1. Permutation tests
2. Visualization
3. Means in many combinations of groups, i.e., multi-way ANOVA

## 
##  Welch Two Sample t-test
## 
## data:  airbnb$price[airbnb$instant_bookable] and airbnb$price[!airbnb$instant_bookable]
## t = 3.6482, df = 5039.8, p-value = 0.0002667
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   4.475555 14.872518
## sample estimates:
## mean of x mean of y 
##  124.6409  114.9668

But, the \(t\) test relies on Normality. Is the distribution of AirBnB prices too “wierd”? How can we be sure?

Remove the big values

(demonstration)

The permutation test

Observation: If there was no meaningful difference in prices between “instant bookable” and not, then randomly shuffling that label won’t change anything.

Shuffle once

fake_is_instant <- sample(airbnb$instant_bookable)
(mean(airbnb$price[fake_is_instant], na.rm=TRUE) - 
                mean(airbnb$price[!fake_is_instant], na.rm=TRUE))

## [1] 2.837541

Many times

real_diff <- (mean(airbnb$price[airbnb$instant_bookable], na.rm=TRUE) - 
               mean(airbnb$price[!airbnb$instant_bookable], na.rm=TRUE))
permuted_diffs <- replicate(1000, {
        fake_is_instant <- sample(airbnb$instant_bookable)
        (mean(airbnb$price[fake_is_instant], na.rm=TRUE) - 
               mean(airbnb$price[!fake_is_instant], na.rm=TRUE))
   } )
hist(permuted_diffs, xlab="shuffled differences in mean", xlim=range(c(permuted_diffs, real_diff)))
abline(v=real_diff, col='red', lwd=3)

How surprising was the real value?

mean(abs(permuted_diffs) > abs(real_diff))

## [1] 0

Your turn

Do the analogous thing for the ANOVA comparing price between neighbourhoods:

anova(lm(price ~ neighbourhood, data=airbnb))

## Analysis of Variance Table
## 
## Response: price
##                 Df   Sum Sq Mean Sq F value    Pr(>F)    
## neighbourhood   91  6015248   66102  7.6277 < 2.2e-16 ***
## Residuals     5510 47749952    8666                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

in class

true_F <- anova(lm(price ~ neighbourhood, data=airbnb))[["F value"]][1]

# do this a lot of times:
## DO NOT put the randomness here: fake_neighbourhood <- sample(airbnb$neighbourhood)
fake_Fs <- replicate(1000, {
    fake_neighbourhood <- sample(airbnb$neighbourhood)  # randomness must be here
    anova(lm(price ~ fake_neighbourhood, data=airbnb))[["F value"]][1]
   })
hist(fake_Fs, xlim=range(fake_Fs, c(-1,1)*true_F), xlab="permuted F values")
abline(v=true_F, col='red', lwd=2)

Goals

• pattern discovery

• efficient summary of information

• visual/spatial analogy for quantitative patterns

Considerations

• Is the visual analogy appropriate for the type of data?

• Are important comparisons clear?

• Are units easily interpretable?

Principles of effective display

• Show the data
• Encourage the eye to compare differences
• Represent magnitudes honestly and accurately
• Draw graphical elements clearly, minimizing clutter
• Make displays easy to interpret

Above all else show the data.

Case study:

Distributions of litter sizes by Order, and Family, in the PanTHERIA dataset:

pantheria <- read_pantheria("../Datasets/PanTHERIA")
# look at most common orders
order_nums <- sort(table(pantheria$Order))
big_orders <- names(order_nums)[order_nums > 150]

## 
##   Microbiotheria    Tubulidentata       Dermoptera Notoryctemorphia 
##                1                1                2                2 
##      Proboscidea       Hyracoidea      Monotremata          Sirenia 
##                3                4                5                5 
## Paucituberculata        Pholidota           Pilosa    Macroscelidea 
##                6                8               10               15 
##   Perissodactyla       Scandentia        Cingulata  Peramelemorphia 
##               17               20               21               21 
##   Erinaceomorpha     Afrosoricida   Dasyuromorphia          Cetacea 
##               24               51               71               84 
##  Didelphimorphia       Lagomorpha    Diprotodontia     Artiodactyla 
##               87               92              143              240 
##        Carnivora         Primates     Soricomorpha       Chiroptera 
##              286              376              428             1116 
##         Rodentia 
##             2277

note the pipe

px <- (pantheria %>% filter(Order %in% big_orders)
       %>% filter(!is.na(LitterSize))
       %>% select(Order, Family, Genus, Species, LitterSize))
for (xn in c("Order", "Family", "Genus")) px[[xn]] <- factor(px[[xn]])
summary(px)

