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Text of the page (random words):
ing trials is the number of times you want to test each sample size higher values for trials are slower but make the results more reliable i suggest starting with 100 or 1000 for exploratory purposes and then going to 10 000 once you re pretty sure you have a good value and want to confirm it the arithmetic is much simpler if you stick with powers of ten nrange is a vector of values you want to test out note that the z value for your pilot gives you a hint if it s about 2 you should try values similar to those in the pilot if it s much smaller than 2 you should try values much bigger trials 1000 how many resamples per sample size nrange c 50 60 70 80 90 100 values of sample size to test set up resampled data do the regressions and store the results this is the main part of the script it creates the resampled datasets in a list called dflist the list is initialized empty and dataframes are stored in the list as they are generated store z scores and sample size in matrix results dflist list k 1 this object keeps track of which row of the results object to write to results matrix nrow length nrange trials ncol 3 data frame adjust ncol value to be length as vector z_emp 1 colnames results c int treatment n replace the vector with names for as vector z_emp positions followed by n the nanes need not match the names in the regression table but should capture the same concepts for i in 1 length nrange dflist i list for j in 1 trials dflist i j sample_n pilot_small size nrange i replace t est glm outcome treatment data dflist i j family binomial summary adjust the estimation to be similar to whatever you did in the test estimation block of code just using data dflist i j instead of data pilot z est coefficients 3 you may need to tweak this line if not using glm results k c as vector z nrange i k k 1 create vector summarizing each resample as significant 1 or not significant 0 results treatment stars 0 results treatment stars abs results treatment 1 96 1 interpret results dist of z by sample size as an optional first step plot the distributions of z scores across resamples by sample size results ggplot mapping aes x treatment geom_density alpha 0 4 theme_classic facet_wrap n number of significant resamples for treatment effect next make a table for what you really want to know which is how often resamples of a given sample size gives you statistical significance this rate can be interpreted as power table results n results treatment stars 0 1 50 355 645 60 252 748 70 195 805 80 137 863 90 105 895 100 66 934 as you can see n 70 seems to give about 80 power to confirm this and get a more precise value you d probably want to run the script again but this time with nrange c 67 68 69 70 71 72 73 and trials 10000 stratified samples 50 50 strata common for rfts note that you can modify the approach slightly to have stratified resamples for instance you might want to ensure an equal number of treatment and outcome cases in each resample to mirror a 50 50 random assignment design this should mostly be an issue for relatively small resamples as for large resamples you are likely to get very close to the ratio in the pilot test just by chance to do this we modify the algorithm by first splitting the pilot data into treatment and control data frames and then sampling separately from each before recombining but otherwise using the same approach as before pilot_control pilot_small filter treatment 0 pilot_treatment pilot_small filter treatment 1 trials_5050 1000 how many resamples per sample size nrange_5050 c 50 60 70 80 90 100 values of sample size to test nrange_5050 2 round nrange_5050 2 ensure all values of nrange are even dflist_5050 list k 1 this object keeps track of which row of the results object to write to results_5050 matrix nrow length nrange_5050 trials_5050 ncol 3 data frame adjust ncol value to be length as vector z_emp 1 colnames results_5050 c int treatment n replace the vector with names for as vector z_emp positions followed by n the nanes need not match the names in the regression table but should capture the same concepts for i in 1 length nrange_5050 dflist_5050 i list for j in 1 trials_5050 dflist_5050 i j rbind sample_n pilot_control size nrange_5050 i 2 replace t sample_n pilot_treatment size nrange_5050 i 2 replace t est glm outcome treatment data dflist_5050 i j family binomial summary z est coefficients 3 results_5050 k c as vector z nrange_5050 i k k 1 results_5050 treatment stars 0 results_5050 treatment stars abs results_5050 treatment 1 96 1 number of significant resamples for treatment effect with 50 50 strata table results_5050 n results_5050 treatment stars 0 1 50 330 670 60 248 752 70 201 799 80 141 859 90 91 909 100 63 937 not surprisingly our 80 power estimate is still about 70 one fixed strata and the other estimated or perhaps you know the size of a sample in one strata and want to test the necessary size of another strata perhaps a power