Solved – How to bootstrap F-statistics in a repeated measures ANOVA

I have a repeated measures design. Each subject was tested in 2 conditions (RE, re) with different cognitive load levels (low, mid, high). I originally analysed this dataset using a repeated measures ANOVA (mu_N1 ~ lang*load + Error (subj/lang * load)). This is an unbalanced design, i.e. the number of observations per each cell is slightly different (e.g. subject "KOS" has fewer observations in "ER" and "low" than, say, subject "GRU").
Now I want to bootstrap F-statistics. The question is how do I resample the data? In the simple case of comparing the means of two samples (unpaired t-test), the bootstrap is straightforward: put all the observations into one pile, then take two random samples of the original size from that pile, compute t-statistic, repeat many times. With my data, there are "nested" levels (i.e. each subject was subjected to ER and re, and within RE and ER subjected to low, mid, high. Below is a rough slice of my data (disregard the column CLred). Would it be reasonable to leave the the order of columns "subj", "lang", "load" unchanged, but only reshuffle (resample with replacement) the numbers in column mu_N1 at each bootstrap resample?

`"subj" "lang" "CLred" "load" "mu_N1" "1" "KOS" "RE" 0.21077 "low" 2.039479 "2" "KOS" "RE" 0.50301 "mid" 7.050688 "3" "KOS" "RE" 0.50301 "mid" 6.321543 "4" "KOS" "RE" 0.30664 "low" -7.347104 "5" "KOS" "RE" 0.5031 "mid" 4.850391 "1412" "KOS" "er" 0.22893 "low" -3.867834 "1413" "KOS" "er" 0.77563 "mid" -2.939469 "1414" "KOS" "er" 1.1121 "mid" 17.26057 "1415" "KOS" "er" 1.669 "mid" -4.96131 "1416" "KOS" "er" 1.9141 "high" 11.5676 "1417" "KOS" "er" 1.3287 "mid" 2.687416 "1418" "KOS" "er" 1.2408 "mid" -9.099418 "6835" "GRU" "er" 4.0121 "mid" -9.006017 "6836" "GRU" "er" 4.4279 "mid" -18.26898 "6837" "GRU" "er" 4.782 "mid" -10.48242 "6838" "GRU" "er" 4.9231 "mid" 17.72892 "6839" "GRU" "er" 5.3071 "high" -7.620954 "6840" "GRU" "er" 5.7038 "high" 0.7890218 "6841" "GRU" "er" 6.4355 "high" 3.29691 "6842" "GRU" "er" 7.0723 "high" -7.693555 "7218" "GRU" "RE" 2.0459 "mid" 2.386349 "7219" "GRU" "RE" 2.3365 "mid" -3.752826 "7220" "GRU" "RE" 2.7053 "high" -0.5608671 "7221" "GRU" "RE" 2.7053 "high" -1.798806 "7222" "GRU" "RE" 1.8141 "mid" -2.58064 "7223" "GRU" "RE" 2.2764 "mid" 2.066321 "7224" "GRU" "RE" 2.2764 "mid" 2.385393 "7225" "GRU" "RE" 1.9051 "mid" 0.9645662 "7226" "GRU" "RE" 1.907 "mid" -3.036294 "7227" "GRU" "RE" 1.907 "mid" 1.307736 "26" "KOS" "RE" 0.42917 "mid" -5.46118 "27" "KOS" "RE" 0.22734 "low" -15.93142 "28" "KOS" "RE" 0.35941 "low" -11.60953 "29" "KOS" "RE" 0.62127 "mid" -16.10649 "30" "KOS" "RE" 0.62127 "mid" -4.435908`
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