STATISTICAL TESTS
The traditional approach is based on a number of statistical tests where every single test has its own formula and tests a very specific null-hypothesis. The approach of linear modelling works with first specifiying a linear model for the data. For the inference regarding statistical significance it is not important which approach is used. However, there are two main advantages of the linear model. First, the family of linear models is so large that you can test infinitely more hypotheses with a linear model than with a specially-designed test-statistic. Second, the syntaxes of SPSS and codes used in R all follow the same structure which makes it more accessible and understandable.
Linear model
At the University of Twente we encourage students to use linear models for their statistical analyses. Also we as the Methodology Shop would like to advise you to focus on linear models.
Generally, linear models follow the structure of y=b0 + b1x1 + b2x2 + ... + e. This is often recognized as a regression model which is one form of a linear model. By including categorical variables you can extend the model and cover ANOVA-type of analyses. The linear models themselves can also be extended to linear mixed models to model dependencies in the data, e.g. when you used repeated measures, clustered data, multilevel etc. Also, generalized linear models can be used to model non-numeric dependent variables, such as dichotomous (e.g. logistic regression) or when your data consist of counts (poisson regression).
BELOW YOU CAN FIND AN OVERVIEW OF WHAT IS THE BEST LINEAR APPROACH TO ANSWER YOUR RESEARCH QUESTION
To be able to choose the right approach you need to know what you dependent and independent variables are. You also need to know what type of variables you have (e.g. categorical, numerical etc.). Please write this down first and have a look at this overview afterwards.
The mentioned chapters refer to the following book.