analysis for a hypothesis specific to strata one gives n 1 as its necessary sample size but you want to estimate a power analysis for a pooled sample where n n 1 n 2 likewise you may wish to estimate the necessary size of an oversample note that if you already have one strata in hand you could modify this code to work but should just use the data for that strata not resamples of it for one fixed and one estimated strata let s assume our pilot test is departments a and b from the ucbadmissions file that we know we need n 500 for 80 power on some hypothesis specific to department a and we are trying to determine how many we need for department b in order to pool and analyze them together i specify dummies for gender male and a dummy for department a vs b ucb_tidy ucbadmissions as_tibble uncount mutate male gender male admitted admit admitted select male admitted dept ucb_a ucb_tidy filter dept a mutate depa 1 ucb_b ucb_tidy filter dept b mutate depa 0 n_a 500 trials_b 1000 how many resamples per sample size nrange_b c 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 values of sample size to test dflist_b list k 1 this object keeps track of which row of the results object to write to results_b matrix nrow length nrange_b trials_b ncol 4 data frame adjust ncol value to be length as vector z_emp 1 colnames results_b c int male depa n replace the vector with names for as vector z_emp positions followed by n the nanes need not match the names in the regression table but should capture the same concepts for i in 1 length nrange_b dflist_b i list for j in 1 trials_b dflist_b i j rbind sample_n ucb_b size nrange_b i replace t sample_n ucb_a size n_a replace t est glm admitted male depa data dflist_b i j family binomial summary z est coefficients 3 results_b k c as vector z nrange_b i k k 1 add dummy for dept results_b male stars 0 results_b male stars abs results_b male 1 96 1 number of significant resamples for gender effect with unbalanced strata table results_b n results_b male stars 0 1 50 108 892 100 132 868 150 128 872 200 120 880 250 144 856 300 133 867 350 153 847 400 194 806 450 181 819 500 159 841 550 186 814 600 168 832 650 185 815 700 197 803 750 201 799 800 194 806 850 191 809 900 209 791 950 183 817 1000 214 786 this reveals a tricky pattern we see about 90 power when there are either 50 or 100 cases from department b i e 550 600 total including the 500 from department a with trials_b 1000 it s a bit noisy but still apparent that the power drops as we add cases from b and then rises again along a u shaped curve normally you d expect that more sample size would mean more statistical power because standard error is inversely proportional to the square root of degrees of freedom the trick is that this assumes nothing happens to β as it happens ucbadmissions is a famous example of simpson s paradox and specifically the gender effects are much stronger for department a glm admitted male data ucb_a family binomial summary call glm formula admitted male family binomial data ucb_a deviance residuals min 1q median 3q max 1 8642 1 3922 0 9768 0 9768 0 9768 coefficients estimate std error z value pr z intercept 1 5442 0 2527 6 110 9 94e 10 maletrue 1 0521 0 2627 4 005 6 21e 05 signif codes 0 0 001 0 01 0 05 0 1 1 dispersion parameter for binomial family taken to be 1 null deviance 1214 7 on 932 degrees of freedom residual deviance 1195 7 on 931 degrees of freedom aic 1199 7 number of fisher scoring iterations 4 than the gender effects are for department b glm admitted male data ucb_b family binomial summary call glm formula admitted male family binomial data ucb_b deviance residuals min 1q median 3q max 1 5096 1 4108 0 9607 0 9607 0 9607 coefficients estimate std error z value pr z intercept 0 7538 0 4287 1 758 0 0787 maletrue 0 2200 0 4376 0 503 0 6151 signif codes 0 0 001 0 01 0 05 0 1 1 dispersion parameter for binomial family taken to be 1 null deviance 769 42 on 584 degrees of freedom residual deviance 769 16 on 583 degrees of freedom aic 773 16 number of fisher scoring iterations 4 specifically department a strongly prefers to admit women whereas department b has only a weak preference for admitting women the pooled model has a dummy to account for department a generally being much less selective than department b but it tacitly assumes that the gender effect is the same as it has no interaction effect this means that as we increase the size of the department b resample we re effectively flattening the gender slope through compositional shifts towards department b and its weaker preference for women december 3 2021 at 2 14 pm gr dungeon crawling together i ve been reading a lot of osr games and they remind me a lot of the traditionalist phase of the genre trajectory model from lena and peterson s 2008 asr and lena s book banding together osr games are attempts to recreate dungeons and dragons as it was played in the 1970s often by using the ogl think creative commons or gpl for the 2000s version of the game but then changing the rules to be more