mosaic Daniel Kaplan * 1 Nicholas J. Horton * 2 Randall Pruim * 3 Macalester College Amherst College Calvin College St. Paul, MN Amherst, MA Grand Rap

Size: px

Start display at page:

Download "mosaic Daniel Kaplan * 1 Nicholas J. Horton * 2 Randall Pruim * 3 Macalester College Amherst College Calvin College St. Paul, MN Amherst, MA Grand Rap"

かおりつまがみ
4 years ago
Views:

1 mosaic Daniel Kaplan * 1 Nicholas J. Horton * 2 Randall Pruim * 3 Macalester College Amherst College Calvin College St. Paul, MN Amherst, MA Grand Rapids, MI R RStudio Lock mosaic R mosaic *1 dtkaplan@gmail.com *2 rpruim@calvin.edu *3 nhorton@amherst.edu 1

2 ˆ ˆ ˆ ˆ ˆ George Cobb 3 Rs Randomization Replication Rejection Cobb R Terry Speed 2001 Robin Lock USCOTS United States Conference on Teaching Statistics) uscots/breakout/breakout3_6.php mosaic 1 MOSAIC Efron and Tibshirani, 1993; Hesterberg et al Lock mosaic Lock 2

3 mosaic R RStudio R R RStudio R 2.2 mosaic R install.packages("mosaic") require(mosaic) options(digits = 3) R mosaic R R read.csv() R URL URL mosaic fetchdata() fetchdata() Lock Lock 1 mustangs <- fetchdata("mustangprice.csv") 3

3 Lock Lock Robin Lock 2011 Lock 1 Mustang MustangPrice.csv 1000 1000 1000 90% R 2 lattice 1.

4 3 Lock Lock Robin Lock 2011 Lock 1 Mustang MustangPrice.csv % R 2 lattice 1. mosaic 2. histogram(~price, data = mustangs) lattice ~ data= mosaic mean(~price, data = mustangs) [1] 16 R 4

5 mean(mustangs$price) mean(~price, data = mustangs) redample() simple = c(1,2,3,4,5) resample(simple) [1] resample(simple) [1] resample(simple) [1] resample() resample(mustangs) Age Miles Price orig.ids and so on

6 mean(~price, data=resample(mustangs)) [1] mean(~price, data = resample(mustangs)) [1] do(5) * mean(~price, data = resample(mustangs)) $result [1] attr(,"row.names") [1] attr(,"class") [1] "do.data.frame" 1000 trials trials <- do(1000) * mean(~price, data = resample(mustangs)) histogram(~ result, data = trials, xlab = " ") confint(trials, level = 0.90, method = "quantile") name 5 % 95 % 1 result

confint(trials, level = 0.90, method = "stderr") name lower upper 1 result 12.4 19.5 confint() confint() 2 ˆ 90% qdata(c(.05,.

7 confint(trials, level = 0.90, method = "stderr") name lower upper 1 result confint() confint() 2 ˆ 90% qdata(c(.05,.95), result, data = trials) 5% 95% ˆ t t z 90% 0.95 tstar <- qt(.95 df = 24) zstar <- qnorm(0.95) tstar * sd(~result, data = trials) [1] 3.68 zstar * sd(~result, data = trials) [1]

8 confint() level method quantile stderr R mosaic Lock 2 NFL National Football League NFL NFL /2= prop(rbinom(100000, prob=0.5, size=428) >= 240) TRUE prop(rbinom(100000, prob=0.5, size=428) >= 240) TRUE

9 pbinom(239, prob=0.5, size=428) [1] mosaic do(1) * rflip(428) $n [1] 428 $heads [1] 206 $tails [1] 222 attr(, "row.names") [1] attr(,"class") [1] "do.data.frame" trials <- do(1000) * rflip(428) prop(trials$heads >= 240, data=trials) TRUE histogram(~heads, groups = (heads >= 240), data = trials) 240 groups = Lock 3 2 Mednicj et al,

10 2 sleep <- fetchdata("sleepcaffeine.csv") The Sleep group seems to have remembered somewhat more words on average: mean(words ~ Group, data=sleep) Caffeine Sleep obs <- diff(mean(words ~ Group, data=sleep)) obs Sleep 3 bwplot(words ~ Group, data=sleep) Words Group 10

