The One proportion Z-test is used to compare an observed proportion to a theoretical one, when there are only two categories. This article describes the basics of one-proportion z-test and provides practical examples using R software.
For example, we have a population of mice containing half male and have female (p = 0.5 = 50%). Some of these mice (n = 160) have developed a spontaneous cancer, including 95 male and 65 female.
In this setting:
the number of successes (male with cancer) is 95
The observed proportion (po) of male is 95/160
The observed proportion (q) of female is 1-po
The expected proportion (pe) of male is 0.5 (50%)
The number of observations (nn) is 160
The R functions binom.test() and prop.test() can be used to perform one-proportion test:
binom.test(): compute exact binomial test. Recommended when sample size is small
prop.test(): can be used when sample size is large ( N > 30). It uses a normal approximation to binomial
prop.test(x=95,n=160,p=0.5, correct=FALSE)
1-sample proportions test without continuity correction
data: 95 out of 160, null probability 0.5
X-squared = 5.625, df = 1, p-value = 0.01771
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
0.5163169 0.6667870
sample estimates:
p
0.59375 prop.test(x = 95, n = 160, p = 0.5, correct = FALSE,alternative = "less")
1-sample proportions test without continuity correction
data: 95 out of 160, null probability 0.5
X-squared = 5.625, df = 1, p-value = 0.9911
alternative hypothesis: true p is less than 0.5
95 percent confidence interval:
0.0000000 0.6555425
sample estimates:
p
0.59375 res <- prop.test(x = 95, n = 160, p = 0.5, correct = FALSE)
res
1-sample proportions test without continuity correction
data: 95 out of 160, null probability 0.5
X-squared = 5.625, df = 1, p-value = 0.01771
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
0.5163169 0.6667870
sample estimates:
p
0.59375 # printing the p-value
res$p.value[1] 0.01770607# printing the mean
res$estimate p
0.59375 # printing the confidence interval
res$conf.int[1] 0.5163169 0.6667870
attr(,"conf.level")
[1] 0.95The two-proportions z-test is used to compare two observed proportions. This article describes the basics of two-proportions *z-test and provides pratical examples using R software.
res <- prop.test(x = c(490, 400), n = c(500, 500))
# Printing the results
res
2-sample test for equality of proportions with continuity correction
data: c(490, 400) out of c(500, 500)
X-squared = 80.909, df = 1, p-value < 2.2e-16
alternative hypothesis: two.sided
95 percent confidence interval:
0.1408536 0.2191464
sample estimates:
prop 1 prop 2
0.98 0.80 The chi-square goodness of fit test is used to compare the observed distribution to an expected distribution, in a situation where we have two or more categories in a discrete data. In other words, it compares multiple observed proportions to expected probabilities.
tulip <- c(81, 50, 27)
res <- chisq.test(tulip, p = c(1/3, 1/3, 1/3))
res
Chi-squared test for given probabilities
data: tulip
X-squared = 27.886, df = 2, p-value = 8.803e-07# Import the data
housetasks<- read.table("~/Penguin/housetasks.txt", header = TRUE)head(housetasks) Wife Alternating Husband Jointly
Laundry 156 14 2 4
Main_meal 124 20 5 4
Dinner 77 11 7 13
Breakfeast 82 36 15 7
Tidying 53 11 1 57
Dishes 32 24 4 53str(housetasks)'data.frame': 13 obs. of 4 variables:
$ Wife : int 156 124 77 82 53 32 33 12 10 13 ...
$ Alternating: int 14 20 11 36 11 24 23 46 51 13 ...
$ Husband : int 2 5 7 15 1 4 9 23 75 21 ...
