completing the Certificate are required to take at least five courses. At least one course must be from the *Probability and Statistics *group of courses outlined below and at least one course must be from the *Inference and Quantitative Research Design *group of courses. In addition, students must take at least two courses from one of the three focus areas (*Longitudinal and Time Series Data Analysis, Multivariate and Machine Learning Analysis, Data Mining and Specialized Research Tools*), with both courses in the same focus area. The fifth course can be from any of the three focus areas or can be a second course from the Probability and Statistics group. Of note, some courses appear in more than one area, but a course can only be used to fill one of the requirements. In consultation with the certificate advisor, students may substitute equivalent coursework or more demanding mathematical treatments of the same course material. This Certificate is open to students enrolled in Ph.D. programs in the Arts & Sciences Social Science Departments, including the Ph.D. programs in Psychological & Brain Sciences, Economics, Political Science, Anthropology, and Education.

In addition, students can achieve credit for one of the courses listed below if they serve as the Assistant to the Instructor or Instructor in that class. Students should consult with Deanna Barch about the process for doing so, which involves signing up for a 3 credit “readings” graduate course in psychology (Psych 560/561).

**Probability and Statistics **(at least one)

- L33 5066 Quantitative Methods I
- L33 5067 Quantitative Methods II
- S50 5230 Applied Linear Modeling
- L32 581 Quantitative Methods I
- L32 582 Quantitative Methods II
- L48 5365 Problems in Applied Data Analysis
- L32 572 Quantitative Methods in Pol Analysis II: Linear Models (Generalized Linear Models)
- L11 508 Mathematics for Economics (Probability and Statistics Review)
- S90 6900 Applied Linear Regression Analysis

**Inference and Quantitative Research Design (**at least one, but no more than one for certificate)

- L32 5024 Causal Inference
- L33 5011 Research Designs and Methods
- L12 503 Foundations of Educational Research
- L24 420 Experimental Design (with graduate extension)

**Longitudinal and Time-Series Data Analysis **

- S90 6600 Multilevel and Longitudinal Modeling
- S90 6905 Propensity Score Analysis
- L33 5068 Hierarchical Linear Models
- B54 661 Analysis of Time Series Data
- M21 618 Survival Analysis
- L32 584 Multilevel Models in Quantitative Research
- L33 5165 Applied Longitudinal Data Analysis
- S90 6901 SEM class in the Brown School

**Multivariate and Machine Learning Analysis **

- L33 5012 Selected Topics in Design and Statistics
- L33 516 Applied Multivariate Analysis
- E81 517A Machine Learning
- L24 535 Topics in Combinatorics
- E81 514A Data Mining
- L24 470 Graph Theory (with graduate extension)
- S90 6901 Structural Equation Modeling
S90 6901 SEM class in the Brown School

**Data Mining and Specialized Research Tools **

- S65 5082 Foundations of Geographic Information System (GIS) for the Applied Social Sciences
- E81 514A Data Mining
- E81 517A Machine Learning
- M21 550 Introduction to Bioinformatics
- L24 459 Bayesian Statistics (with graduate extension)
- E81 316 Social Network Analysis (with graduate extension)
- S90 SWDT 5010 Social Network Analysis
- L11 5161 Applied Econometrics