11 diff(mean(words ~ shuffle(group), data = sleep)) Sleep diff(mean(words ~ shuffle(group), data=sleep)) Sleep Lock % cor(price, Miles, data = mustangs) [1] trials <- do(1000) * cor(price, Miles, data = mustangs) quantiles <- qdata(c(.025,.975), result, data = trials) 2.5% 97.5% histogram(~result, data = trials, groups=cut(result, c(-inf, quantiles, Inf)), nbin = 30) trials <- do(1000) * diff(mean(words ~ shuffle(group), data = sleep)) histogram(~ Sleep, groups=(sleep >= obs), data=trials, xlab=" \n ") p p

12 35 p Lock Lock Mustang xyplot(price ~ Miles, data = mustangs) Lock 12

13 R lm() lm(price ~ Miles, data = mustangs) Call: lm(formula = Price ~ Miles, data = mustangs) Coefficients: (Intercept) Miles Mustang Mustang mean(price, data = mustangs ) [1] 16 lm(price ~ 1, data = mustangs) Call: lm(formula = Price ~ 1, data = mustangs) Coefficients: (Intercept) 16 lm() ~ Price ~ Miles Price Miles Price ~ 1 1 mean() 13

14 mean(price ~ 1, data = mustangs) 1 16 Lock sleep mean(words ~ 1, data=sleep ) mean(words ~ Group, data = sleep ) Caffeine Sleep Mustang Miles sleep Group lm(words ~ Group, data = sleep ) Call: lm(formula = Words ~ Group, data = sleep) Coefficients: (Intercept) GroupSleep mean() lm() lm() GroupSleep 2 14

15 diff(mean(words ~ Group, data = sleep )) Sleep 3 lm() 1 HELPrct prop(homeless ~ 1, data = HELPrct) homeless: prop(homeless ~ sex, data = HELPrct ) homeless:female homeless:male diff(prop(homeless ~ sex, data = HELPrct )) homeless:male lm() homeless housed lm(homeless == "homeless" ~ 1, data = HELPrct ) Call: lm(formula = homeless == "homeless" ~ 1, data = HELPrct) Coefficients: (Intercept) 15

16 0.461 mean() prop() diff() lm() lm() lm() lm() mean() prop() ~1 lm(homeless == "homeless" ~ sex, data = HELPrct) Call: lm(formula = homeless == "homeless" ~ sex, data = HELPrct) Coefficients: (Intercept) sexmale lm() mean() prop() Mustang trials <- do(1000) * lm(price ~ Miles, data = resample(mustangs)) confint(trials) name lower upper 1 Intercept Miles Sigma r.squared HELPrct nulldist <- do(1000) * lm(homeless == "homeless" ~ shuffle(sex), data=helprct) prop(~ abs(sexmale) > , data = nulldist) TRUE

17 4.2 Mustangs Age Miles trialsmod1 <- do(1000) * lm(price ~ Age, data = resample(mustangs)) trialsmod2 <- do(1000) * lm(price ~ Miles, data = resample(mustangs)) trialsmod3 <- do(1000) * lm(price ~ Miles + Age, data = resample(mustangs)) 1 Price confint(trialsmod1) name lower upper 1 Intercept Age Sigma r.squared confint(trialsmod2) name lower upper 1 Intercept Miles Sigma r.squared Age Miles confint(trialsmod3) name lower upper 1 Intercept Miles Age Sigma r.squared

18 1 Miles Age Miles Age Mustangs Price Miles Age 1 anova(lm(price ~ Miles + Age, data = mustangs)) Analysis of Variance Table Response: Price Df Sum Sq Mean Sq F value Pr(>F) Miles e-07 *** Age Residuals Signif. codes: 0 *** ** 0.01 * Age p Age anova(lm(price ~ Age + Miles, data = mustangs)) Analysis of Variance Table Response: Price Df Sum Sq Mean Sq F value Pr(>F) Age e-06 *** Miles ** Residuals Signif. codes: 0 *** ** 0.01 * ANOVA R 2 Age Miles 18

