Hypothesis testing

omon das

2025-05-09

library(tidyverse)
data=starwars
colnames(data)
##  [1] "name"       "height"     "mass"       "hair_color" "skin_color"
##  [6] "eye_color"  "birth_year" "sex"        "gender"     "homeworld" 
## [11] "species"    "films"      "vehicles"   "starships"

shaprio test for normality

H0:Data is maybe normally distributed

shapiro.test(data$height)
## 
##  Shapiro-Wilk normality test
## 
## data:  data$height
## W = 0.87452, p-value = 1.05e-06

p<0.05 i.e it is not normally distributed

Kolmogorov-Smirnov tests

H0: equal distribution

one sample Kolmogorov-Smirnov tests

H0: Distribution is equal with normal distribution

library(dgof)

normaldata=rnorm(100)

ks.test(normaldata,"pnorm")
## 
##  One-sample Kolmogorov-Smirnov test
## 
## data:  normaldata
## D = 0.12076, p-value = 0.1082
## alternative hypothesis: two-sided

p>0.05 > H0 not rejected > it is maybe similar to normal distribution

two sample ks test:

###normaldata


uniformdata=runif(100)

ks.test(normaldata,uniformdata)
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  normaldata and uniformdata
## D = 0.48, p-value = 1.972e-10
## alternative hypothesis: two-sided

p<0.05 > H0 rejected > distribution is not normal

starwars=starwars %>% 
  mutate(sex=as.factor(sex))

sapply(starwars, class)
##        name      height        mass  hair_color  skin_color   eye_color 
## "character"   "integer"   "numeric" "character" "character" "character" 
##  birth_year         sex      gender   homeworld     species       films 
##   "numeric"    "factor" "character" "character" "character"      "list" 
##    vehicles   starships 
##      "list"      "list"

variance spread equal test:

  1. Leven’s test (in case non-normal)
  2. Bartlett test (in case normal)

H0: spread of variance is equal

library(car)

leveneTest(starwars$height~starwars$sex,center=median)
## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  3  1.2534 0.2968
##       73
###note for normally distributed data center the data by mean
###and for other case center the data by median
### although median is the most versatile out of every central tendency

p>0.05 > H0 is not rejected > spread of variance is equal

###parametric tests:

t.tests() / wilcox.test() : 1. one sample t-tests (mean) ||| Wilcoxon signed rank test(median) 2. two sample t-tests (mean) ||| Mann whitney test or wilcoxon rank sum test (median) 3. paired t-tests (mean) ||| wilcoxon signed rank test (median)

###one sample t-test

starwars %>% 
  select(height) %>% 
  t.test(mu = 160,
         alternative = c("two.sided"),
         conf.level = 0.95
  )
## 
##  One Sample t-test
## 
## data:  .
## t = 3.7799, df = 80, p-value = 0.0003008
## alternative hypothesis: true mean is not equal to 160
## 95 percent confidence interval:
##  166.9157 182.2941
## sample estimates:
## mean of x 
##  174.6049

p<0.05 >> Ho is rejected >> true mean is not equal to 160

###two sample t-test

starwars %>% 
  filter(sex %in% c("male","female")) %>% 
  select(height,sex) %>% 
  drop_na() %>% 
   t.test(height~sex,
         alternative = c( "two.sided" ),
         conf.level = 0.95, data=.)
## 
##  Welch Two Sample t-test
## 
## data:  height by sex
## t = -1.1817, df = 48.471, p-value = 0.2431
## alternative hypothesis: true difference in means between group female and group male is not equal to 0
## 95 percent confidence interval:
##  -20.396341   5.293584
## sample estimates:
## mean in group female   mean in group male 
##             171.5714             179.1228

p>0.05 >> Ho may not be rejected >> true difference in means between group female and group male is equal to 0

starwars %>%
  select(height,sex) %>% 
  filter(sex %in% c('male','female')) %>% 
  ggplot(mapping = aes(x=height,color=sex,fill = sex))+
  geom_density() + theme(panel.grid.major = element_line(linetype = "blank"),
    panel.grid.minor = element_line(linetype = "blank"),
    plot.title = element_text(family = "AvantGarde"),
    panel.background = element_rect(fill = "gray100"),
    plot.background = element_rect(fill = "aliceblue")) +labs(title = "Height density plot between male and female",
    alpha = 0.8)

height_before_bornvita= c(150, 190, 140, 130, 140, 180)

height_after_bornvita=  c(160, 192, 143, 133, 150, 181)

starwars %>% 
  select(height) %>% 
  t.test(height_before_bornvita , height_after_bornvita,data=.,conf.level = 0.95, paired = TRUE,alternative = "two.sided")
## 
##  Paired t-test
## 
## data:  height_before_bornvita and height_after_bornvita
## t = -2.9087, df = 5, p-value = 0.03345
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -9.1047641 -0.5619025
## sample estimates:
## mean difference 
##       -4.833333

one sample wilcox test:

wilcox.test(starwars$height,mu=160,
              alternative = "two.sided",
              conf.level = 0.95,
              data=.)
## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  starwars$height
## V = 2533.5, p-value = 1.185e-05
## alternative hypothesis: true location is not equal to 160

p<0.05 >> true location is not equal to 160

paired wilcox test

height_before_bornvita= c(150, 190, 140, 130, 140, 180)

height_after_bornvita=  c(160, 192, 143, 133, 150, 181)


wilcox.test(height_before_bornvita,height_after_bornvita,paired = TRUE,conf.level = 0.95)
## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  height_before_bornvita and height_after_bornvita
## V = 0, p-value = 0.03501
## alternative hypothesis: true location shift is not equal to 0
median(height_after_bornvita)
## [1] 155
median(height_before_bornvita)
## [1] 145

p<0.05 >> H0 rejected >> median is not equal to 0 (difference in height exists)

wilcoxon rank sum test or mann whitney test or alternative of two sample t test

data_non_parametric=starwars %>% 
  select(height,sex) %>% 
  filter( sex %in% c('male','female')) %>% 
  drop_na()