like 1970s d d for instance here is the first two sentences to labyrinth lord labyrinth lord is not new or innovative this game exists solely as an attempt to help breathe back life into old school fantasy gaming to do some small part in expanding its fan base and here is the start of the intro to swords and wizardry in 1974 gary gygax 1938 2008 and dave arneson 1947 2009 wrote the world s first fantasy role playing game a simple and very flexible set of rules that launched an entirely new genre of gaming unfortunately the original rules are no longer in print even in electronic format the books themselves are becoming more expensive by the day since they are now collector items indeed there is a very good chance that the original game could effectively disappear that s why this game is published when you play swords wizardry you are using those original rules the intro to the first edition of osric basically says we don t expect you to actually play with this book but with your old copies of the 1978 ad d edition however we are writing this so you can create new content ad d compatible content without getting sued the games vary in whether they are attempting to recreate a very specific edition of d d eg ose is a retro clone of the 1981 b x moldvay edition swords and wizardry is a retro clone of the od d 1974 edition osric is a retro clone of ad d from 1978 etc take the overall feel of 1970s d d while using some rules that were invented much later eg basic fantasy rpg five torches deep labyrinth lord put a distinct twist on the game whether that s distinctive new rules dungeon crawl classics a more metal version of the game eg lamentations of the flame princess mork borg or change the genre of story entirely mecha hack mothership mutant crawl classics approach 2 seemed to dominate early on in part for the practical reason that people didn t know how far they could push the ogl but more recent games tend to follow approach 1 or 3 anyway osr is a traditionalist stage but you can trace the whole game back and see all the stages avant garde dave arneson and gary gygax inventing the game as an oral tradition in midwestern wargaming circles scenes the publication of od d and a distinctive split between the game as played by midwest wargamers who had access to the oral tradition and caltech students who only had the incomprehensible published rules and so had to improvise coming up with an unofficial addendum called warlock which later influenced the published rules in part because the first revised edition of the official rules was by a californian industry an explosion of sales in the late 1970s and early 1980s including tie ins to other media tradition osr community beginning c 2008 anyway this could be a dissertation topic for some grad student but this seems like an obvious mesearch trap and i am always of the opinion that research is not worth doing if it only says case x which i care about for reasons other than theory fits theory y rather research ought to say case x fits theory y in a way that suggests novel twist z and i m not yet sure if there s a novel twist here yet that leads us to reconceptualize lena s theory of creative communities rather than just saying yup as expected rpgs are a creative community just like music if you find that twist email me and let me know what you re doing with it november 21 2021 at 1 01 pm gr some notes on online teaching i spent basically all of spring quarter working on advice for colleagues as to how to teach online in fall quarter i actually did it myself and it was a different experience than the theoretical one i had a huge learning curve over the course of the quarter such a big one that if i ever do another online quarter i am probably re recording most of my lectures even though as you ll see recording and editing them was a ton of work anyway here are my notes and reflections on my first term of online teaching making the videos the single biggest lesson is that online teaching is far more work than regular teaching there s always a lot of work answering emails rewriting exams etc but in traditional teaching for an existing prep the actual lecture is just printing out my notes trying to remember my microphone and hdmi dongle and standing in front of an auditorium for two hours and change per week i get the lecture hall 75 minutes twice a week for ten weeks so that s about 25 hours of lecture per quarter and maybe add an hour or two total for walking to the hall and printing out the notes so about 27 hours spent lecturing per class per quarter i spent almost that much time per class per week of instruction on the lectures that is i spent almost ten times more time on recording lectures in fall quarter than i usually do delivering lectures and this is on top of the usual amount of work for emails office hours etc actually i spent more time than usual on this stuff but not absurdly more if you think i m exaggerating or you re wondering how i fo...
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