I've been looking for an introductory book in statistics and experiment design for a methods course for psychology students. I think I've been looking through at least 30 books and all go through the same old motions. Fist hypothesis testing, then t-test, Anova, two-Way Anova and ordinary least square regression. And all of them insist on explaining these models by tedious calculations. A t-test requires you to calculate a t-statistic, an Anova requires you to sum squares of this and that, regression instead is done my minimizing the squared error.
From my perspective I find it much easier and intuitive to understand these types of models from a likelihood perspective. For example, a t-test is the model $y \sim \text{Normal}(\beta_0 + \beta_1x,\sigma^2)$ and an Anova is $y \sim \text{Normal}(\beta_0 + \beta_1x_1 + \beta_2x_2 + \ldots,\sigma^2)$ where $x, x_1, x_2$ are dummy coded variables. To fit such a model one would then use, for example, maximum likelihood which I find intuitive and easy to explain. This kind formulation also makes the connection between a t-test, an ANOVA and regression trivial to understand.
So what I've been looking for an introductory book in statistics and experiment design that teaches statistics from this likelihood perspective. I would be very grateful for any suggestion!