tibble(data_non_parametric)
## # A tibble: 71 × 2
##    height sex   
##     <int> <fct> 
##  1    172 male  
##  2    202 male  
##  3    150 female
##  4    178 male  
##  5    165 female
##  6    183 male  
##  7    182 male  
##  8    188 male  
##  9    180 male  
## 10    228 male  
## # ℹ 61 more rows
wilcox.test(data_non_parametric$height~data_non_parametric$sex, 
            alternative="two.sided",
            conf.level=0.95)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  data_non_parametric$height by data_non_parametric$sex
## W = 228, p-value = 0.01364
## alternative hypothesis: true location shift is not equal to 0
### quick comparison of  why i prefer non parametric over parametric

p<0.05 >> ho rejected >> median difference is not equal 0

ANOVA

anova_data=
  starwars %>% 
  select(height,species) %>% 
  mutate(species=as.factor(species)) %>% 
  drop_na() %>% 
  tibble()
### regardless i want to see if the variance is normally distributed ('~')
model= aov(anova_data$height~anova_data$species)
summary(model)
##                    Df Sum Sq Mean Sq F value   Pr(>F)    
## anova_data$species 36  81843  2273.4   6.299 3.86e-08 ***
## Residuals          40  14437   360.9                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#to check homogenity of variance
plot(model,1)

#to check normality in te data
plot(model,2)

This means according to the residual vs fitted plot we can conclude the is heteroscedesticy in the data i.e spread of variance is unequal, as the is a clear relation between fitted values and residual. We also could have used levenes test for this

ggplot(sample_n(anova_data,5),aes(x=species,y=height,color=species))+
  geom_boxplot()+
  facet_wrap(vars(species))

###homoscedesticity is a must condition for anova, we can identify it using levene's test as shown above. But for the sake of quick analysis we will assume there is already homoscedesticity in the data.