$ Jointly : int 4 4 13 7 57 53 55 15 3 66 ...save(housetasks, file="housetasks.RData")
load("housetasks.RData")
housetasks Wife Alternating Husband Jointly
Laundry 156 14 2 4
Main_meal 124 20 5 4
Dinner 77 11 7 13
Breakfeast 82 36 15 7
Tidying 53 11 1 57
Dishes 32 24 4 53
Shopping 33 23 9 55
Official 12 46 23 15
Driving 10 51 75 3
Finances 13 13 21 66
Insurance 8 1 53 77
Repairs 0 3 160 2
Holidays 0 1 6 153library(gplots)
Attaching package: 'gplots'The following object is masked from 'package:stats':
lowess# 1. convert the data as a table
dt <- as.table(as.matrix(housetasks))
dt Wife Alternating Husband Jointly
Laundry 156 14 2 4
Main_meal 124 20 5 4
Dinner 77 11 7 13
Breakfeast 82 36 15 7
Tidying 53 11 1 57
Dishes 32 24 4 53
Shopping 33 23 9 55
Official 12 46 23 15
Driving 10 51 75 3
Finances 13 13 21 66
Insurance 8 1 53 77
Repairs 0 3 160 2
Holidays 0 1 6 153# 2. Graph
balloonplot(t(dt), main="housetasks", xlab = "", ylab = "", label=FALSE, show.margins = FALSE)
library("graphics")
mosaicplot(dt, shade = TRUE, las=2,
main = "housetasks")
library(vcd)Loading required package: grid# plot just a subset of the table
assoc(head(dt, 5), shade = TRUE, las=3)
library(chisquare)
chisq <- chisq.test(housetasks)
chisq
Pearson's Chi-squared test
data: housetasks
X-squared = 1944.5, df = 36, p-value < 2.2e-16#observed counts
chisq$observed Wife Alternating Husband Jointly
Laundry 156 14 2 4
Main_meal 124 20 5 4
Dinner 77 11 7 13
Breakfeast 82 36 15 7
Tidying 53 11 1 57
Dishes 32 24 4 53
Shopping 33 23 9 55
Official 12 46 23 15
Driving 10 51 75 3
Finances 13 13 21 66
Insurance 8 1 53 77
Repairs 0 3 160 2
Holidays 0 1 6 153# Expected counts
round(chisq$expected,2) Wife Alternating Husband Jointly
Laundry 60.55 25.63 38.45 51.37
Main_meal 52.64 22.28 33.42 44.65
Dinner 37.16 15.73 23.59 31.52
Breakfeast 48.17 20.39 30.58 40.86
Tidying 41.97 17.77 26.65 35.61
Dishes 38.88 16.46 24.69 32.98
Shopping 41.28 17.48 26.22 35.02
Official 33.03 13.98 20.97 28.02
Driving 47.82 20.24 30.37 40.57
Finances 38.88 16.46 24.69 32.98
Insurance 47.82 20.24 30.37 40.57
Repairs 56.77 24.03 36.05 48.16
Holidays 55.05 23.30 34.95 46.70round(chisq$residuals, 3) Wife Alternating Husband Jointly
Laundry 12.266 -2.298 -5.878 -6.609
Main_meal 9.836 -0.484 -4.917 -6.084
Dinner 6.537 -1.192 -3.416 -3.299
Breakfeast 4.875 3.457 -2.818 -5.297
Tidying 1.702 -1.606 -4.969 3.585
Dishes -1.103 1.859 -4.163 3.486
Shopping -1.289 1.321 -3.362 3.376
Official -3.659 8.563 0.443 -2.459
Driving -5.469 6.836 8.100 -5.898
Finances -4.150 -0.852 -0.742 5.750
Insurance -5.758 -4.277 4.107 5.720
Repairs -7.534 -4.290 20.646 -6.651
Holidays -7.419 -4.620 -4.897 15.556library(corrplot)corrplot 0.95 loadedcorrplot(chisq$residuals, is.cor = FALSE)
library(ggplot2)
library(dplyr)
