First, let's just see if the question responses are the same or different for each class. Load each class $($probably with a loop$)$ and use the different ANOVA tests $($ANOVA$,$ Alexander Govern, and Kurskal$)$ for all $9$ questions in each class. Do any of the classes

have significant results $($p

b$)$ In class we saw an example of including the discrete error correction for Welch's t$-$ test by using random trials for many test and averaging the resulting p$-$values. Extend this to the ANOVA testing $($ANOVA$,$ Alexander Govern, and Kurskal$)$ trials. Then run the

responses for each class through. How do the new $($average$)$ p$-$values compare to the p$-$values from part a$)?$

c$)$ We'd also like to know if there are differences between classes. There's three ways I

cna think to do this. One would be to take all the responses to all the questions for each class and do and ANOVA for the $5$ classes. But the problem is the respones in each class aren't independant, so lumping them together isn't really valid. $($So don't do this.$)$ A second was is to treat the respones to each question as a data set $($so you have $5*9=45$ data sets$)$ and do a big ANOVA $($etc$.)$ on all of them. Give this a try, using the methods in part a$)$ and b$).$ What results to you get?

d$)$ The third way would be to treat each question seperately and compare the classes for that question with an ANOA. Give this a try. What p$-$values do you get for each question? And there any questions where $($at least$)$ one class gave a significantly different response?

e$)$ Really what were doing isn't totally valid anyway $-$ the reponses to the SPOT survey

aren't actually numbers, they're strongly agree, agree, etc. Really, a $1$ or $2$ is a "postive"

reponse and an $4$ or $5$ is a "negative" response, and a $3$ is "neutral". If we group

"postive" and "negative" repsones, and irgnore neutral respones $($which is not a great

idea$),$ we can treat the repsones as a binomial distribution. Doing this, we can estimate

how many respones we need in a class to get useful data. For example, how many

students would need to respond for you to be confident more students gave positive

respones than negative responses? You can calculate this using the Chernoff$\_$trials, if

you pick a good value for p$,$ delta, and epsilon. What might some good values be$?$ How many respones are needed for those values?

$($A one$-$sided version of the Chernoff$\_$tails calculation might actually be more useful

here, but don't worry about coming up with one for the homework.$)$

f$)$ Based on your results, do you think the survey questions in SPOT contain much

$($statistically valid$)$ information? Possible Data Loss Some features might be lost if you save this workbook in the comma$-$delimited $(.$csv$)$ format. To preserve these features, save it in an Excel file format. Possible Data Loss Some features might be lost if you save this workbook in the comma$-$delimited $(.$csv$)$ format. To preserve these features, save it in an Excel file format. Possible Data Loss Some features might be lost if you save this workbook in the comma$-$delimited $(.$csv$)$ format. To preserve these features, save it in an Excel file format.