aov(height~species,data = anova_data) %>% 
  TukeyHSD()
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = height ~ species, data = anova_data)
## 
## $species
##                                      diff          lwr        upr     p adj
## Besalisk-Aleena              1.190000e+02    7.4555670 230.544433 0.0242690
## Cerean-Aleena                1.190000e+02    7.4555670 230.544433 0.0242690
## Chagrian-Aleena              1.170000e+02    5.4555670 228.544433 0.0295892
## Clawdite-Aleena              8.900000e+01  -22.5444330 200.544433 0.3110998
## Droid-Aleena                 5.220000e+01  -34.2019463 138.601946 0.8267352
## Dug-Aleena                   3.300000e+01  -78.5444330 144.544433 0.9999975
## Ewok-Aleena                  9.000000e+00 -102.5444330 120.544433 1.0000000
## Geonosian-Aleena             1.040000e+02   -7.5444330 215.544433 0.0987228
## Gungan-Aleena                1.296667e+02   38.5910185 220.742315 0.0003123
## Human-Aleena                 9.900000e+01   18.8223871 179.177613 0.0033732
## Hutt-Aleena                  9.600000e+01  -15.5444330 207.544433 0.1893017
## Iktotchi-Aleena              1.090000e+02   -2.5444330 220.544433 0.0632941
## Kaleesh-Aleena               1.370000e+02   25.4555670 248.544433 0.0036545
## Kaminoan-Aleena              1.420000e+02   45.3996874 238.600313 0.0001721
## Kel Dor-Aleena               1.090000e+02   -2.5444330 220.544433 0.0632941
## Mirialan-Aleena              8.900000e+01   -7.6003126 185.600313 0.1096896
## Mon Calamari-Aleena          1.010000e+02  -10.5444330 212.544433 0.1272042
## Muun-Aleena                  1.120000e+02    0.4555670 223.544433 0.0479032
## Nautolan-Aleena              1.170000e+02    5.4555670 228.544433 0.0295892
## Neimodian-Aleena             1.120000e+02    0.4555670 223.544433 0.0479032
## Pau'an-Aleena                1.270000e+02   15.4555670 238.544433 0.0106916
## Quermian-Aleena              1.850000e+02   73.4555670 296.544433 0.0000149
## Rodian-Aleena                9.400000e+01  -17.5444330 205.544433 0.2198230
## Skakoan-Aleena               1.140000e+02    2.4555670 225.544433 0.0396050
## Sullustan-Aleena             8.100000e+01  -30.5444330 192.544433 0.4965797
## Tholothian-Aleena            1.050000e+02   -6.5444330 216.544433 0.0905166
## Togruta-Aleena               9.900000e+01  -12.5444330 210.544433 0.1497133
## Toong-Aleena                 8.400000e+01  -27.5444330 195.544433 0.4224067
## Toydarian-Aleena             5.800000e+01  -53.5444330 169.544433 0.9570515
## Trandoshan-Aleena            1.110000e+02   -0.5444330 222.544433 0.0526137
## Twi'lek-Aleena               1.000000e+02    3.3996874 196.600313 0.0343633
## Vulptereen-Aleena            1.500000e+01  -96.5444330 126.544433 1.0000000
## Wookiee-Aleena               1.520000e+02   55.3996874 248.600313 0.0000449
## Xexto-Aleena                 4.300000e+01  -68.5444330 154.544433 0.9994249
## Yoda's species-Aleena       -1.300000e+01 -124.5444330  98.544433 1.0000000
## Zabrak-Aleena                9.400000e+01   -2.6003126 190.600313 0.0659958
## Cerean-Besalisk             -3.694822e-13 -111.5444330 111.544433 1.0000000
## Chagrian-Besalisk           -2.000000e+00 -113.5444330 109.544433 1.0000000
## Clawdite-Besalisk           -3.000000e+01 -141.5444330  81.544433 0.9999997
## Droid-Besalisk              -6.680000e+01 -153.2019463  19.601946 0.3703530
## Dug-Besalisk                -8.600000e+01 -197.5444330  25.544433 0.3757375
## Ewok-Besalisk               -1.100000e+02 -221.5444330   1.544433 0.0577346
## Geonosian-Besalisk          -1.500000e+01 -126.5444330  96.544433 1.0000000
## Gungan-Besalisk              1.066667e+01  -80.4089815 101.742315 1.0000000
## Human-Besalisk              -2.000000e+01 -100.1776129  60.177613 1.0000000
## Hutt-Besalisk               -2.300000e+01 -134.5444330  88.544433 1.0000000
## Iktotchi-Besalisk           -1.000000e+01 -121.5444330 101.544433 1.0000000
## Kaleesh-Besalisk             1.800000e+01  -93.5444330 129.544433 1.0000000
## Kaminoan-Besalisk            2.300000e+01  -73.6003126 119.600313 1.0000000
## Kel Dor-Besalisk            -1.000000e+01 -121.5444330 101.544433 1.0000000
## Mirialan-Besalisk           -3.000000e+01 -126.6003126  66.600313 0.9999925
## Mon Calamari-Besalisk       -1.800000e+01 -129.5444330  93.544433 1.0000000
## Muun-Besalisk               -7.000000e+00 -118.5444330 104.544433 1.0000000
## Nautolan-Besalisk           -2.000000e+00 -113.5444330 109.544433 1.0000000
## Neimodian-Besalisk          -7.000000e+00 -118.5444330 104.544433 1.0000000
## Pau'an-Besalisk              8.000000e+00 -103.5444330 119.544433 1.0000000
## Quermian-Besalisk            6.600000e+01  -45.5444330 177.544433 0.8529483
## Rodian-Besalisk             -2.500000e+01 -136.5444330  86.544433 1.0000000
## Skakoan-Besalisk            -5.000000e+00 -116.5444330 106.544433 1.0000000
## Sullustan-Besalisk          -3.800000e+01 -149.5444330  73.544433 0.9999459
## Tholothian-Besalisk         -1.400000e+01 -125.5444330  97.544433 1.0000000
## Togruta-Besalisk            -2.000000e+01 -131.5444330  91.544433 1.0000000
## Toong-Besalisk              -3.500000e+01 -146.5444330  76.544433 0.9999906
## Toydarian-Besalisk          -6.100000e+01 -172.5444330  50.544433 0.9274059
## Trandoshan-Besalisk         -8.000000e+00 -119.5444330 103.544433 1.0000000
## Twi'lek-Besalisk            -1.900000e+01 -115.6003126  77.600313 1.0000000
## Vulptereen-Besalisk         -1.040000e+02 -215.5444330   7.544433 0.0987228
## Wookiee-Besalisk             3.300000e+01  -63.6003126 129.600313 0.9999428
## Xexto-Besalisk              -7.600000e+01 -187.5444330  35.544433 0.6254897
## Yoda's species-Besalisk     -1.320000e+02 -243.5444330 -20.455567 0.0062873
## Zabrak-Besalisk             -2.500000e+01 -121.6003126  71.600313 0.9999999
## Chagrian-Cerean             -2.000000e+00 -113.5444330 109.544433 1.0000000
## Clawdite-Cerean             -3.000000e+01 -141.5444330  81.544433 0.9999997
## Droid-Cerean                -6.680000e+01 -153.2019463  19.601946 0.3703530
## Dug-Cerean                  -8.600000e+01 -197.5444330  25.544433 0.3757375
## Ewok-Cerean                 -1.100000e+02 -221.5444330   1.544433 0.0577346
## Geonosian-Cerean            -1.500000e+01 -126.5444330  96.544433 1.0000000
## Gungan-Cerean                1.066667e+01  -80.4089815 101.742315 1.0000000
## Human-Cerean                -2.000000e+01 -100.1776129  60.177613 1.0000000
## Hutt-Cerean                 -2.300000e+01 -134.5444330  88.544433 1.0000000
## Iktotchi-Cerean             -1.000000e+01 -121.5444330 101.544433 1.0000000
## Kaleesh-Cerean               1.800000e+01  -93.5444330 129.544433 1.0000000
## Kaminoan-Cerean              2.300000e+01  -73.6003126 119.600313 1.0000000
## Kel Dor-Cerean              -1.000000e+01 -121.5444330 101.544433 1.0000000
## Mirialan-Cerean             -3.000000e+01 -126.6003126  66.600313 0.9999925
## Mon Calamari-Cerean         -1.800000e+01 -129.5444330  93.544433 1.0000000
## Muun-Cerean                 -7.000000e+00 -118.5444330 104.544433 1.0000000
## Nautolan-Cerean             -2.000000e+00 -113.5444330 109.544433 1.0000000
## Neimodian-Cerean            -7.000000e+00 -118.5444330 104.544433 1.0000000
## Pau'an-Cerean                8.000000e+00 -103.5444330 119.544433 1.0000000
## Quermian-Cerean              6.600000e+01  -45.5444330 177.544433 0.8529483
## Rodian-Cerean               -2.500000e+01 -136.5444330  86.544433 1.0000000
## Skakoan-Cerean              -5.000000e+00 -116.5444330 106.544433 1.0000000
## Sullustan-Cerean            -3.800000e+01 -149.5444330  73.544433 0.9999459
## Tholothian-Cerean           -1.400000e+01 -125.5444330  97.544433 1.0000000
## Togruta-Cerean              -2.000000e+01 -131.5444330  91.544433 1.0000000
## Toong-Cerean                -3.500000e+01 -146.5444330  76.544433 0.9999906
## Toydarian-Cerean            -6.100000e+01 -172.5444330  50.544433 0.9274059
## Trandoshan-Cerean           -8.000000e+00 -119.5444330 103.544433 1.0000000
## Twi'lek-Cerean              -1.900000e+01 -115.6003126  77.600313 1.0000000
## Vulptereen-Cerean           -1.040000e+02 -215.5444330   7.544433 0.0987228
## Wookiee-Cerean               3.300000e+01  -63.6003126 129.600313 0.9999428
## Xexto-Cerean                -7.600000e+01 -187.5444330  35.544433 0.6254897
## Yoda's species-Cerean       -1.320000e+02 -243.5444330 -20.455567 0.0062873
## Zabrak-Cerean               -2.500000e+01 -121.6003126  71.600313 0.9999999
## Clawdite-Chagrian           -2.800000e+01 -139.5444330  83.544433 1.0000000
## Droid-Chagrian              -6.480000e+01 -151.2019463  21.601946 0.4306729
## Dug-Chagrian                -8.400000e+01 -195.5444330  27.544433 0.4224067
## Ewok-Chagrian               -1.080000e+02 -219.5444330   3.544433 0.0693217
## Geonosian-Chagrian          -1.300000e+01 -124.5444330  98.544433 1.0000000
## Gungan-Chagrian              1.266667e+01  -78.4089815 103.742315 1.0000000
## Human-Chagrian              -1.800000e+01  -98.1776129  62.177613 1.0000000
## Hutt-Chagrian               -2.100000e+01 -132.5444330  90.544433 1.0000000
## Iktotchi-Chagrian           -8.000000e+00 -119.5444330 103.544433 1.0000000
## Kaleesh-Chagrian             2.000000e+01  -91.5444330 131.544433 1.0000000
## Kaminoan-Chagrian            2.500000e+01  -71.6003126 121.600313 0.9999999
## Kel Dor-Chagrian            -8.000000e+00 -119.5444330 103.544433 1.0000000
## Mirialan-Chagrian           -2.800000e+01 -124.6003126  68.600313 0.9999985
## Mon Calamari-Chagrian       -1.600000e+01 -127.5444330  95.544433 1.0000000
## Muun-Chagrian               -5.000000e+00 -116.5444330 106.544433 1.0000000
## Nautolan-Chagrian            2.842171e-14 -111.5444330 111.544433 1.0000000
## Neimodian-Chagrian          -5.000000e+00 -116.5444330 106.544433 1.0000000
## Pau'an-Chagrian              1.000000e+01 -101.5444330 121.544433 1.0000000
## Quermian-Chagrian            6.800000e+01  -43.5444330 179.544433 0.8145320
## Rodian-Chagrian             -2.300000e+01 -134.5444330  88.544433 1.0000000
## Skakoan-Chagrian            -3.000000e+00 -114.5444330 108.544433 1.0000000
## Sullustan-Chagrian          -3.600000e+01 -147.5444330  75.544433 0.9999826
## Tholothian-Chagrian         -1.200000e+01 -123.5444330  99.544433 1.0000000
## Togruta-Chagrian            -1.800000e+01 -129.5444330  93.544433 1.0000000
## Toong-Chagrian              -3.300000e+01 -144.5444330  78.544433 0.9999975
## Toydarian-Chagrian          -5.900000e+01 -170.5444330  52.544433 0.9483549
## Trandoshan-Chagrian         -6.000000e+00 -117.5444330 105.544433 1.0000000
## Twi'lek-Chagrian            -1.700000e+01 -113.6003126  79.600313 1.0000000
## Vulptereen-Chagrian         -1.020000e+02 -213.5444330   9.544433 0.1170356
## Wookiee-Chagrian             3.500000e+01  -61.6003126 131.600313 0.9998171
## Xexto-Chagrian              -7.400000e+01 -185.5444330  37.544433 0.6763866
## Yoda's species-Chagrian     -1.300000e+02 -241.5444330 -18.455567 0.0077867
## Zabrak-Chagrian             -2.300000e+01 -119.6003126  73.600313 1.0000000
## Droid-Clawdite              -3.680000e+01 -123.2019463  49.601946 0.9969629
## Dug-Clawdite                -5.600000e+01 -167.5444330  55.544433 0.9711956
## Ewok-Clawdite               -8.000000e+01 -191.5444330  31.544433 0.5220973
## Geonosian-Clawdite           1.500000e+01  -96.5444330 126.544433 1.0000000
## Gungan-Clawdite              4.066667e+01  -50.4089815 131.742315 0.9938239
## Human-Clawdite               1.000000e+01  -70.1776129  90.177613 1.0000000
## Hutt-Clawdite                7.000000e+00 -104.5444330 118.544433 1.0000000
## Iktotchi-Clawdite            2.000000e+01  -91.5444330 131.544433 1.0000000
## Kaleesh-Clawdite             4.800000e+01  -63.5444330 159.544433 0.9964396
## Kaminoan-Clawdite            5.300000e+01  -43.6003126 149.600313 0.9250498
## Kel Dor-Clawdite             2.000000e+01  -91.5444330 131.544433 1.0000000
## Mirialan-Clawdite            2.842171e-14  -96.6003126  96.600313 1.0000000
## Mon Calamari-Clawdite        1.200000e+01  -99.5444330 123.544433 1.0000000
## Muun-Clawdite                2.300000e+01  -88.5444330 134.544433 1.0000000
## Nautolan-Clawdite            2.800000e+01  -83.5444330 139.544433 1.0000000
## Neimodian-Clawdite           2.300000e+01  -88.5444330 134.544433 1.0000000
## Pau'an-Clawdite              3.800000e+01  -73.5444330 149.544433 0.9999459
## Quermian-Clawdite            9.600000e+01  -15.5444330 207.544433 0.1893017
## Rodian-Clawdite              5.000000e+00 -106.5444330 116.544433 1.0000000
## Skakoan-Clawdite             2.500000e+01  -86.5444330 136.544433 1.0000000
## Sullustan-Clawdite          -8.000000e+00 -119.5444330 103.544433 1.0000000
## Tholothian-Clawdite          1.600000e+01  -95.5444330 127.544433 1.0000000
## Togruta-Clawdite             1.000000e+01 -101.5444330 121.544433 1.0000000
## Toong-Clawdite              -5.000000e+00 -116.5444330 106.544433 1.0000000
## Toydarian-Clawdite          -3.100000e+01 -142.5444330  80.544433 0.9999994
## Trandoshan-Clawdite          2.200000e+01  -89.5444330 133.544433 1.0000000
## Twi'lek-Clawdite             1.100000e+01  -85.6003126 107.600313 1.0000000
## Vulptereen-Clawdite         -7.400000e+01 -185.5444330  37.544433 0.6763866
## Wookiee-Clawdite             6.300000e+01  -33.6003126 159.600313 0.7074325
## Xexto-Clawdite              -4.600000e+01 -157.5444330  65.544433 0.9981838
## Yoda's species-Clawdite     -1.020000e+02 -213.5444330   9.544433 0.1170356
## Zabrak-Clawdite              5.000000e+00  -91.6003126 101.600313 1.0000000
## Dug-Droid                   -1.920000e+01 -105.6019463  67.201946 1.0000000
## Ewok-Droid                  -4.320000e+01 -129.6019463  43.201946 0.9725592
## Geonosian-Droid              5.180000e+01  -34.6019463 138.201946 0.8367375
## Gungan-Droid                 7.746667e+01   19.8653692 135.067964 0.0008541
## Human-Droid                  4.680000e+01    8.7003229  84.899677 0.0036480
## Hutt-Droid                   4.380000e+01  -42.6019463 130.201946 0.9677435
## Iktotchi-Droid               5.680000e+01  -29.6019463 143.201946 0.6931171
## Kaleesh-Droid                8.480000e+01   -1.6019463 171.201946 0.0605894
## Kaminoan-Droid               8.980000e+01   23.8094235 155.790576 0.0006979
## Kel Dor-Droid                5.680000e+01  -29.6019463 143.201946 0.6931171
## Mirialan-Droid               3.680000e+01  -29.1905765 102.790576 0.9124014
## Mon Calamari-Droid           4.880000e+01  -37.6019463 135.201946 0.9014421
## Muun-Droid                   5.980000e+01  -26.6019463 146.201946 0.5944466
## Nautolan-Droid               6.480000e+01  -21.6019463 151.201946 0.4306729
## Neimodian-Droid              5.980000e+01  -26.6019463 146.201946 0.5944466
## Pau'an-Droid                 7.480000e+01  -11.6019463 161.201946 0.1812688
## Quermian-Droid               1.328000e+02   46.3980537 219.201946 0.0000722
## Rodian-Droid                 4.180000e+01  -44.6019463 128.201946 0.9816777
## Skakoan-Droid                6.180000e+01  -24.6019463 148.201946 0.5276581
## Sullustan-Droid              2.880000e+01  -57.6019463 115.201946 0.9999655
## Tholothian-Droid             5.280000e+01  -33.6019463 139.201946 0.8111718
## Togruta-Droid                4.680000e+01  -39.6019463 133.201946 0.9340014
## Toong-Droid                  3.180000e+01  -54.6019463 118.201946 0.9997537
## Toydarian-Droid              5.800000e+00  -80.6019463  92.201946 1.0000000
## Trandoshan-Droid             5.880000e+01  -27.6019463 145.201946 0.6277932
## Twi'lek-Droid                4.780000e+01  -18.1905765 113.790576 0.5017419
## Vulptereen-Droid            -3.720000e+01 -123.6019463  49.201946 0.9964111
## Wookiee-Droid                9.980000e+01   33.8094235 165.790576 0.0000995
## Xexto-Droid                 -9.200000e+00  -95.6019463  77.201946 1.0000000
## Yoda's species-Droid        -6.520000e+01 -151.6019463  21.201946 0.4182741
## Zabrak-Droid                 4.180000e+01  -24.1905765 107.790576 0.7569909
## Ewok-Dug                    -2.400000e+01 -135.5444330  87.544433 1.0000000
## Geonosian-Dug                7.100000e+01  -40.5444330 182.544433 0.7490383
## Gungan-Dug                   9.666667e+01    5.5910185 187.742315 0.0257843
## Human-Dug                    6.600000e+01  -14.1776129 146.177613 0.2569853
## Hutt-Dug                     6.300000e+01  -48.5444330 174.544433 0.9014496
## Iktotchi-Dug                 7.600000e+01  -35.5444330 187.544433 0.6254897
## Kaleesh-Dug                  1.040000e+02   -7.5444330 215.544433 0.0987228
## Kaminoan-Dug                 1.090000e+02   12.3996874 205.600313 0.0120422
## Kel Dor-Dug                  7.600000e+01  -35.5444330 187.544433 0.6254897
## Mirialan-Dug                 5.600000e+01  -40.6003126 152.600313 0.8759616
