Finding correct statistical test for my study So I have a study that I have carried out with 40 test subjects. The study consisted of reading two different texts using different methods and answering a number of questions corresponding to each text. Half the population read text $t_1$ using method $m_1$ and $t_2$ using method $m_2$. The other half read text $t_1$ using method $m_2$ and text $t_2$ using method $m_1$. 
I'm trying to figure out if there's any inherent difference in difficulty between the two texts, but I can't figure out which statistical test to use. It feels as if a paired t-test is wrong since the same person read the two texts using different methods, but I'm not really sure what else to use.
 A: IMO you since are doing comparisons between four different groups (results sets), an ANOVA (Analysis of Variance) approach would be the best approach.


*

*Analyse and look at your data, and remove any outliers first.

*Check if the all the assumptions for ANOVA have been satisfied. 
I will presume that the assumption of the dependent variable being normally distributed for each group is not satisfied (can be checked via anderson-darling test, and graphs of the data).


*Now you need to check for homogeneity of variances. One can do this via Levene's test.


$H_0: \sigma_1 = \sigma_2 = \sigma_3 = \sigma_4$
$H_1: \sigma_i \ne \sigma_j , i\ne j, i,j=(1,2,3,4)$
https://en.m.wikipedia.org/wiki/Levene%27s_test
After obtaining the results of Levene's test:
i. If any of the p-values are greater than or equal to $0.05$ then:


*

*$H_0$ is rejected and homogeneity of variances assumption is violated, as well as normality. 

*This would imply a nonparametric ANOVA is appropriate - such as Kruskal-Wallace. Software such as SAS, SPSS have this. MS Excel may have also.
https://en.m.wikipedia.org/wiki/Kruskal%E2%80%93Wallis_one-way_analysis_of_variance
Read section "Reasons to Use Parametric Tests" on http://blog.minitab.com/blog/adventures-in-statistics-2/choosing-between-a-nonparametric-test-and-a-parametric-test
If there are significant differences found between the 4 groups, you will need to do post adhoc comparisons for determining which of the four groups are significantly different from each other. Holm's t-test could be used for these.
ii. Otherwise if all p-values are less than $0.05$ then one can assume that $H_0$ is accepted - all variances of groups are the same. Then you would need to research which test to do next (with non-normal data, and equal variances).