##           Order                  Family              Genus     
##  Artiodactyla:178   Muridae         : 242   Microtus    :  38  
##  Carnivora   :209   Cricetidae      : 239   Myotis      :  38  
##  Chiroptera  :465   Sciuridae       : 158   Crocidura   :  36  
##  Primates    :209   Vespertilionidae: 135   Peromyscus  :  32  
##  Rodentia    :883   Bovidae         : 110   Sorex       :  32  
##  Soricomorpha:116   Phyllostomidae  : 106   Spermophilus:  31  
##                     (Other)         :1070   (Other)     :1853  
##    Species            LitterSize    
##  Length:2060        Min.   : 0.960  
##  Class :character   1st Qu.: 1.000  
##  Mode  :character   Median : 1.970  
##                     Mean   : 2.489  
##                     3rd Qu.: 3.490  
##                     Max.   :11.300  
## 

Raw numbers

px$LitterSize

##    [1]  0.98  4.50  3.74  5.72  4.98  1.22  1.00  1.22  1.01  1.02  1.02
##   [12]  1.02  1.02  1.39  1.39  3.89  2.00  1.09  1.73  1.45  1.11  1.02
##   [23]  1.01  1.01  1.00  1.01  1.02  1.02  1.01  1.01  1.05  1.84  2.00
##   [34]  2.00  2.00  2.31  2.00  2.00  1.93  1.04  1.94  3.00  2.19  1.94
##   [45]  2.36  2.62  3.00  1.29  4.91  5.30  4.29  6.27  4.00  4.99  1.50
##   [56]  1.50  2.00  3.40  1.01  1.02  1.01  2.00  1.22  1.00  1.73  1.00
##   [67]  0.99  1.00  7.29  6.12  1.00  1.00  1.00  1.00  1.00  1.01  1.01
##   [78]  1.01  1.02  1.01  1.02  1.01  1.02  1.01  1.02  1.02  1.02  1.00
##   [89]  1.00  1.00  1.02  1.00  1.02  1.01  1.02  1.02  1.01  1.02  3.09
##  [100]  1.09  1.00  1.00  0.99  1.00  0.99  2.91  3.68  4.00  3.45  5.28
##  [111]  5.34  5.53  3.46  3.40  3.50  6.06  5.71  5.20  7.14  3.99  0.99
##  [122]  2.99  2.99  3.00  3.59  4.29  1.99  3.37  1.99  1.73  3.74  3.00
##  [133]  2.99  3.89  3.00  2.44  4.04  3.99  3.49  1.22  1.50  4.86  1.00
##  [144]  1.00  1.00  1.01  1.50  2.50  2.29  2.12  0.96  0.98  1.00  3.40
##  [155]  5.39  3.95  2.62  2.52  1.21  0.98  1.00  0.98  1.02  1.00  1.00
##  [166]  1.00  1.00  1.34  1.41  1.38  3.49  3.97  3.94  2.95  3.45  4.62
##  [177]  1.70  2.75  3.63  2.60  2.62  1.00  1.00  3.78  3.49  3.85  2.79
##  [188]  2.50  1.97  0.99  4.99  1.18  4.34  3.88  6.24  4.99  4.99  3.46
##  [199]  4.66  3.67  1.00  0.99  1.00 11.30  2.83  2.75  3.06  1.93  1.01
##  [210]  4.00  1.00  1.00  1.53  1.10  1.04  1.11  1.01  0.96  1.29  2.60
##  [221]  2.19  3.54  2.25  2.50  1.00  1.00  1.00  1.50  1.22  1.22  1.00
##  [232]  1.00  1.39  4.14  3.00  1.73  1.00  3.00  2.00  3.49  2.89  