## Mon Calamari-Dug             6.800000e+01  -43.5444330 179.544433 0.8145320
## Muun-Dug                     7.900000e+01  -32.5444330 190.544433 0.5478549
## Nautolan-Dug                 8.400000e+01  -27.5444330 195.544433 0.4224067
## Neimodian-Dug                7.900000e+01  -32.5444330 190.544433 0.5478549
## Pau'an-Dug                   9.400000e+01  -17.5444330 205.544433 0.2198230
## Quermian-Dug                 1.520000e+02   40.4555670 263.544433 0.0006814
## Rodian-Dug                   6.100000e+01  -50.5444330 172.544433 0.9274059
## Skakoan-Dug                  8.100000e+01  -30.5444330 192.544433 0.4965797
## Sullustan-Dug                4.800000e+01  -63.5444330 159.544433 0.9964396
## Tholothian-Dug               7.200000e+01  -39.5444330 183.544433 0.7254717
## Togruta-Dug                  6.600000e+01  -45.5444330 177.544433 0.8529483
## Toong-Dug                    5.100000e+01  -60.5444330 162.544433 0.9913517
## Toydarian-Dug                2.500000e+01  -86.5444330 136.544433 1.0000000
## Trandoshan-Dug               7.800000e+01  -33.5444330 189.544433 0.5737476
## Twi'lek-Dug                  6.700000e+01  -29.6003126 163.600313 0.5902109
## Vulptereen-Dug              -1.800000e+01 -129.5444330  93.544433 1.0000000
## Wookiee-Dug                  1.190000e+02   22.3996874 215.600313 0.0034942
## Xexto-Dug                    1.000000e+01 -101.5444330 121.544433 1.0000000
## Yoda's species-Dug          -4.600000e+01 -157.5444330  65.544433 0.9981838
## Zabrak-Dug                   6.100000e+01  -35.6003126 157.600313 0.7619671
## Geonosian-Ewok               9.500000e+01  -16.5444330 206.544433 0.2041387
## Gungan-Ewok                  1.206667e+02   29.5910185 211.742315 0.0010992
## Human-Ewok                   9.000000e+01    9.8223871 170.177613 0.0128886
## Hutt-Ewok                    8.700000e+01  -24.5444330 198.544433 0.3534296
## Iktotchi-Ewok                1.000000e+02  -11.5444330 211.544433 0.1380873
## Kaleesh-Ewok                 1.280000e+02   16.4555670 239.544433 0.0096244
## Kaminoan-Ewok                1.330000e+02   36.3996874 229.600313 0.0005693
## Kel Dor-Ewok                 1.000000e+02  -11.5444330 211.544433 0.1380873
## Mirialan-Ewok                8.000000e+01  -16.6003126 176.600313 0.2471215
## Mon Calamari-Ewok            9.200000e+01  -19.5444330 203.544433 0.2537667
## Muun-Ewok                    1.030000e+02   -8.5444330 214.544433 0.1075520
## Nautolan-Ewok                1.080000e+02   -3.5444330 219.544433 0.0693217
## Neimodian-Ewok               1.030000e+02   -8.5444330 214.544433 0.1075520
## Pau'an-Ewok                  1.180000e+02    6.4555670 229.544433 0.0268073
## Quermian-Ewok                1.760000e+02   64.4555670 287.544433 0.0000425
## Rodian-Ewok                  8.500000e+01  -26.5444330 196.544433 0.3987484
## Skakoan-Ewok                 1.050000e+02   -6.5444330 216.544433 0.0905166
## Sullustan-Ewok               7.200000e+01  -39.5444330 183.544433 0.7254717
## Tholothian-Ewok              9.600000e+01  -15.5444330 207.544433 0.1893017
## Togruta-Ewok                 9.000000e+01  -21.5444330 201.544433 0.2911454
## Toong-Ewok                   7.500000e+01  -36.5444330 186.544433 0.6511041
## Toydarian-Ewok               4.900000e+01  -62.5444330 160.544433 0.9951393
## Trandoshan-Ewok              1.020000e+02   -9.5444330 213.544433 0.1170356
## Twi'lek-Ewok                 9.100000e+01   -5.6003126 187.600313 0.0899037
## Vulptereen-Ewok              6.000000e+00 -105.5444330 117.544433 1.0000000
## Wookiee-Ewok                 1.430000e+02   46.3996874 239.600313 0.0001506
## Xexto-Ewok                   3.400000e+01  -77.5444330 145.544433 0.9999951
## Yoda's species-Ewok         -2.200000e+01 -133.5444330  89.544433 1.0000000
## Zabrak-Ewok                  8.500000e+01  -11.6003126 181.600313 0.1602051
## Gungan-Geonosian             2.566667e+01  -65.4089815 116.742315 0.9999992
## Human-Geonosian             -5.000000e+00  -85.1776129  75.177613 1.0000000
## Hutt-Geonosian              -8.000000e+00 -119.5444330 103.544433 1.0000000
## Iktotchi-Geonosian           5.000000e+00 -106.5444330 116.544433 1.0000000
## Kaleesh-Geonosian            3.300000e+01  -78.5444330 144.544433 0.9999975
## Kaminoan-Geonosian           3.800000e+01  -58.6003126 134.600313 0.9991794
## Kel Dor-Geonosian            5.000000e+00 -106.5444330 116.544433 1.0000000
## Mirialan-Geonosian          -1.500000e+01 -111.6003126  81.600313 1.0000000
## Mon Calamari-Geonosian      -3.000000e+00 -114.5444330 108.544433 1.0000000
## Muun-Geonosian               8.000000e+00 -103.5444330 119.544433 1.0000000
## Nautolan-Geonosian           1.300000e+01  -98.5444330 124.544433 1.0000000
## Neimodian-Geonosian          8.000000e+00 -103.5444330 119.544433 1.0000000
## Pau'an-Geonosian             2.300000e+01  -88.5444330 134.544433 1.0000000
## Quermian-Geonosian           8.100000e+01  -30.5444330 192.544433 0.4965797
## Rodian-Geonosian            -1.000000e+01 -121.5444330 101.544433 1.0000000
## Skakoan-Geonosian            1.000000e+01 -101.5444330 121.544433 1.0000000
## Sullustan-Geonosian         -2.300000e+01 -134.5444330  88.544433 1.0000000
## Tholothian-Geonosian         1.000000e+00 -110.5444330 112.544433 1.0000000
## Togruta-Geonosian           -5.000000e+00 -116.5444330 106.544433 1.0000000
## Toong-Geonosian             -2.000000e+01 -131.5444330  91.544433 1.0000000
## Toydarian-Geonosian         -4.600000e+01 -157.5444330  65.544433 0.9981838
## Trandoshan-Geonosian         7.000000e+00 -104.5444330 118.544433 1.0000000
## Twi'lek-Geonosian           -4.000000e+00 -100.6003126  92.600313 1.0000000
## Vulptereen-Geonosian        -8.900000e+01 -200.5444330  22.544433 0.3110998
## Wookiee-Geonosian            4.800000e+01  -48.6003126 144.600313 0.9745227
## Xexto-Geonosian             -6.100000e+01 -172.5444330  50.544433 0.9274059
## Yoda's species-Geonosian    -1.170000e+02 -228.5444330  -5.455567 0.0295892
## Zabrak-Geonosian            -1.000000e+01 -106.6003126  86.600313 1.0000000
## Human-Gungan                -3.066667e+01  -78.4271395  17.093806 0.7344694
## Hutt-Gungan                 -3.366667e+01 -124.7423148  57.408981 0.9997327
## Iktotchi-Gungan             -2.066667e+01 -111.7423148  70.408981 1.0000000
## Kaleesh-Gungan               7.333333e+00  -83.7423148  98.408981 1.0000000
## Kaminoan-Gungan              1.233333e+01  -59.6682886  84.334955 1.0000000
## Kel Dor-Gungan              -2.066667e+01 -111.7423148  70.408981 1.0000000
## Mirialan-Gungan             -4.066667e+01 -112.6682886  31.334955 0.9014421
## Mon Calamari-Gungan         -2.866667e+01 -119.7423148  62.408981 0.9999899
## Muun-Gungan                 -1.766667e+01 -108.7423148  73.408981 1.0000000
## Nautolan-Gungan             -1.266667e+01 -103.7423148  78.408981 1.0000000
## Neimodian-Gungan            -1.766667e+01 -108.7423148  73.408981 1.0000000
## Pau'an-Gungan               -2.666667e+00  -93.7423148  88.408981 1.0000000
## Quermian-Gungan              5.533333e+01  -35.7423148 146.408981 0.8191965
## Rodian-Gungan               -3.566667e+01 -126.7423148  55.408981 0.9992409
## Skakoan-Gungan              -1.566667e+01 -106.7423148  75.408981 1.0000000
## Sullustan-Gungan            -4.866667e+01 -139.7423148  42.408981 0.9425371
## Tholothian-Gungan           -2.466667e+01 -115.7423148  66.408981 0.9999997
## Togruta-Gungan              -3.066667e+01 -121.7423148  60.408981 0.9999575
## Toong-Gungan                -4.566667e+01 -136.7423148  45.408981 0.9716175
## Toydarian-Gungan            -7.166667e+01 -162.7423148  19.408981 0.3366888
## Trandoshan-Gungan           -1.866667e+01 -109.7423148  72.408981 1.0000000
## Twi'lek-Gungan              -2.966667e+01 -101.6682886  42.334955 0.9982097
## Vulptereen-Gungan           -1.146667e+02 -205.7423148 -23.591019 0.0025023
## Wookiee-Gungan               2.233333e+01  -49.6682886  94.334955 0.9999927
## Xexto-Gungan                -8.666667e+01 -177.7423148   4.408981 0.0818483
## Yoda's species-Gungan       -1.426667e+02 -233.7423148 -51.591019 0.0000492
## Zabrak-Gungan               -3.566667e+01 -107.6682886  36.334955 0.9754549
## Hutt-Human                  -3.000000e+00  -83.1776129  77.177613 1.0000000
## Iktotchi-Human               1.000000e+01  -70.1776129  90.177613 1.0000000
## Kaleesh-Human                3.800000e+01  -42.1776129 118.177613 0.9859367
## Kaminoan-Human               4.300000e+01  -14.6012975 100.601298 0.4400705
## Kel Dor-Human                1.000000e+01  -70.1776129  90.177613 1.0000000
## Mirialan-Human              -1.000000e+01  -67.6012975  47.601298 1.0000000
## Mon Calamari-Human           2.000000e+00  -78.1776129  82.177613 1.0000000
## Muun-Human                   1.300000e+01  -67.1776129  93.177613 1.0000000
## Nautolan-Human               1.800000e+01  -62.1776129  98.177613 1.0000000
## Neimodian-Human              1.300000e+01  -67.1776129  93.177613 1.0000000
## Pau'an-Human                 2.800000e+01  -52.1776129 108.177613 0.9999109
## Quermian-Human               8.600000e+01    5.8223871 166.177613 0.0227529
## Rodian-Human                -5.000000e+00  -85.1776129  75.177613 1.0000000
## Skakoan-Human                1.500000e+01  -65.1776129  95.177613 1.0000000
## Sullustan-Human             -1.800000e+01  -98.1776129  62.177613 1.0000000
## Tholothian-Human             6.000000e+00  -74.1776129  86.177613 1.0000000
## Togruta-Human               -2.842171e-14  -80.1776129  80.177613 1.0000000
## Toong-Human                 -1.500000e+01  -95.1776129  65.177613 1.0000000
## Toydarian-Human             -4.100000e+01 -121.1776129  39.177613 0.9643588
## Trandoshan-Human             1.200000e+01  -68.1776129  92.177613 1.0000000
## Twi'lek-Human                1.000000e+00  -56.6012975  58.601298 1.0000000
## Vulptereen-Human            -8.400000e+01 -164.1776129  -3.822387 0.0299928
## Wookiee-Human                5.300000e+01   -4.6012975 110.601298 0.1109449
## Xexto-Human                 -5.600000e+01 -136.1776129  24.177613 0.5761292
## Yoda's species-Human        -1.120000e+02 -192.1776129 -31.822387 0.0004405
## Zabrak-Human                -5.000000e+00  -62.6012975  52.601298 1.0000000
## Iktotchi-Hutt                1.300000e+01  -98.5444330 124.544433 1.0000000
## Kaleesh-Hutt                 4.100000e+01  -70.5444330 152.544433 0.9997596
## Kaminoan-Hutt                4.600000e+01  -50.6003126 142.600313 0.9850430
## Kel Dor-Hutt                 1.300000e+01  -98.5444330 124.544433 1.0000000
## Mirialan-Hutt               -7.000000e+00 -103.6003126  89.600313 1.0000000
## Mon Calamari-Hutt            5.000000e+00 -106.5444330 116.544433 1.0000000
## Muun-Hutt                    1.600000e+01  -95.5444330 127.544433 1.0000000
## Nautolan-Hutt                2.100000e+01  -90.5444330 132.544433 1.0000000
## Neimodian-Hutt               1.600000e+01  -95.5444330 127.544433 1.0000000
## Pau'an-Hutt                  3.100000e+01  -80.5444330 142.544433 0.9999994
## Quermian-Hutt                8.900000e+01  -22.5444330 200.544433 0.3110998
## Rodian-Hutt                 -2.000000e+00 -113.5444330 109.544433 1.0000000
## Skakoan-Hutt                 1.800000e+01  -93.5444330 