ANOVA, t-tests, and linear regression are three of the simplest statistical tests, and for the scope of this class, they will likely get you what you need. However, it's possible you might need more complex statistical tests. For example, what if you wanted to analyze the impact of both gender and international status on perception of the OMS program? What about interactions that you suspect will be non-linear, like the interaction between forum interactivity and class performance?

The following are three potentially useful classes of more advanced statistical analyses. To run these, you'll generally need a tool like SPSS or R, and you should see the section on available online statistics courses for more on how to use those. Note that even more powerful methods exist, but once you start looking at the more powerful methods, you're getting very close to performing machine learning.

A MANOVA, or Multivariate Analysis of Variance, evaluates whether multiple categories predict variance across some variable. For example, a MANVOA could tell us if there are interactions between gender and international status in predicting students' perception of the OMS program. Here are some sources on MANOVA:

- Multivariate Analysis of Variance (MANOVA), from Penn State University
- A Primer on Multivariate Analysis of Variance (MANOVA) for Behavioral Scientists, from Russell Warne of Utah Valley University
- MANOVA n R, from Quick-R

Linear regression attempts to find a linear interaction between one explanatory variable and one outcome variable. Multiple linear regression allows the same type of analysis, but with multiple explanatory variables. For example, perhaps class performance is a function of both time spent watching class videos and time spent interacting on Piazza: multiple linear regression would allow us to evaluate both of these together. Here are some sources on multiple linear regression:

- Multiple Linear Regression, from Penn State University
- Multiple Linear Regression, from Yale University
- Multiple Linear regression analysis using Microsoft Excel's data analysis toolpak and ANOVA Concepts (Video), from Knowledge Varsity

You might speculate that the interaction between study time and class performance is non-linear. After all, is the difference between 100 hours of studying and 101 going to be as significant as the difference between 0 hours and 1? Non-linear regression generalizes linear regression to apply not just to straight lines, but to any function, such as exponential and logarithmic functions. The mathematics are still the same, but the power introduced can be useful.

Here are some sources on non-linear regression:

- Getting started with nonlinear regression, from GraphPad Software
- Data Driven Fitting, from Loren Shure of MathWorks
- itting curves to data using nonlinear regression: a practical and nonmathematical review, from Harvey Motulsky and Lennary Ransnas of the University of California-San Diego

For more comprehensive information, see:

- Research Methods in Education (Chapter 20)

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