1.71
##  [243]  0.96  1.00  3.49  4.00  1.00  3.88  1.50  1.00  1.00  1.00  1.22
##  [254]  1.01  4.37  0.97  2.50  1.87  5.83  3.42  1.94  1.00  0.99  0.98
##  [265]  0.99  0.98  1.65  1.01  1.00  2.68  2.15  1.07  1.01  1.02  1.02
##  [276]  1.02  1.00  1.50  1.00  1.79  2.00  1.00  1.22  2.00  2.30  1.00
##  [287]  0.98  0.99  1.00  0.98  1.94  0.98  3.60  2.95  2.47  1.50  2.14
##  [298]  1.34  3.45  1.90  1.01  1.05  1.01  1.00  1.01  0.98  0.99  1.00
##  [309]  3.14  3.49  1.66  3.29  3.36  2.99  1.99  3.94  3.00  3.99  2.49
##  [320]  2.99  2.00  0.98  2.26  2.04  0.98  0.98  0.99  0.99  2.00  2.31
##  [331]  0.99  0.98  1.00  0.98  1.00  1.01  1.00  1.00  0.99  1.02  1.97
##  [342]  5.39  3.49  3.60  3.49  2.00  1.00  2.00  1.40  1.50  1.25  0.99
##  [353]  1.00  0.99  1.00  4.50  3.00  0.97  1.94  0.98  1.00  0.99  1.00
##  [364]  2.34  1.94  1.94  1.94  5.23  0.97  3.11  2.00  1.99  3.49  5.99
##  [375]  1.91  4.00  4.29  1.07  3.00  1.84  2.48  2.60  3.00  2.98  2.99
##  [386]  2.99  4.55  2.00  2.00  2.00  3.00  4.34  2.50  1.01  1.00  4.30
##  [397]  2.15  2.30  0.98  0.99  1.00  4.48  5.40  4.43  4.18  4.89  0.99
##  [408]  1.50  1.00  1.00  1.00  0.98  1.41  2.67  1.01  3.19  4.68  2.60
##  [419]  2.60  1.94  3.36  2.91  3.11  4.77  2.39  2.37  1.94  2.14  2.95
##  [430]  3.78  2.59  2.67  2.68  1.73  3.49  0.99  0.99  0.99  0.99  0.98
##  [441]  0.98  1.00  1.75  1.94  4.00  1.00  3.68  4.18  3.24  3.00  1.94
##  [452]  0.99  1.22  1.08  2.14  1.00  1.22  0.96  3.74  7.50  1.00  1.00
##  [463]  1.80  4.77  3.42  2.00  1.00  0.99  0.98  0.99  0.99  0.98  1.00
##  [474]  1.46  1.86  1.85  1.50  2.76  1.73  1.04  4.71  1.89  2.53  3.14
##  [485]  3.09  1.68  4.00  5.94  3.40  3.92  4.06  2.74  4.00  4.50  4.44
##  [496]  5.26  3.94  3.64  4.40  3.87  3.89  8.00  1.00  1.00  0.98  0.99
##  [507]  1.04  2.46  1.94  2.94  4.83  4.12  1.78  4.99  5.17  4.99  2.84
##  [518]  1.94  1.90  0.96  1.01  1.50  1.00  0.98  1.00  1.10  2.46  3.00
##  [529]  2.21  2.50  3.00  3.59  1.00  1.00  2.43  2.62  2.95  2.00  2.64
##  [540]  1.32  2.44  0.98  1.80  0.97  1.26  1.00  1.29  1.29  0.99  1.60
##  [551]  1.50  4.00  4.86  3.16  4.65  3.30  1.29  3.00  3.13  1.12  4.00
##  [562]  5.17  1.00  0.98  0.98  0.98  1.00  1.00  0.98  4.83  1.05  1.97
##  [573]  6.97  4.99  3.16  4.41  4.99  3.00  3.11  2.90  3.11  2.43  3.88
##  [584]  3.24  2.41  4.00  1.00  0.98  2.91  2.00  2.91  3.49  1.73  1.41
##  [595]  1.00  1.01  3.49  2.00  1.00  1.00  1.00  1.00  1.50  0.99  0.99
