326 homework
jiru shih
2018年3月29日
setwd("~/")
options(digits = 4, show.signif.stars = FALSE)
pacman::p_load(tidyverse, ggplot2, car, HSAUR3, Ecdat, GGally, lattice, mlmRev, memisc)ex2
## 寫進資料並觀察資料
dta<-Ecdat::Caschool
knitr::kable## function (x, format, digits = getOption("digits"), row.names = NA,
## col.names = NA, align, caption = NULL, format.args = list(),
## escape = TRUE, ...)
## {
## if (missing(format) || is.null(format))
## format = getOption("knitr.table.format")
## if (is.null(format))
## format = if (is.null(pandoc_to()))
## switch(out_format() %n% "markdown", latex = "latex",
## listings = "latex", sweave = "latex", html = "html",
## markdown = "markdown", rst = "rst", stop("table format not implemented yet!"))
## else if (isTRUE(opts_knit$get("kable.force.latex")) &&
## is_latex_output()) {
## "latex"
## }
## else "pandoc"
## if (is.function(format))
## format = format()
## if (format != "latex" && !missing(align) && length(align) ==
## 1L)
## align = strsplit(align, "")[[1]]
## if (!is.null(caption) && !is.na(caption))
## caption = paste0(create_label("tab:", opts_current$get("label"),
## latex = (format == "latex")), caption)
## if (inherits(x, "list")) {
## if (format == "pandoc" && is_latex_output())
## format = "latex"
## res = lapply(x, kable, format = format, digits = digits,
## row.names = row.names, col.names = col.names, align = align,
## caption = NA, format.args = format.args, escape = escape,
## ...)
## res = unlist(lapply(res, paste, collapse = "\n"))
## res = if (format == "latex") {
## kable_latex_caption(res, caption)
## }
## else if (format == "html" || (format == "pandoc" && is_html_output()))
## kable_html(matrix(paste0("\n\n", res, "\n\n"), 1),
## caption = caption, escape = FALSE, table.attr = "class=\"kable_wrapper\"")
## else {
## res = paste(res, collapse = "\n\n")
## if (format == "pandoc")
## kable_pandoc_caption(res, caption)
## else res
## }
## return(structure(res, format = format, class = "knitr_kable"))
## }
## if (!is.matrix(x))
## x = as.data.frame(x)
## if (identical(col.names, NA))
## col.names = colnames(x)
## m = ncol(x)
## isn = if (is.matrix(x))
## rep(is.numeric(x), m)
## else sapply(x, is.numeric)
## if (missing(align) || (format == "latex" && is.null(align)))
## align = ifelse(isn, "r", "l")
## digits = rep(digits, length.out = m)
## for (j in seq_len(m)) {
## if (is_numeric(x[, j]))
## x[, j] = round(x[, j], digits[j])
## }
## if (any(isn)) {
## if (is.matrix(x)) {
## if (is.table(x) && length(dim(x)) == 2)
## class(x) = "matrix"
## x = format_matrix(x, format.args)
## }
## else x[, isn] = format_args(x[, isn], format.args)
## }
## if (is.na(row.names))
## row.names = has_rownames(x)
## if (!is.null(align))
## align = rep(align, length.out = m)
## if (row.names) {
## x = cbind(` ` = rownames(x), x)
## if (!is.null(col.names))
## col.names = c(" ", col.names)
## if (!is.null(align))
## align = c("l", align)
## }
## n = nrow(x)
## x = replace_na(to_character(as.matrix(x)), is.na(x))
## if (!is.matrix(x))
## x = matrix(x, nrow = n)
## x = trimws(x)
## colnames(x) = col.names
## if (format != "latex" && length(align) && !all(align %in%
## c("l", "r", "c")))
## stop("'align' must be a character vector of possible values 'l', 'r', and 'c'")
## attr(x, "align") = align
## res = do.call(paste("kable", format, sep = "_"), list(x = x,
## caption = caption, escape = escape, ...))
## structure(res, format = format, class = "knitr_kable")
## }
## <environment: namespace:knitr>head(dta)## distcod county district grspan enrltot teachers
## 1 75119 Alameda Sunol Glen Unified KK-08 195 10.90
## 2 61499 Butte Manzanita Elementary KK-08 240 11.15
## 3 61549 Butte Thermalito Union Elementary KK-08 1550 82.90
## 4 61457 Butte Golden Feather Union Elementary KK-08 243 14.00
## 5 61523 Butte Palermo Union Elementary KK-08 1335 71.50
## 6 62042 Fresno Burrel Union Elementary KK-08 137 6.40
## calwpct mealpct computer testscr compstu expnstu str avginc elpct
## 1 0.5102 2.041 67 690.8 0.3436 6385 17.89 22.690 0.000
## 2 15.4167 47.917 101 661.2 0.4208 5099 21.52 9.824 4.583
## 3 55.0323 76.323 169 643.6 0.1090 5502 18.70 8.978 30.000
## 4 36.4754 77.049 85 647.7 0.3498 7102 17.36 8.978 0.000
## 5 33.1086 78.427 171 640.8 0.1281 5236 18.67 9.080 13.858
## 6 12.3188 86.956 25 605.6 0.1825 5580 21.41 10.415 12.409
## readscr mathscr
## 1 691.6 690.0
## 2 660.5 661.9
## 3 636.3 650.9
## 4 651.9 643.5
## 5 641.8 639.9
## 6 605.7 605.4## 隨機抽取並繪製散佈圖
set.seed(20180329)
dta2 <- dta %>%
group_by(county) %>%
sample_n(1)
with(dta2, plot(mathscr ~ readscr,
xlab = "average math score",
ylab = "average reading score"))
ex3
options(digits=3) # 小數點位數
options(width=72) # 輸出資料的寬度
ds = read.csv("http://www.amherst.edu/~nhorton/r2/datasets/help.csv") # 從網址讀取資料並儲存
library(dplyr) # 載入package
detach(package:memisc) # 由於select衝突無法順利產生指令，故多加這兩個detach解決
detach(package:MASS)
newds = select(ds, cesd, female, i1, i2, id, treat, f1a, f1b, f1c, f1d, f1e, f1f, f1g, f1h, f1i, f1j, f1k, f1l, f1m, f1n, f1o, f1p, f1q, f1r, f1s, f1t) # 選擇變項names(newds) # 變項名稱## [1] "cesd" "female" "i1" "i2" "id" "treat" "f1a"
## [8] "f1b" "f1c" "f1d" "f1e" "f1f" "f1g" "f1h"
## [15] "f1i" "f1j" "f1k" "f1l" "f1m" "f1n" "f1o"
## [22] "f1p" "f1q" "f1r" "f1s" "f1t"str(newds[,1:10]) # structure of the first 10 variables # 檢查前十筆資料結構## 'data.frame': 453 obs. of 10 variables:
## $ cesd : int 49 30 39 15 39 6 52 32 50 46 ...
## $ female: int 0 0 0 1 0 1 1 0 1 0 ...
## $ i1 : int 13 56 0 5 10 4 13 12 71 20 ...
## $ i2 : int 26 62 0 5 13 4 20 24 129 27 ...
## $ id : int 1 2 3 4 5 6 7 8 9 10 ...
## $ treat : int 1 1 0 0 0 1 0 1 0 1 ...
## $ f1a : int 3 3 3 0 3 1 3 1 3 2 ...
## $ f1b : int 2 2 2 0 0 0 1 1 2 3 ...
## $ f1c : int 3 0 3 1 3 1 3 2 3 3 ...
## $ f1d : int 0 3 0 3 3 3 1 3 1 0 ...summary(newds[,1:10]) # summary of the first 10 # variables檢查前十筆資料摘要## cesd female i1 i2
## Min. : 1.0 Min. :0.000 Min. : 0.0 Min. : 0.0
## 1st Qu.:25.0 1st Qu.:0.000 1st Qu.: 3.0 1st Qu.: 3.0
## Median :34.0 Median :0.000 Median : 13.0 Median : 15.0
## Mean :32.8 Mean :0.236 Mean : 17.9 Mean : 22.6
## 3rd Qu.:41.0 3rd Qu.:0.000 3rd Qu.: 26.0 3rd Qu.: 32.0
## Max. :60.0 Max. :1.000 Max. :142.0 Max. :184.0
## id treat f1a f1b
## Min. : 1 Min. :0.000 Min. :0.00 Min. :0.00
## 1st Qu.:119 1st Qu.:0.000 1st Qu.:1.00 1st Qu.:0.00
## Median :233 Median :0.000 Median :2.00 Median :1.00
## Mean :233 Mean :0.497 Mean :1.63 Mean :1.39
## 3rd Qu.:348 3rd Qu.:1.000 3rd Qu.:3.00 3rd Qu.:2.00
## Max. :470 Max. :1.000 Max. :3.00 Max. :3.00
## f1c f1d
## Min. :0.00 Min. :0.00
## 1st Qu.:1.00 1st Qu.:0.00
## Median :2.00 Median :1.00
## Mean :1.92 Mean :1.56
## 3rd Qu.:3.00 3rd Qu.:3.00
## Max. :3.00 Max. :3.00head(newds, n=3) # 查看前三筆資料## cesd female i1 i2 id treat f1a f1b f1c f1d f1e f1f f1g f1h f1i f1j
## 1 49 0 13 26 1 1 3 2 3 0 2 3 3 0 2 3
## 2 30 0 56 62 2 1 3 2 0 3 3 2 0 0 3 0
## 3 39 0 0 0 3 0 3 2 3 0 2 2 1 3 2 3
## f1k f1l f1m f1n f1o f1p f1q f1r f1s f1t
## 1 3 0 1 2 2 2 2 3 3 2
## 2 3 0 0 3 0 0 0 2 0 0
## 3 1 0 1 3 2 0 0 3 2 0comment(newds) = "HELP baseline dataset" # 在newds中加上HELP baseline dataset註解
comment(newds) # 確認newds的註解## [1] "HELP baseline dataset"save(ds, file="savedfile") # 存檔write.csv(ds, file="ds.csv") # 把ds這個資料轉成csv檔library(foreign) # 載入foreign以便其他統計程式使用
write.foreign(newds, "file.dat", "file.sas", package="SAS") # 寫成SAS可以利用的格式with(newds, cesd[cesd > 56]) #在newds中變項cesd數值大於56的資料## [1] 57 58 57 60 58 58 57library(dplyr) # 載入dplyr
filter(newds, cesd > 56) %>% select(id, cesd) ## 先選newds中cesd大於56的數值，再選id和cesd兩欄資料檢視。## id cesd
## 1 71 57
## 2 127 58
## 3 200 57
## 4 228 60
## 5 273 58
## 6 351 58
## 7 13 57with(newds, sort(cesd)[1:4]) # 將cesd由小排到大再取第1~4筆資料## [1] 1 3 3 4with(newds, which.min(cesd)) # 找最小值在哪裡## [1] 199library(mosaic) # 載入mosaic## Loading required package: ggformula##