Attaching package: 'dplyr'The following objects are masked from 'package:stats':
filter, lagThe following objects are masked from 'package:base':
intersect, setdiff, setequal, unionlibrary(tidyr)
library(knitr) #for printing html-friendly tables.mpg%>%
group_by(class, cyl)%>%
summarize(n=n())%>%
kable()`summarise()` has grouped output by 'class'. You can override using the
`.groups` argument.| class | cyl | n |
|---|---|---|
| 2seater | 8 | 5 |
| compact | 4 | 32 |
| compact | 5 | 2 |
| compact | 6 | 13 |
| midsize | 4 | 16 |
| midsize | 6 | 23 |
| midsize | 8 | 2 |
| minivan | 4 | 1 |
| minivan | 6 | 10 |
| pickup | 4 | 3 |
| pickup | 6 | 10 |
| pickup | 8 | 20 |
| subcompact | 4 | 21 |
| subcompact | 5 | 2 |
| subcompact | 6 | 7 |
| subcompact | 8 | 5 |
| suv | 4 | 8 |
| suv | 6 | 16 |
| suv | 8 | 38 |
mpg%>%
group_by(class, cyl)%>%
summarise(n=n())%>%
spread(cyl, n)%>%
kable()`summarise()` has grouped output by 'class'. You can override using the
`.groups` argument.| class | 4 | 5 | 6 | 8 |
|---|---|---|---|---|
| 2seater | NA | NA | NA | 5 |
| compact | 32 | 2 | 13 | NA |
| midsize | 16 | NA | 23 | 2 |
| minivan | 1 | NA | 10 | NA |
| pickup | 3 | NA | 10 | 20 |
| subcompact | 21 | 2 | 7 | 5 |
| suv | 8 | NA | 16 | 38 |
mpg%>%
group_by(class, cyl)%>%
summarise(mean_cty=mean(cty))%>%
spread(cyl, mean_cty)%>%
kable()`summarise()` has grouped output by 'class'. You can override using the
`.groups` argument.| class | 4 | 5 | 6 | 8 |
|---|---|---|---|---|
| 2seater | NA | NA | NA | 15.40000 |
| compact | 21.37500 | 21 | 16.92308 | NA |
| midsize | 20.50000 | NA | 17.78261 | 16.00000 |
| minivan | 18.00000 | NA | 15.60000 | NA |
| pickup | 16.00000 | NA | 14.50000 | 11.80000 |
| subcompact | 22.85714 | 20 | 17.00000 | 14.80000 |
| suv | 18.00000 | NA | 14.50000 | 12.13158 |
mpg%>%
group_by(class)%>%
summarize(n=n())%>%
mutate(prop=n/sum(n))%>% # our new proportion variable
kable()| class | n | prop |
|---|---|---|
| 2seater | 5 | 0.0213675 |
| compact | 47 | 0.2008547 |
| midsize | 41 | 0.1752137 |
| minivan | 11 | 0.0470085 |
| pickup | 33 | 0.1410256 |
| subcompact | 35 | 0.1495726 |
| suv | 62 | 0.2649573 |
mpg%>%
group_by(class, cyl)%>%
summarize(n=n())%>%
mutate(prop=n/sum(n))%>%
subset(select=c("class","cyl","prop"))%>% #drop the frequency value
spread(class, prop)%>%
kable()`summarise()` has grouped output by 'class'. You can override using the
`.groups` argument.| cyl | 2seater | compact | midsize | minivan | pickup | subcompact | suv |
|---|---|---|---|---|---|---|---|
| 4 | NA | 0.6808511 | 0.3902439 | 0.0909091 | 0.0909091 | 0.6000000 | 0.1290323 |
| 5 | NA | 0.0425532 | NA | NA | NA | 0.0571429 | NA |
| 6 | NA | 0.2765957 | 0.5609756 | 0.9090909 | 0.3030303 | 0.2000000 | 0.2580645 |
| 8 | 1 | NA | 0.0487805 | NA | 0.6060606 | 0.1428571 | 0.6129032 |