##  [606]  0.99  0.98  0.99  1.00  1.00  1.00  0.99  1.00  0.99  0.98  0.98
##  [617]  1.00  0.99  1.00  0.98  1.00  0.98  1.00  1.39  3.88  3.12  1.00
##  [628]  2.10  2.30  2.44  2.72  2.30  2.00  3.49  4.99  3.51  3.00  0.96
##  [639]  1.22  1.02  1.01  1.01  2.73  2.95  3.41  0.98  1.94  1.77  3.12
##  [650]  1.96  2.14  2.97  2.68  0.99  5.11  1.00  1.02  1.00  4.00  4.18
##  [661]  3.00  4.61  3.11  0.99  2.23  2.00  1.07  1.00  2.50  2.50  1.26
##  [672]  1.40  2.00  1.51  1.41  1.73  1.73  2.35  1.94  2.00  2.30  0.99
##  [683]  0.97  1.00  1.01  2.64  3.85  0.97  1.00  1.00  0.98  0.98  1.00
##  [694]  0.98  1.52  1.00  1.00  1.00  1.00  1.00  1.00  5.64  5.83  5.99
##  [705]  5.84  4.04  5.80  5.01  7.48  1.87  2.00  1.00  0.98  1.03  1.00
##  [716]  1.00  1.00  1.45  3.11  2.35  1.01  1.00  1.00  1.71  3.25  3.26
##  [727]  3.78  0.98  0.99  0.99  0.99  0.99  0.99  1.00  0.99  1.00  1.22
##  [738]  1.00  1.00  1.00  0.98  0.99  1.00  0.99  1.50  1.20  1.20  1.74
##  [749]  0.98  2.68  0.99  1.00  5.99  6.20  4.67  4.99  3.65  4.66  4.00
##  [760]  2.73  4.10  4.00  4.50  5.10  6.39  6.86  4.61  3.68  4.64  1.18
##  [771]  2.91  2.04  1.94  1.66  1.50  1.94  3.33  1.01  1.01  1.00  1.02
##  [782]  1.00  2.95  2.35  1.88  1.00  0.99  1.00  0.99  0.98  3.20  4.22
##  [793]  3.67  3.69  0.98  0.99  1.00  0.96  0.98  0.98  0.98  0.98  2.67
##  [804]  2.54  3.69  1.58  1.01  0.98  1.00  0.99  2.30  1.00  1.55  1.94
##  [815]  3.00  1.97  2.75  1.44  4.16  2.91  2.01  3.24  4.88  3.09  3.00
##  [826]  8.10  2.73  2.30  2.50  2.76  1.01  1.00  1.00  1.02  1.01  1.01
##  [837]  1.01  1.01  1.00  1.01  1.01  1.01  1.02  1.01  1.00  4.10  4.54
##  [848]  1.75  1.00  8.79  9.01  8.99  0.97  0.99  0.99  1.00  1.00  2.50
##  [859]  1.00  0.98  0.98  0.98  1.00  1.00  2.50  1.00  2.46  2.91  4.04
##  [870]  1.02  1.07  1.02  2.68  1.69  1.01  1.02  3.59  2.60  3.53  3.78
##  [881]  3.49  3.02  3.13  2.04  1.41  7.96 11.23  9.23  2.91  3.29  3.54
##  [892]  3.00  1.22  1.50  1.00  1.22  1.00  1.41  2.60  2.00  2.00  2.50
##  [903]  2.50  2.20  2.15  2.50  2.17  0.98  1.54  4.68  5.70  4.21  2.09
##  [914]  3.60  6.80  2.33  5.49  3.89  5.54  4.30  3.00  1.20  3.87  5.62
##  [925]  3.32  5.16  2.47  1.40  5.93  7.89  5.51  2.46  2.91  4.32  5.06
##  [936]  2.10  8.10  2.30  5.72  0.98  0.98  0.99  0.99  1.00  0.99  1.00
##  [947]  1.00  1.00  0.99  1.22  1.00  0.98  1.00  5.18  4.50  1.98  3.49
##  [958]  2.48  3.16  3.16  2.00  2.00  2.52  3.94  3.89  4.92  0.99  0.98
##  [969]  