# How to test whether teaching approach and gender affect spelling errors?

What is the most appropriate approach to analyse the effect that pedagogical approach used by a school system and student gender may have upon the types of spelling errors students make? I am looking at English speaking students. I am using a diagnostic spelling test that has 36 words represent four different types of spelling errors. The words are read aloud, students spell them.
The independent variables are gender and pedagogical approach. I have two schools. School A uses the standard approach and school B uses, for example, a Montessori approach. All of the students tested are in the same final year. I will be testing both boys and girls – most likely will not have equal sample sizes. So I will go to School A and give the spelling test. Repeat at School B. The schools use different pedagogical approaches and one separates boys and girls up to the final year. Therefore, I am interested to see if there is any difference due pedagogical approach in terms of type and frequency of errors made across the schools I am also interested to see if there is any gender differences with respect type and frequency of errors made within each school and ideally across the schools. Comparing boys and girls within the same school and across the schools. What test or test would you recommend?

• How many errors are usually expected for each participant? Do you have pre threatment results to compare your measurements to? – TinglTanglBob Jul 22 '18 at 10:14
• I do not expect any specific errors per se for each participant, just that the 34 words on the list elicit errors in four different areas. I am interested if their training leads to better performance in one area or another or are the errors distributed all over – thus no significant patterns. >Do you have pre-treatment results to compare your measurements to? I do not have any pre-treatment to compare to. I am using their English language placement score, all have 90% or higher and all have taken the same set of English classes for the 3 years prior. – Kate Jul 22 '18 at 11:52

model1 <- glm(number_of_spelling_errors ~ school * spelling_error_type * student_gender,

For obtaining mean values per each group and running post-hoc pairwise comparisons, as well as for selecting the most parsimonious model (it may be model1 or some simplified versions of it, either with less interactions between explanatory variables or with less explanatory variables altogether), see this page.