mpg%>%
group_by(class)%>%
summarize(n=n())%>%
mutate(prop=n/sum(n))%>% # our new proportion variable
kable()| class | n | prop |
|---|---|---|
| 2seater | 5 | 0.0213675 |
| compact | 47 | 0.2008547 |
| midsize | 41 | 0.1752137 |
| minivan | 11 | 0.0470085 |
| pickup | 33 | 0.1410256 |
| subcompact | 35 | 0.1495726 |
| suv | 62 | 0.2649573 |
mpg%>%
group_by(class, cyl)%>%
summarize(n=n())%>%
mutate(prop=n/sum(n))%>%
subset(select=c("class","cyl","prop"))%>% #drop the frequency value
spread(class, prop)%>%
kable()`summarise()` has grouped output by 'class'. You can override using the
`.groups` argument.| cyl | 2seater | compact | midsize | minivan | pickup | subcompact | suv |
|---|---|---|---|---|---|---|---|
| 4 | NA | 0.6808511 | 0.3902439 | 0.0909091 | 0.0909091 | 0.6000000 | 0.1290323 |
| 5 | NA | 0.0425532 | NA | NA | NA | 0.0571429 | NA |
| 6 | NA | 0.2765957 | 0.5609756 | 0.9090909 | 0.3030303 | 0.2000000 | 0.2580645 |
| 8 | 1 | NA | 0.0487805 | NA | 0.6060606 | 0.1428571 | 0.6129032 |
table(mpg$class, mpg$cyl)
4 5 6 8
2seater 0 0 0 5
compact 32 2 13 0
midsize 16 0 23 2
minivan 1 0 10 0
pickup 3 0 10 20
subcompact 21 2 7 5
suv 8 0 16 38mpg_table<- table(mpg$class, mpg$cyl) #define object w/table parameters for simple calling
ftable(mpg_table) 4 5 6 8
2seater 0 0 0 5
compact 32 2 13 0
midsize 16 0 23 2
minivan 1 0 10 0
pickup 3 0 10 20
subcompact 21 2 7 5
suv 8 0 16 38margin.table(mpg_table, 1)
2seater compact midsize minivan pickup subcompact suv
5 47 41 11 33 35 62 margin.table(mpg_table, 2)
4 5 6 8
81 4 79 70 prop.table(mpg_table)
4 5 6 8
2seater 0.000000000 0.000000000 0.000000000 0.021367521
compact 0.136752137 0.008547009 0.055555556 0.000000000
midsize 0.068376068 0.000000000 0.098290598 0.008547009
minivan 0.004273504 0.000000000 0.042735043 0.000000000
pickup 0.012820513 0.000000000 0.042735043 0.085470085
subcompact 0.089743590 0.008547009 0.029914530 0.021367521
suv 0.034188034 0.000000000 0.068376068 0.162393162prop.table(mpg_table, 1)
4 5 6 8
2seater 0.00000000 0.00000000 0.00000000 1.00000000
compact 0.68085106 0.04255319 0.27659574 0.00000000
midsize 0.39024390 0.00000000 0.56097561 0.04878049
minivan 0.09090909 0.00000000 0.90909091 0.00000000
pickup 0.09090909 0.00000000 0.30303030 0.60606061
subcompact 0.60000000 0.05714286 0.20000000 0.14285714
suv 0.12903226 0.00000000 0.25806452 0.61290323prop.table(mpg_table, 2)
4 5 6 8
2seater 0.00000000 0.00000000 0.00000000 0.07142857
compact 0.39506173 0.50000000 0.16455696 0.00000000
midsize 0.19753086 0.00000000 0.29113924 0.02857143
minivan 0.01234568 0.00000000 0.12658228 0.00000000
pickup 0.03703704 0.00000000 0.12658228 0.28571429
subcompact 0.25925926 0.50000000 0.08860759 0.07142857