0.99  0.99  3.00  4.65  4.99  4.50  4.41  4.62  3.58  0.98  0.98
##  [980]  0.99  0.99  0.99  0.99  0.99  0.99  0.99  1.44  1.42  2.00  0.99
##  [991]  3.00  1.50  1.00  1.84  2.51  5.34  8.48  6.14  1.97  4.73  1.37
## [1002]  5.96  4.40  4.76  2.95  4.18  3.49  5.54  6.93  3.92  6.69  5.15
## [1013]  1.94  4.40  4.30  5.44  6.74  7.82  6.50  4.50  3.36  5.07  4.00
## [1024]  8.48  6.48  4.04  5.34  3.10  4.83  5.37  4.31  5.01  5.60  4.10
## [1035]  1.00  1.97  1.77  5.25  1.97  2.99  2.99  4.00  2.90  4.50  3.11
## [1046]  1.00  0.98  1.00  1.88  1.00  0.98  0.99  0.99  0.99  0.98  1.00
## [1057]  1.21  0.98  0.99  0.98  0.98  1.00  0.99  0.99  0.98  0.99  0.99
## [1068]  1.00  1.00  1.00  1.50  0.99  0.98  0.98  1.00  1.00  1.00  0.98
## [1079]  4.50  1.02  4.00  3.69  0.99  3.94  4.50  4.86  3.52  2.25  2.25
## [1090]  2.33  7.10  6.39  1.35  0.98  1.96  1.98  1.86  2.00  2.14  0.97
## [1101]  3.45  3.11  2.79  1.29  2.70  2.00  2.59  2.00  1.00  4.00  2.50
## [1112]  2.95  2.81  0.98  3.30  4.95  3.64  4.77  3.59  0.96  6.55  3.72
## [1123]  3.88  4.08  2.50  2.00  1.06  3.20  1.00  1.00  1.00  4.18  2.99
## [1134]  1.94  2.37  3.70  4.86  4.41  0.99  1.01  3.69  4.01  2.95  3.07
## [1145]  3.28  0.99  1.00  1.91  1.82  1.73  1.33  6.36  0.98  1.00  0.99
## [1156]  1.00  0.99  1.00  1.00  1.12  1.75  2.54  1.94  0.98  0.98  0.98
## [1167]  1.00  0.99  1.00  0.99  0.99  0.99  2.00  2.00  1.54  2.62  5.31
## [1178]  2.04  1.22  1.61  1.57  3.15  3.84  3.30  1.40  1.00  0.98  1.97
## [1189]  1.00  1.00  1.00  3.40  3.59  3.23  3.63  4.37  1.68  1.00  4.00
## [1200]  1.14  1.02  2.10  0.99  1.00  2.86  1.59  1.65  3.70  1.29  1.70
## [1211]  1.38  0.99  2.20  0.98  1.01  1.22  1.19  1.16  1.22  1.00  2.51
## [1222]  1.00  3.49  1.00  2.16  1.01  1.05  2.75  1.96  2.14  2.60  8.47
## [1233]  6.28  5.48  1.00  0.98  1.00  1.01  1.01  1.01  1.01  1.01  0.97
## [1244]  2.00  3.40  3.29  3.00  2.50  1.52  1.07  1.69  2.15  1.94  2.00
## [1255]  0.98  4.49  0.97  1.06  2.02  1.22  2.20  1.60  1.50  2.00  2.04
## [1266]  2.91  1.56  1.17  0.98  1.00  1.09  5.48  4.37  3.94  4.00  4.45
## [1277]  4.18  4.86  3.53  3.49  3.18  1.94  3.08  3.88  2.52  1.94  3.70
## [1288]  2.43  1.94  3.09  2.39  5.99  4.27  0.99  0.98  1.21  2.12  1.00
## [1299]  1.00  0.98  2.91  4.76  2.00  2.23  2.91  3.69  2.75  3.40  2.56
## [1310]  4.86  3.88  2.79  3.59  2.38  3.49  3.00  1.94  1.00  0.99  1.00
## [1321]  0.97  1.00  2.00  1.07  1.50  2.00  1.50  2.46  3.20  1.94  1.01
## [1332]  4.66  