In this thesis is analyzed two-way ANOVA model and there are also given some examples in psychology. Two-way ANOVA is used when you need to test the difference between two or more groups. The exact two-way ANOVA model is here built with applications of regression model which is based on projections. In the first chapter are given well known results and definitions. In the second chapter are basic regression properties which will be used. The Two-way ANOVA is a strong statistical test which easily can be used to draw conclusions, but the output of this test includes more tables which you first have to become acquainted with. This is done in the third chapter with illustrative example in psychology. It is an introduction to two-way ANOVA and it contains an intuitive approach to it’s basic features. The main concepts are factors, main effects, simple effects, interaction, orthogonal design and others. In the fourth chapter is introduced exact two-way ANOVA model. It is done separately for saturated and additive model. In the fifth chapter is given pratical example in psychology. Example is based on An experimental study of the effects of three instructional methods in basic probability and statistics. It is an 1974 article published in Journal for Research in Mathematical Education.