suv 0.09876543 0.00000000 0.20253165 0.54285714library(gmodels)Registered S3 method overwritten by 'gdata':
method from
reorder.factor gplotsCrossTable(mpg$class, mpg$cyl)
Cell Contents
|-------------------------|
| N |
| Chi-square contribution |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 234
| mpg$cyl
mpg$class | 4 | 5 | 6 | 8 | Row Total |
-------------|-----------|-----------|-----------|-----------|-----------|
2seater | 0 | 0 | 0 | 5 | 5 |
| 1.731 | 0.085 | 1.688 | 8.210 | |
| 0.000 | 0.000 | 0.000 | 1.000 | 0.021 |
| 0.000 | 0.000 | 0.000 | 0.071 | |
| 0.000 | 0.000 | 0.000 | 0.021 | |
-------------|-----------|-----------|-----------|-----------|-----------|
compact | 32 | 2 | 13 | 0 | 47 |
| 15.210 | 1.782 | 0.518 | 14.060 | |
| 0.681 | 0.043 | 0.277 | 0.000 | 0.201 |
| 0.395 | 0.500 | 0.165 | 0.000 | |
| 0.137 | 0.009 | 0.056 | 0.000 | |
-------------|-----------|-----------|-----------|-----------|-----------|
midsize | 16 | 0 | 23 | 2 | 41 |
| 0.230 | 0.701 | 6.059 | 8.591 | |
| 0.390 | 0.000 | 0.561 | 0.049 | 0.175 |
| 0.198 | 0.000 | 0.291 | 0.029 | |
| 0.068 | 0.000 | 0.098 | 0.009 | |
-------------|-----------|-----------|-----------|-----------|-----------|
minivan | 1 | 0 | 10 | 0 | 11 |
| 2.070 | 0.188 | 10.641 | 3.291 | |
| 0.091 | 0.000 | 0.909 | 0.000 | 0.047 |
| 0.012 | 0.000 | 0.127 | 0.000 | |
| 0.004 | 0.000 | 0.043 | 0.000 | |
-------------|-----------|-----------|-----------|-----------|-----------|
pickup | 3 | 0 | 10 | 20 | 33 |
| 6.211 | 0.564 | 0.117 | 10.391 | |
| 0.091 | 0.000 | 0.303 | 0.606 | 0.141 |
| 0.037 | 0.000 | 0.127 | 0.286 | |
| 0.013 | 0.000 | 0.043 | 0.085 | |
-------------|-----------|-----------|-----------|-----------|-----------|
subcompact | 21 | 2 | 7 | 5 | 35 |
| 6.515 | 3.284 | 1.963 | 2.858 | |
| 0.600 | 0.057 | 0.200 | 0.143 | 0.150 |
| 0.259 | 0.500 | 0.089 | 0.071 | |
| 0.090 | 0.009 | 0.030 | 0.021 | |
-------------|-----------|-----------|-----------|-----------|-----------|
suv | 8 | 0 | 16 | 38 | 62 |
| 8.444 | 1.060 | 1.162 | 20.403 | |
| 0.129 | 0.000 | 0.258 | 0.613 | 0.265 |
| 0.099 | 0.000 | 0.203 | 0.543 | |
| 0.034 | 0.000 | 0.068 | 0.162 | |
-------------|-----------|-----------|-----------|-----------|-----------|
Column Total | 81 | 4 | 79 | 70 | 234 |
| 0.346 | 0.017 | 0.338 | 0.299 | |
-------------|-----------|-----------|-----------|-----------|-----------|
library(gplots)
mpg_table <- table(mpg$manufacturer, mpg$class)
balloonplot(mpg_table, main = "Balloon Plot of Manufacturer vs Car Class",
xlab = "Car Class", ylab = "Manufacturer",
label = TRUE, show.margins = FALSE)
library("graphics")
mosaicplot(mpg_table, shade = TRUE, las=2,
main = "MPG")
library(vcd)
assoc(head(mpg, 1), shade = TRUE, las=3)Warning in legend(residuals, gpfun, residuals_type): All residuals are zero.