4.80  1.00  0.98  1.00  1.00  1.00  1.00  0.99  0.98  0.98
## [1343]  0.99  0.99  0.99  2.79  2.16  2.84  2.25  1.00  3.40  0.99  1.00
## [1354]  1.01  1.02  1.00  1.00  2.50  1.28  0.99  0.98  1.00  1.00  0.99
## [1365]  1.98  1.40  4.59  2.00  0.99  1.07  0.99  6.04  5.74  6.49  4.99
## [1376]  4.19  4.02  4.25  1.00  0.98  1.00  1.01  1.02  1.01  1.01  2.10
## [1387]  1.98  1.40  1.86  2.29  1.21  1.96  1.73  1.37  1.96  1.96  0.98
## [1398]  1.96  1.92  2.00  1.02  1.01  1.14  0.98  1.00  0.98  0.99  0.99
## [1409]  0.98  0.99  0.98  1.22  2.60  2.23  2.15  2.15  2.68  2.81  2.64
## [1420]  2.23  1.07  2.73  3.00  1.11  5.44  3.88  3.75  3.49  3.67  3.28
## [1431]  3.36  1.01  1.01  1.02  1.01  2.50  2.23  2.00  2.30  2.00  1.41
## [1442]  1.00  1.02  2.62  3.06  2.64  2.68  1.47  1.00  3.49  0.97  1.22
## [1453]  3.89  4.90  3.00  3.19  3.00  3.49  2.91  2.00  2.62  3.00  4.43
## [1464]  3.00  3.00  1.00  1.00  1.00  1.00  1.00  0.98  1.00  0.98  0.99
## [1475]  1.00  1.00  1.00  1.00  1.00  0.99  1.00  1.00  1.22  2.76  2.50
## [1486]  1.94  1.00  1.00  1.00  4.00  3.80  1.00  1.01  1.00  5.17  3.35
## [1497]  5.49  0.98  3.00  3.00  0.98  1.00  1.01  1.22  0.98  1.00  1.00
## [1508]  1.01  1.00  1.00  1.00  1.00  0.99  1.00  6.75  5.75  2.00  1.83
## [1519]  2.00  0.98  1.00 10.00  9.85  3.70  4.58  3.45  4.45  6.40  2.47
## [1530]  2.15  3.09  8.99  5.37  4.37  4.23  5.88  2.15  5.99  3.65  3.87
## [1541]  5.34  2.15  2.15  1.50  3.49  0.98  1.00  3.40  3.40  3.40  2.21
## [1552]  3.88  3.76  3.11  3.88  2.99  4.18  2.91  3.94  3.88  3.49  5.28
## [1563]  0.97  0.97  1.00  0.99  0.98  0.99  1.00  1.96  1.00  0.98  0.99
## [1574]  0.99  1.00  1.00  0.99  1.00  0.99  0.98  0.98  1.00  1.00  0.99
## [1585]  0.99  0.98  0.98  1.00  0.98  0.98  1.00  1.00  1.00  0.99  1.00
## [1596]  1.39  1.97  1.84  2.00  2.02  1.93  1.82  1.90  1.50  1.02  3.24
## [1607]  2.91  3.80  4.50  3.88  5.40  6.71  5.71  2.69  7.52  3.91  8.70
## [1618]  5.24  5.84  7.50  6.48  3.54  5.62  5.75  1.01  1.00  1.02  1.02
## [1629]  3.00  2.59  3.89  3.49  3.24  3.63  1.94  3.20  3.00  4.00  3.09
## [1640]  1.94  2.98  2.66  2.91  1.90  2.65  2.43  2.59  4.99  4.50  3.00
## [1651]  1.00  2.46  3.08  1.96  0.98  0.99  2.00  2.20  1.92  1.50  1.38
## [1662]  1.50  2.00  1.41  1.08  1.85  2.90  6.90  1.02  5.29  3.49  4.37
## [1673]  5.18  7.50  5.44  3.00  1.02  1.50  1.64  5.95  6.56  6.69  7.24
## [1684]  5.49  6.49  4.94  4.99  5.99  4.18  5.49  5.33  4.58  4.89  7.00
## [1695]  5.84  7.09  