## New to ggformula? Try the tutorials:
## learnr::run_tutorial("introduction", package = "ggformula")
## learnr::run_tutorial("refining", package = "ggformula")## Loading required package: mosaicData##
## The 'mosaic' package masks several functions from core packages in order to add
## additional features. The original behavior of these functions should not be affected by this.
##
## Note: If you use the Matrix package, be sure to load it BEFORE loading mosaic.##
## Attaching package: 'mosaic'## The following object is masked from 'package:lme4':
##
## factorize## The following object is masked from 'package:Matrix':
##
## mean## The following objects are masked from 'package:car':
##
## deltaMethod, logit## The following objects are masked from 'package:dplyr':
##
## count, do, tally## The following object is masked from 'package:purrr':
##
## cross## The following objects are masked from 'package:stats':
##
## binom.test, cor, cor.test, cov, fivenum, IQR, median,
## prop.test, quantile, sd, t.test, var## The following objects are masked from 'package:base':
##
## max, mean, min, prod, range, sample, sumtally(~ is.na(f1g), data=newds) # 找f1g的遺漏值並改成tbl## is.na(f1g)
## TRUE FALSE
## 1 452favstats(~ f1g, data=newds) # 針對f1g做敘述統計## min Q1 median Q3 max mean sd n missing
## 0 1 2 3 3 1.73 1.1 452 1cesditems = with(newds, cbind(f1a, f1b, f1c, (3 - f1d), f1e, f1f, f1g,
(3 - f1h), f1i, f1j, f1k, (3 - f1l), f1m, f1n, f1o, (3 - f1p),
f1q, f1r, f1s, f1t)) # 將反向題挑出來重新編碼
nmisscesd = apply(is.na(cesditems), 1, sum) # 計算遺漏值的數量
ncesditems = cesditems # 另存新檔
ncesditems[is.na(cesditems)] = 0 # ncesditems中的遺漏值變成0
newcesd = apply(ncesditems, 1, sum) # 計算排除遺漏值後的平均
imputemeancesd = 20/(20-nmisscesd)*newcesd # 用平均值代替遺漏值data.frame(newcesd, newds$cesd, nmisscesd, imputemeancesd)[nmisscesd>0,] # 將剛才對遺漏值所做的處理列成一個表格## newcesd newds.cesd nmisscesd imputemeancesd
## 4 15 15 1 15.8
## 17 19 19 1 20.0
## 87 44 44 1 46.3
## 101 17 17 1 17.9
## 154 29 29 1 30.5
## 177 44 44 1 46.3
## 229 39 39 1 41.1library(dplyr) # 載入dplyr
library(memisc) # 載入memisc## Loading required package: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:Ecdat':
##
## SP500## The following object is masked from 'package:dplyr':
##
## select##
## Attaching package: 'memisc'## The following object is masked from 'package:Matrix':
##
## as.array## The following object is masked from 'package:car':
##
## recode## The following objects are masked from 'package:dplyr':
##
## collect, recode, rename## The following objects are masked from 'package:stats':
##
## contr.sum, contr.treatment, contrasts## The following object is masked from 'package:base':
##
## as.arraynewds = mutate(newds, drinkstat=
cases(
"abstinent" = i1==0,
"moderate" = (i1>0 & i1<=1 & i2<=3 & female==1) |
(i1>0 & i1<=2 & i2<=4 & female==0),
"highrisk" = ((i1>1 | i2>3) & female==1) |
((i1>2 | i2>4) & female==0)))
## 將連續資料變成類別資料library(mosaic) # 載入mosaic
detach(package:memisc) # 移除memisc的物件
detach(package:MASS) # 移除MASS的物件library(dplyr) # 載入dplyr
tmpds = select(newds, i1, i2, female, drinkstat) # 選i1, i2, female, drinkstat這四個變項
tmpds[365:370,] # 找第365~370筆資料## i1 i2 female drinkstat
## 365 6 24 0 highrisk
## 366 6 6 0 highrisk
## 367 0 0 0 abstinent
## 368 0 0 1 abstinent
## 369 8 8 0 highrisk
## 370 32 32 0 highriskfilter(tmpds, drinkstat=="moderate" & female==1) #找飲酒程度是moderate的女性## i1 i2 female drinkstat
## 1 1 1 1 moderate
## 2 1 3 1 moderate
## 3 1 2 1 moderate
## 4 1 1 1 moderate
## 5 1 1 1 moderate
## 6 1 1 1 moderate
## 7 1 1 1 moderatelibrary(gmodels) # 載入gmodels
with(tmpds, CrossTable(drinkstat)) # 次數分配表##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 453