library(dplyr)
library(tidyr)
library(knitr)
library(gmodels)library(summariser)
library(ggplot2)
mpg_table
2seater compact midsize minivan pickup subcompact suv
audi 0 15 3 0 0 0 0
chevrolet 5 0 5 0 0 0 9
dodge 0 0 0 11 19 0 7
ford 0 0 0 0 7 9 9
honda 0 0 0 0 0 9 0
hyundai 0 0 7 0 0 7 0
jeep 0 0 0 0 0 0 8
land rover 0 0 0 0 0 0 4
lincoln 0 0 0 0 0 0 3
mercury 0 0 0 0 0 0 4
nissan 0 2 7 0 0 0 4
pontiac 0 0 5 0 0 0 0
subaru 0 4 0 0 0 4 6
toyota 0 12 7 0 7 0 8
volkswagen 0 14 7 0 0 6 0mpg%>%
group_by(class, cyl)%>%
summarise(n=n())%>%
kable()`summarise()` has grouped output by 'class'. You can override using the
`.groups` argument.| class | cyl | n |
|---|---|---|
| 2seater | 8 | 5 |
| compact | 4 | 32 |
| compact | 5 | 2 |
| compact | 6 | 13 |
| midsize | 4 | 16 |
| midsize | 6 | 23 |
| midsize | 8 | 2 |
| minivan | 4 | 1 |
| minivan | 6 | 10 |
| pickup | 4 | 3 |
| pickup | 6 | 10 |
| pickup | 8 | 20 |
| subcompact | 4 | 21 |
| subcompact | 5 | 2 |
| subcompact | 6 | 7 |
| subcompact | 8 | 5 |
| suv | 4 | 8 |
| suv | 6 | 16 |
| suv | 8 | 38 |
# summary by group
mpg%>%
group_by(class, cyl)%>%
summarize(n=n())%>%
kable()`summarise()` has grouped output by 'class'. You can override using the
`.groups` argument.| class | cyl | n |
|---|---|---|
| 2seater | 8 | 5 |
| compact | 4 | 32 |
| compact | 5 | 2 |
| compact | 6 | 13 |
| midsize | 4 | 16 |
| midsize | 6 | 23 |
| midsize | 8 | 2 |
| minivan | 4 | 1 |
| minivan | 6 | 10 |
| pickup | 4 | 3 |
| pickup | 6 | 10 |
| pickup | 8 | 20 |
| subcompact | 4 | 21 |
| subcompact | 5 | 2 |
| subcompact | 6 | 7 |
| subcompact | 8 | 5 |
| suv | 4 | 8 |
| suv | 6 | 16 |
| suv | 8 | 38 |
# 1. Contingency table
mpg_counts <- mpg %>%
group_by(class, cyl) %>%
summarise(n = n(), .groups = "drop") %>%
spread(cyl, n, fill = 0)
mpg_counts# A tibble: 7 × 5
class `4` `5` `6` `8`
<chr> <dbl> <dbl> <dbl> <dbl>
1 2seater 0 0 0 5
2 compact 32 2 13 0
3 midsize 16 0 23 2
4 minivan 1 0 10 0
5 pickup 3 0 10 20
6 subcompact 21 2 7 5
7 suv 8 0 16 38mpg_matrix <- as.matrix(mpg_counts[, -1])
rownames(mpg_matrix) <- mpg_counts$class
chisq <- chisq.test(mpg_matrix)Warning in chisq.test(mpg_matrix): Chi-squared approximation may be incorrect#chi-squared
library(chisquare)
chisq <- chisq.test(mpg_matrix)Warning in chisq.test(mpg_matrix): Chi-squared approximation may be incorrect# 1. Contingency table
mpg_counts <- mpg %>%
group_by(class, cyl) %>%
summarise(n = n(), .groups = "drop") %>%
spread(cyl, n, fill = 0)
# Convert to matrix format for the chi-square test
mpg_matrix <- as.matrix(mpg_counts[, -1])
rownames(mpg_matrix) <- mpg_counts$class# 1. Chi-square test of the data
chisq <- chisq.test(mpg_matrix)Warning in chisq.test(mpg_matrix): Chi-squared approximation may be incorrectError occurred New method
library(ggplot2)
data("mpg")table_mpg <- table(mpg$class, mpg$drv)
print(table_mpg)
4 f r
2seater 0 0 5
compact 12 35 0
midsize 3 38 0
minivan 0 11 0
pickup 33 0 0
subcompact 4 22 9
suv 51 0 11chisq_test <- chisq.test(table_mpg)Warning in chisq.test(table_mpg): Chi-squared approximation may be incorrectprint(chisq_test)
Pearson's Chi-squared test
data: table_mpg
X-squared = 221.6, df = 12, p-value < 2.2e-16chisq