3.99  5.99  8.99  5.46  4.89  3.14  0.98  1.07  0.99
## [1706]  7.77  8.69  5.99  5.18  4.34  5.91  6.50  7.97  6.50  6.07  7.08
## [1717]  4.89  7.59  6.94  5.49  6.32  8.49  8.08  7.77  4.93  7.88  4.99
## [1728]  0.97  1.00  3.09  2.05  3.00  3.56  1.62  1.70  5.07  4.00  4.62
## [1739]  3.96  4.41  0.99  2.38  0.99  0.99  0.98  0.99  0.99  0.99  0.98
## [1750]  0.98  0.98  0.98  3.49  4.00  2.99  1.89  3.10  3.49  1.00  1.00
## [1761]  1.00  1.00  0.98  0.96  1.44  1.00  1.01  1.02  1.01  0.98  1.00
## [1772]  2.43  2.50  2.71  2.29  3.23  2.46  3.11  1.41  1.49  3.86  6.59
## [1783]  4.58  3.24  6.24  3.66  4.52  5.47  1.00  0.98  0.98  1.78  2.69
## [1794]  1.99  1.02  4.27  3.09  1.08  1.00  1.40  1.41  0.99  1.00  1.11
## [1805]  0.98  4.37  4.59  3.49  3.89  4.50  4.99  2.43  3.88  4.89  4.99
## [1816]  2.38  4.50  4.95  3.49  3.93  4.04  5.93  3.92  4.85  4.37  5.01
## [1827]  4.00  4.14  3.75  6.80  5.49  3.93  2.59  2.38  3.40  1.00  1.00
## [1838]  0.99  1.00  0.99  1.00  0.99  1.02  1.01  1.00  4.86  2.19  3.70
## [1849]  5.34  0.98  1.00  0.98  3.28  4.59  4.86  3.89  3.77  1.00  0.98
## [1860]  1.25  1.00  2.52  4.47  4.99  3.49  3.93  3.44  5.15  1.01  1.00
## [1871]  5.19  4.99  1.01  1.02  1.01  1.42  4.57  5.44  7.77  6.90  0.98
## [1882]  1.00  6.32  9.36  8.00  8.90  1.22  0.99  2.91  0.98  1.00  2.50
## [1893]  0.97  0.99  1.22  0.99  2.82  1.00  1.93  1.22  1.78  2.62  1.47
## [1904]  1.00  1.01  1.02  1.06  1.02  2.46  5.64  4.94  3.88  4.41  3.56
## [1915]  4.47  5.16  5.72  1.00  2.73  2.91  2.00  2.50  1.01  1.00  1.00
## [1926]  1.00  1.00  1.00  1.00  1.00  1.40  2.79  3.00  0.99  0.98  0.99
## [1937]  0.99  0.98  0.98  1.00  1.00  0.98  0.99  0.99  1.00  4.86  4.76
## [1948]  3.21  0.99  1.00  4.99  3.76  4.00  4.47  1.00  2.76  2.00  1.65
## [1959]  3.20  1.33  1.01  4.61  4.99  6.50  3.79  3.49  4.86  6.15  2.20
## [1970]  0.98  3.20  2.91  3.88  0.98  0.98  0.98  1.01  1.50  1.02  1.02
## [1981]  1.01  1.00  1.01  1.00  1.00  1.00  1.00  2.00  3.00  1.37  0.97
## [1992]  1.00  1.64  4.24  2.47  2.91  1.92  2.00  2.12  4.07  3.71  2.17
## [2003]  0.99  0.98  4.30  1.46  3.00  3.49  2.39  2.24  1.66  1.50  0.98
## [2014]  0.98  0.99  0.98  0.98  1.00  4.00  3.24  2.16  1.50  1.21  1.00
## [2025]  1.00  1.50  2.00  1.00  1.92  2.89  3.74  5.07  3.49  2.00  2.50
## [2036]  5.62  3.49  7.65  4.50  4.00  2.12  4.25  4.59  2.36  3.80  1.60
## [2047]  2.00  3.45  2.06  2.00  1.94  1.41  5.36  5.04  5.47  5.75  4.99
## [2058]  4.23  2.76  2.23