19 do(1) * lm(price ~ Miles, data = mustangs) $Intercept [1] 30.5 $Miles [1] $Sigma [1] 6.42 $r.squared [1] 0.68 attr(,"row.names") [1] 1 attr(,"class") [1] "do.data.frame" do(1) * lm(price ~ Miles + Age, data = mustangs) $Intercept [1] 30.9 $Miles [1] $Age [1] $Sigma [1] 6.55 $r.squared [1] 0.68 attr(,"row.names") [1] 1 attr(,"class") [1] "do.data.frame" do() Age R Age R 2 19

20 trials1 <- do(1000) * lm(price ~ Miles + shuffle(age), data = mustangs ) confint(trials1) name lower upper 1 Intercept Miles Age Sigma r.squared Price ~ Miles + Age R 2 Age Miles trials2 <- do(1000) * lm(price ~ shuffle(miles) + Age, data = mustangs ) confint(trials2) name lower upper 1 Intercept Miles Age Sigma r.squared R 2 = Miles 5 p t F HELPrct homeless sex χ 2 p 1. chisq.test(tally( ~ homeless + sex, data = HELPrct, margins = FALSE)) Yates Pearson data: tally(~homeless + sex, data = HELPrct, margins = FALSE) X-squared = 3.87, df = 1, p-value =

2. p pval(chisq.test(tally( ~ homeless + sex, data = HELPrct, margins = FALSE))) p.value p 0.0491 3. pval(chisq.test(tally( ~ shuffle(homeless) + sex, data=helprct, margins=false))) p.value p 0.976 4.

21 2. p pval(chisq.test(tally( ~ homeless + sex, data = HELPrct, margins = FALSE))) p.value p pval(chisq.test(tally( ~ shuffle(homeless) + sex, data=helprct, margins=false))) p.value p trials = do(1000)* pval(chisq.test( tally( ~ shuffle(homeless) + sex, data=helprct, margins=false))) p 0.05 p 0 1 p < % prop(~(p.value < 0.05), data=trials) TRUE histogram( ~p.value, data=trials, width = 0.05) 21

22 χ 2 age trials = do(1000) * glm(homeless=="homeless" ~ age + sex, data = resample(helprct), family = "binomial") confint(trials) name lower upper 1 Intercept age sexmale Sarah Anoke USCOTS St. Lawrence Robin Lock MOSAIC US National Science Foundation DUE MOSAIC 7 ˆ G. W. Cobb, The introductory statistics course: a Ptolemaic curriculum?, Technology Innovations in Statistics Education, 2007, 1(1). ˆ B. Efron & R. J. Tibshirani, An Introduction to the Bootstrap, 1993, Chapman & Hall, New York. ˆ T. Hesterberg, D. S. Moore, S. Monaghan, A. Clipson & R. Epstein. Bootstrap Methods and Permutation Tests (2nd edition), (2005), W.H. Freeman, New York. ˆ D.T. Kaplan, Statistical Modeling: A Fresh Approach, 2nd edition, mosaic-web.org/statisticalmodeling. ˆ S.C. Mednicj, D. J. Cai, J. Kanady, S. P. Drummond. Comparing the benefits of caffeine, naps and placebo on verbal, motor and perceptual memory, Behavioural Brain Research, 2008, 193(1): ˆ T. Speed, Simulation, IMS Bulletin, 2011, 40(3):18. 22

R John Fox R R R Console library(rcmdr) Rcmdr R GUI Windows R R SDI 1 R Console R 1 2 Windows XP Windows 2 R R Console R ˆ R

R John Fox R R R Console library(rcmdr) Rcmdr R GUI Windows R R SDI *1 R Console R 1 2 Windows XP Windows * 2 R R Console R ˆ R R John Fox 2006 8 26 2008 8 28 1 R R R Console library(rcmdr) Rcmdr R GUI Windows R R SDI *1 R Console R 1 2 Windows XP Windows * 2 R R Console R ˆ R GUI R R R Console > ˆ 2 ˆ Fox(2005) jfox@mcmaster.ca