##
##
## | abstinent | moderate | highrisk |
## |-----------|-----------|-----------|
## | 68 | 28 | 357 |
## | 0.150 | 0.062 | 0.788 |
## |-----------|-----------|-----------|
##
##
##
## with(tmpds, CrossTable(drinkstat, female,
prop.t=FALSE, prop.c=FALSE, prop.chisq=FALSE)) # 列是飲酒程度、欄是性別##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## |-------------------------|
##
##
## Total Observations in Table: 453
##
##
## | female
## drinkstat | 0 | 1 | Row Total |
## -------------|-----------|-----------|-----------|
## abstinent | 42 | 26 | 68 |
## | 0.618 | 0.382 | 0.150 |
## -------------|-----------|-----------|-----------|
## moderate | 21 | 7 | 28 |
## | 0.750 | 0.250 | 0.062 |
## -------------|-----------|-----------|-----------|
## highrisk | 283 | 74 | 357 |
## | 0.793 | 0.207 | 0.788 |
## -------------|-----------|-----------|-----------|
## Column Total | 346 | 107 | 453 |
## -------------|-----------|-----------|-----------|
##
## newds = transform(newds,
gender=factor(female, c(0,1), c("Male","Female")))
tally(~ female + gender, margin=FALSE, data=newds)## gender
## female Male Female
## 0 346 0
## 1 0 107# 根據性別(0,1)的變項，創一個為(Male, Female)的變項library(dplyr) # 載入dplyr
newds = arrange(ds, cesd, i1) # 根據ds和cesd排序
newds[1:5, c("cesd", "i1", "id")] # 呈現第1~5筆資料## cesd i1 id
## 1 1 3 233
## 2 3 1 139
## 3 3 13 418
## 4 4 4 251
## 5 4 9 95females = filter(ds, female==1) # 選ds中的女性
with(females, mean(cesd)) # 計算女性平均cesd## [1] 36.9# an alternative approach
mean(ds$cesd[ds$female==1])## [1] 36.9with(ds, tapply(cesd, female, mean)) # 計算男性與女性的cesd平均值## 0 1
## 31.6 36.9library(mosaic) # 載入mosaic
mean(cesd ~ female, data=ds) # 用~界定根據甚麼計算平均(ds中的female)## 0 1
## 31.6 36.9ex4
library(pacman)
p_load(HSAUR3)
head(dta4 <- backpain)## ID status driver suburban
## 1 1 case yes yes
## 2 1 control yes no
## 3 2 case yes yes
## 4 2 control yes yes
## 5 3 case yes no
## 6 3 control yes yesdta4 <- backpain %>%
group_by(status, driver, suburban) %>%
summarise(n = n()) %>%
ungroup() %>%
spread(status, n) %>%
mutate(total = case + control); dta4## # A tibble: 4 x 5
## driver suburban case control total
## <fct> <fct> <int> <int> <int>
## 1 no no 26 47 73
## 2 no yes 6 7 13
## 3 yes no 64 63 127
## 4 yes yes 121 100 221ex5
library(datasets)
dta <- merge(state.x77, USArrests, "row.names")
cor(dta[, -1])## Population Income Illiteracy Life Exp Murder.x HS Grad
## Population 1.0000 0.2082 0.1076 -0.0681 0.3436 -0.0985
## Income 0.2082 1.0000 -0.4371 0.3403 -0.2301 0.6199
## Illiteracy 0.1076 -0.4371 1.0000 -0.5885 0.7030 -0.6572
## Life Exp -0.0681 0.3403 -0.5885 1.0000 -0.7808 0.5822
## Murder.x 0.3436 -0.2301 0.7030 -0.7808 1.0000 -0.4880
## HS Grad -0.0985 0.6199 -0.6572 0.5822 -0.4880 1.0000
## Frost -0.3322 0.2263 -0.6719 0.2621 -0.5389 0.3668
## Area 0.0225 0.3633 0.0773 -0.1073 0.2284 0.3335
## Murder.y 0.3202 -0.2152 0.7068 -0.7785 0.9337 -0.5216
## Assault 0.3170 0.0409 0.5110 -0.6267 0.7398 -0.2303
## UrbanPop 0.5126 0.4805 -0.0622 0.2715 0.0164 0.3587
## Rape 0.3052 0.3574 0.1546 -0.2696 0.5800 0.2707
## Frost Area Murder.y Assault UrbanPop Rape
## Population -0.3322 0.0225 0.3202 0.3170 0.5126 0.305
## Income 0.2263 0.3633 -0.2152 0.0409 0.4805 0.357
## Illiteracy -0.6719 