stem-and-leaf “plot”

stem(px$LitterSize)

## 
##   The decimal point is at the |
## 
##    0 | 
##    1 | 00000000000000000000000000000000000000000000000000000000000000000000+937
##    2 | 00000000000000000000000000000000000000000000000000000000000000000000+259
##    3 | 00000000000000000000000000000000000000000000000000000000000000000000+230
##    4 | 00000000000000000000000000000000000000000011111111122222222222222233+103
##    5 | 00000000000000000000000000000111111222222222222223333333333333444444+35
##    6 | 00000000000111122223333444455555555666777788899999
##    7 | 001111235555567888899
##    8 | 000011155557789
##    9 | 0000249
##   10 | 0
##   11 | 23

five(-ish) number summary

summary(px$LitterSize)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.960   1.000   1.970   2.489   3.490  11.300

Points

plot(px$LitterSize, xlab='', ylab='Litter size', pch=20, cex=0.5)

Points, sorted

plot(sort(px$LitterSize), xlab='rank', ylab='Litter size', pch=20, cex=0.5)

Points, sorted and colored

plot(sort(px$LitterSize), col=px$Order, xlab='rank', ylab='Litter size', pch=20, cex=0.5)
legend("topleft", pch=20, col=1:nlevels(px$Order), legend=levels(px$Order))

Histogram

layout(t(1:2))
with(px, hist(LitterSize))
with(px, hist(LitterSize, breaks=40))

Histograms

layout(matrix(1:6, ncol=3, byrow=TRUE), heights=c(1, 1.2))
opar <- par(mar=c(1, 3, 1, 1)+.1)
xh <- hist(px$LitterSize, plot=FALSE, breaks=30)
for (k in 1:nlevels(px$Order)) {
    ord <- levels(px$Order)[k]
    if (k == 4) par(opar)
    with(subset(px, Order == ord), 
        hist(LitterSize, xlim=c(0, max(px$LitterSize)),
             breaks=xh$breaks, main=ord,
             xaxt=if (k > 3) 's' else 'n',
             xlab=if (k > 3) 'litter size' else '') )
}

Histograms

Overlaid histograms

overlay_hist <- function (x, f, breaks=30, ...) {
    xh <- hist(x, breaks=breaks, plot=FALSE)
    ymax <- do.call(max, with(px, lapply(tapply(LitterSize, Order, hist, plot=FALSE), "[[", "counts")))
    for (k in 1:nlevels(f)) {
        hist(x[f==levels(f)[k]], breaks=xh$breaks, ...,
             add=(k>1), col=adjustcolor(k, 0.4), ylim=c(0, ymax))
    }
    legend("topright", fill=adjustcolor(1:nlevels(f), 0.4),
           legend=levels(f))
}

Overlaid histograms

with(px, overlay_hist(LitterSize, Order, xlab='litter size', main=''))

boxplots

with(px, boxplot(LitterSize ~ Order))

Many boxes

par(mar=c(9, 3, 1, 1) + 0.1)
with(px, boxplot(LitterSize ~ Family, las=2, xlab=''))

Your turn

Challenge: visualize LitterSize by TeatNumber, using a boxplot.

or, “gg”

• introduced by Leland Wilkinson

• adopted by Hadley Wickham in the ggplot library

• thinks of plots as objects

• see this chapter of R for Data Science

Ingredients of a visualization

• data

• coordinate axes

• a geometric representation of numbers

• a mapping from (summaries of) variables to properties of the geoms

• maybe more plots

basic template

ggplot(data = <DATA>) + 
  <GEOM_FUNCTION>(mapping = aes(<MAPPINGS>))

more options

ggplot(data = <DATA>) + 
  <GEOM_FUNCTION>(
     mapping = aes(<MAPPINGS>),
     stat = <STAT>, 
     position = <POSITION>
  ) +
  <COORDINATE_FUNCTION> +
  <FACET_FUNCTION>

Reference: the ggplot2 book.

Points

ggplot(px, mapping=aes(x=Order, y=LitterSize)) + geom_point()

Histogram

ggplot(px, mapping=aes(LitterSize)) + geom_histogram(bins=40) + facet_wrap(~ Order)

Histogram, stacked

ggplot(px, mapping=aes(LitterSize, fill=Order)) + geom_histogram(bins=40)

Boxplot

ggplot(px, mapping=aes(y=LitterSize, x=Order)) + geom_boxplot()

Your turn, again

Challenge: make this plot.

The cheatsheet might be helpful.