Pearson's Chi-squared test
data: mpg_matrix
X-squared = 138.03, df = 18, p-value < 2.2e-16# 2. Observed counts
chisq$observed 4 5 6 8
2seater 0 0 0 5
compact 32 2 13 0
midsize 16 0 23 2
minivan 1 0 10 0
pickup 3 0 10 20
subcompact 21 2 7 5
suv 8 0 16 38# 3. Expected counts
round(chisq$expected,2) 4 5 6 8
2seater 1.73 0.09 1.69 1.50
compact 16.27 0.80 15.87 14.06
midsize 14.19 0.70 13.84 12.26
minivan 3.81 0.19 3.71 3.29
pickup 11.42 0.56 11.14 9.87
subcompact 12.12 0.60 11.82 10.47
suv 21.46 1.06 20.93 18.55# 1. extraction of the Pearson residual
round(chisq$residuals, 3) 4 5 6 8
2seater -1.316 -0.292 -1.299 2.865
compact 3.900 1.335 -0.720 -3.750
midsize 0.480 -0.837 2.462 -2.931
minivan -1.439 -0.434 3.262 -1.814
pickup -2.492 -0.751 -0.342 3.224
subcompact 2.553 1.812 -1.401 -1.691
suv -2.906 -1.029 -1.078 4.517# 2. Visualizing Pearson residual
library(corrplot)
corrplot(chisq$residuals, is.cor = FALSE)
#create a cross table
CrossTable(mpg$class, mpg$cyl)
Cell Contents
|-------------------------|
| N |
| Chi-square contribution |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 234
| mpg$cyl
mpg$class | 4 | 5 | 6 | 8 | Row Total |
-------------|-----------|-----------|-----------|-----------|-----------|
2seater | 0 | 0 | 0 | 5 | 5 |
| 1.731 | 0.085 | 1.688 | 8.210 | |
| 0.000 | 0.000 | 0.000 | 1.000 | 0.021 |
| 0.000 | 0.000 | 0.000 | 0.071 | |
| 0.000 | 0.000 | 0.000 | 0.021 | |
-------------|-----------|-----------|-----------|-----------|-----------|
compact | 32 | 2 | 13 | 0 | 47 |
| 15.210 | 1.782 | 0.518 | 14.060 | |
| 0.681 | 0.043 | 0.277 | 0.000 | 0.201 |
| 0.395 | 0.500 | 0.165 | 0.000 | |
| 0.137 | 0.009 | 0.056 | 0.000 | |
-------------|-----------|-----------|-----------|-----------|-----------|
midsize | 16 | 0 | 23 | 2 | 41 |
| 0.230 | 0.701 | 6.059 | 8.591 | |
| 0.390 | 0.000 | 0.561 | 0.049 | 0.175 |
| 0.198 | 0.000 | 0.291 | 0.029 | |
| 0.068 | 0.000 | 0.098 | 0.009 | |
-------------|-----------|-----------|-----------|-----------|-----------|
minivan | 1 | 0 | 10 | 0 | 11 |
| 2.070 | 0.188 | 10.641 | 3.291 | |
| 0.091 | 0.000 | 0.909 | 0.000 | 0.047 |
| 0.012 | 0.000 | 0.127 | 0.000 | |
| 0.004 | 0.000 | 0.043 | 0.000 | |
-------------|-----------|-----------|-----------|-----------|-----------|
pickup | 3 | 0 | 10 | 20 | 33 |
| 6.211 | 0.564 | 0.117 | 10.391 | |
| 0.091 | 0.000 | 0.303 | 0.606 | 0.141 |
| 0.037 | 0.000 | 0.127 | 0.286 | |
| 0.013 | 0.000 | 0.043 | 0.085 | |
-------------|-----------|-----------|-----------|-----------|-----------|
subcompact | 21 | 2 | 7 | 5 | 35 |
| 6.515 | 3.284 | 1.963 | 2.858 | |
| 0.600 | 0.057 | 0.200 | 0.143 | 0.150 |
| 0.259 | 0.500 | 0.089 | 0.071 | |
| 0.090 | 0.009 | 0.030 | 0.021 | |
-------------|-----------|-----------|-----------|-----------|-----------|
suv | 8 | 0 | 16 | 38 | 62 |
| 8.444 | 1.060 | 1.162 | 20.403 | |
| 0.129 | 0.000 | 0.258 | 0.613 | 0.265 |
| 0.099 | 0.000 | 0.203 | 0.543 | |
| 0.034 | 0.000 | 0.068 | 0.162 | |
-------------|-----------|-----------|-----------|-----------|-----------|
Column Total | 81 | 4 | 79 | 70 | 234 |
| 0.346 | 0.017 | 0.338 | 0.299 | |
-------------|-----------|-----------|-----------|-----------|-----------|