0.0773 0.7068 0.5110 -0.0622 0.155
## Life Exp 0.2621 -0.1073 -0.7785 -0.6267 0.2715 -0.270
## Murder.x -0.5389 0.2284 0.9337 0.7398 0.0164 0.580
## HS Grad 0.3668 0.3335 -0.5216 -0.2303 0.3587 0.271
## Frost 1.0000 0.0592 -0.5414 -0.4682 -0.2462 -0.279
## Area 0.0592 1.0000 0.1481 0.2312 -0.0615 0.525
## Murder.y -0.5414 0.1481 1.0000 0.8019 0.0696 0.564
## Assault -0.4682 0.2312 0.8019 1.0000 0.2589 0.665
## UrbanPop -0.2462 -0.0615 0.0696 0.2589 1.0000 0.411
## Rape -0.2792 0.5250 0.5636 0.6652 0.4113 1.000ggpairs(dta[, -1])
我只看出“在地區的變項有較低的相關”
ex6
library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:Ecdat':
##
## SP500## The following object is masked from 'package:dplyr':
##
## selectdta <- merge(rownames_to_column(mammals), rownames_to_column(Animals), all = TRUE)
duplicated(dta)## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [12] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [23] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [34] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [45] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [56] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [67] FALSEdim(dta)## [1] 67 3ex7
p_load(Ecdat)
dta7 <- Caschool %>%
mutate(ratio = enrltot/teachers,
Reading = cut(readscr, breaks = quantile(readscr, probs = c(0, .33, .67, 1)),
label = c("L", "M", "H"), ordered = T))
library(lattice)
xyplot(readscr ~ ratio | Reading, data = dta7,
type = c("p", "g", "r"), layout = c(3, 1),
xlab = "Student-Teacher Ratio",
ylab = "Reading Score")
ex8
p_load(car)
head(Prestige)## education income women prestige census type
## gov.administrators 13.1 12351 11.16 68.8 1113 prof
## general.managers 12.3 25879 4.02 69.1 1130 prof
## accountants 12.8 9271 15.70 63.4 1171 prof
## purchasing.officers 11.4 8865 9.11 56.8 1175 prof
## chemists 14.6 8403 11.68 73.5 2111 prof
## physicists 15.6 11030 5.13 77.6 2113 profstr(Prestige)## 'data.frame': 102 obs. of 6 variables:
## $ education: num 13.1 12.3 12.8 11.4 14.6 ...
## $ income : int 12351 25879 9271 8865 8403 11030 8258 14163 11377 11023 ...
## $ women : num 11.16 4.02 15.7 9.11 11.68 ...
## $ prestige : num 68.8 69.1 63.4 56.8 73.5 77.6 72.6 78.1 73.1 68.8 ...
## $ census : int 1113 1130 1171 1175 2111 2113 2133 2141 2143 2153 ...
## $ type : Factor w/ 3 levels "bc","prof","wc": 2 2 2 2 2 2 2 2 2 2 ...8-1
dta81 <- Prestige %>%
group_by(type) %>%
summarize(m = median(prestige, na.rm = TRUE)); dta81## # A tibble: 4 x 2
## type m
## <fct> <dbl>
## 1 bc 35.9
## 2 prof 68.4
## 3 wc 41.5
## 4 <NA> 35.08-2
dta8.2 <- Prestige %>%
na.omit %>%
group_by(type) %>%
mutate(m = median(prestige),
PrestigeLevel = memisc::cases("High" = prestige >= m,
"Low" = prestige < m))
library(lattice)
xyplot(income ~ education |type,
group = PrestigeLevel,
data = dta8.2,
type = c("p", "g", "r"),
layout = c(3, 1),
auto.key=list(space="right", row=2),
xlab = "Average education of occupational incumbents in 1971",
ylab = "Average income of incumbents in 1971")
三種職業聲望的高低，對於教育程度與收入之間所產生的關係效果不同。
ex9
p_load(mlmRev)
dta09 <- Hsb82 %>%
group_by(sector, school) %>%
summarise(m = mean(mAch, na.rm = TRUE),
s = sd(mAch, na.rm = TRUE),
n = n(),
se = s/sqrt(n)) %>%
mutate(lower.ci = m-2*se, upper.ci = m+2*se)
library(ggplot2)
ggplot(dta09, aes(x = school, y = m)) +
geom_point() +
geom_errorbar(aes(ymax = upper.ci, ymin = lower.ci))+
coord_flip()+
facet_wrap(~sector)+
labs(x = "School",y = "Math Mean Score by School")