I used the following materials when I taught Statistics 614 (Statistical Methods) in Fall 2018 at American University.
This course was designed for non-statistics graduate students who would need to use statistical methods in preparation of their master’s theses. Most of these students had very little (or no) statistics prior to this course, so I focused a great deal on the fundamentals of inference before introducing ANOVA and linear regression.
I used the fantastic textbook The Statistical Sleuth. I think this is the greatest treatment of statistical methods from a non-mathematical perspective that I have read. The authors introduce all methods using interesting examples and focus on statistical intuition, using only as much mathematics as is needed to understand the concepts (but no more). Their suggestions are practical, their reasoning is intuitive, and their writing is clear.