ANOVAtype tests involve comparing three or more cells, most commonly in rows of a table. They are conducted automatically when:
 ANOVAType Test is selected in in the Column comparisons settings of Statistical Assumptions.
 When appropriate data is selected when pressing (i.e., when conducting Planned Tests Of Statistical Significance). See Planned ANOVAType Tests.
 When using Smart Tables with a Numeric variable set by a Nominal variable set.
There are two basic variants of these tests:

Independent samples tests, which compare data between different subgroups. This is sometimes referred to as OneWay ANOVA and OneWay Layouts. In the software, these occur when you have
 The table has numeric data in the rows (i.e., Numeric or Numeric  Multi question in the brown dropdown).
 The table has mutually exclusive categories within spans in the columns (i.e., has no NETs).
 Repeated measures tests, where each respondent has provided multiple responses and these are to be compared (e.g., evaluations of different products). These are sometimes referred to as TwoWay ANOVA and TwoWay Layouts. In Q, these occur when you have a Nominal – Multi question selected in the blue dropdown menu with the variables appearing as the columns. (Where you wish to compare averages rather than categories, select STATISTICS > Below and Average.)
Additionally, whether the setting for Means in Statistical tests for categorical and numeric data is set to Nonparametric and the Structure of the question in the blue dropdown are also determinants of how the tests are computed, as described in the table below.
Independent samples  Dependent samples  

Not Nonparametric and the data in the rows is numeric (i.e., Numeric or Numeric  Multi)  FTest (ANOVA)  Repeated Measures ANOVA with Greenhouse & Geisser Epsilon Correction . 
Nonparametric and the data in the rows is numeric (i.e., Numeric or Numeric  Multi)  KruskalWallis Test  Friedman Test for Correlated Samples 
Nonparametric and the data in the rows is categorical (Nominal, BinaryMulti or BinaryMulti (Compact)  Pearson's ChiSquare Test of Independence  Cochran's Q 
Nonparametric and the data in the rows is mutually exclusive (e.g., choices on a rating scale)  Pearson's ChiSquare Test of Independence  ChiSquare Test for Compatibility of K Counts 