129.544433 1.0000000
## Sullustan-Hutt              -1.500000e+01 -126.5444330  96.544433 1.0000000
## Tholothian-Hutt              9.000000e+00 -102.5444330 120.544433 1.0000000
## Togruta-Hutt                 3.000000e+00 -108.5444330 114.544433 1.0000000
## Toong-Hutt                  -1.200000e+01 -123.5444330  99.544433 1.0000000
## Toydarian-Hutt              -3.800000e+01 -149.5444330  73.544433 0.9999459
## Trandoshan-Hutt              1.500000e+01  -96.5444330 126.544433 1.0000000
## Twi'lek-Hutt                 4.000000e+00  -92.6003126 100.600313 1.0000000
## Vulptereen-Hutt             -8.100000e+01 -192.5444330  30.544433 0.4965797
## Wookiee-Hutt                 5.600000e+01  -40.6003126 152.600313 0.8759616
## Xexto-Hutt                  -5.300000e+01 -164.5444330  58.544433 0.9854639
## Yoda's species-Hutt         -1.090000e+02 -220.5444330   2.544433 0.0632941
## Zabrak-Hutt                 -2.000000e+00  -98.6003126  94.600313 1.0000000
## Kaleesh-Iktotchi             2.800000e+01  -83.5444330 139.544433 1.0000000
## Kaminoan-Iktotchi            3.300000e+01  -63.6003126 129.600313 0.9999428
## Kel Dor-Iktotchi            -2.842171e-14 -111.5444330 111.544433 1.0000000
## Mirialan-Iktotchi           -2.000000e+01 -116.6003126  76.600313 1.0000000
## Mon Calamari-Iktotchi       -8.000000e+00 -119.5444330 103.544433 1.0000000
## Muun-Iktotchi                3.000000e+00 -108.5444330 114.544433 1.0000000
## Nautolan-Iktotchi            8.000000e+00 -103.5444330 119.544433 1.0000000
## Neimodian-Iktotchi           3.000000e+00 -108.5444330 114.544433 1.0000000
## Pau'an-Iktotchi              1.800000e+01  -93.5444330 129.544433 1.0000000
## Quermian-Iktotchi            7.600000e+01  -35.5444330 187.544433 0.6254897
## Rodian-Iktotchi             -1.500000e+01 -126.5444330  96.544433 1.0000000
## Skakoan-Iktotchi             5.000000e+00 -106.5444330 116.544433 1.0000000
## Sullustan-Iktotchi          -2.800000e+01 -139.5444330  83.544433 1.0000000
## Tholothian-Iktotchi         -4.000000e+00 -115.5444330 107.544433 1.0000000
## Togruta-Iktotchi            -1.000000e+01 -121.5444330 101.544433 1.0000000
## Toong-Iktotchi              -2.500000e+01 -136.5444330  86.544433 1.0000000
## Toydarian-Iktotchi          -5.100000e+01 -162.5444330  60.544433 0.9913517
## Trandoshan-Iktotchi          2.000000e+00 -109.5444330 113.544433 1.0000000
## Twi'lek-Iktotchi            -9.000000e+00 -105.6003126  87.600313 1.0000000
## Vulptereen-Iktotchi         -9.400000e+01 -205.5444330  17.544433 0.2198230
## Wookiee-Iktotchi             4.300000e+01  -53.6003126 139.600313 0.9940958
## Xexto-Iktotchi              -6.600000e+01 -177.5444330  45.544433 0.8529483
## Yoda's species-Iktotchi     -1.220000e+02 -233.5444330 -10.455567 0.0179317
## Zabrak-Iktotchi             -1.500000e+01 -111.6003126  81.600313 1.0000000
## Kaminoan-Kaleesh             5.000000e+00  -91.6003126 101.600313 1.0000000
## Kel Dor-Kaleesh             -2.800000e+01 -139.5444330  83.544433 1.0000000
## Mirialan-Kaleesh            -4.800000e+01 -144.6003126  48.600313 0.9745227
## Mon Calamari-Kaleesh        -3.600000e+01 -147.5444330  75.544433 0.9999826
## Muun-Kaleesh                -2.500000e+01 -136.5444330  86.544433 1.0000000
## Nautolan-Kaleesh            -2.000000e+01 -131.5444330  91.544433 1.0000000
## Neimodian-Kaleesh           -2.500000e+01 -136.5444330  86.544433 1.0000000
## Pau'an-Kaleesh              -1.000000e+01 -121.5444330 101.544433 1.0000000
## Quermian-Kaleesh             4.800000e+01  -63.5444330 159.544433 0.9964396
## Rodian-Kaleesh              -4.300000e+01 -154.5444330  68.544433 0.9994249
## Skakoan-Kaleesh             -2.300000e+01 -134.5444330  88.544433 1.0000000
## Sullustan-Kaleesh           -5.600000e+01 -167.5444330  55.544433 0.9711956
## Tholothian-Kaleesh          -3.200000e+01 -143.5444330  79.544433 0.9999988
## Togruta-Kaleesh             -3.800000e+01 -149.5444330  73.544433 0.9999459
## Toong-Kaleesh               -5.300000e+01 -164.5444330  58.544433 0.9854639
## Toydarian-Kaleesh           -7.900000e+01 -190.5444330  32.544433 0.5478549
## Trandoshan-Kaleesh          -2.600000e+01 -137.5444330  85.544433 1.0000000
## Twi'lek-Kaleesh             -3.700000e+01 -133.6003126  59.600313 0.9994874
## Vulptereen-Kaleesh          -1.220000e+02 -233.5444330 -10.455567 0.0179317
## Wookiee-Kaleesh              1.500000e+01  -81.6003126 111.600313 1.0000000
## Xexto-Kaleesh               -9.400000e+01 -205.5444330  17.544433 0.2198230
## Yoda's species-Kaleesh      -1.500000e+02 -261.5444330 -38.455567 0.0008555
## Zabrak-Kaleesh              -4.300000e+01 -139.6003126  53.600313 0.9940958
## Kel Dor-Kaminoan            -3.300000e+01 -129.6003126  63.600313 0.9999428
## Mirialan-Kaminoan           -5.300000e+01 -131.8738250  25.873825 0.6522926
## Mon Calamari-Kaminoan       -4.100000e+01 -137.6003126  55.600313 0.9971243
## Muun-Kaminoan               -3.000000e+01 -126.6003126  66.600313 0.9999925
## Nautolan-Kaminoan           -2.500000e+01 -121.6003126  71.600313 0.9999999
## Neimodian-Kaminoan          -3.000000e+01 -126.6003126  66.600313 0.9999925
## Pau'an-Kaminoan             -1.500000e+01 -111.6003126  81.600313 1.0000000
## Quermian-Kaminoan            4.300000e+01  -53.6003126 139.600313 0.9940958
## Rodian-Kaminoan             -4.800000e+01 -144.6003126  48.600313 0.9745227
## Skakoan-Kaminoan            -2.800000e+01 -124.6003126  68.600313 0.9999985
## Sullustan-Kaminoan          -6.100000e+01 -157.6003126  35.600313 0.7619671
## Tholothian-Kaminoan         -3.700000e+01 -133.6003126  59.600313 0.9994874
## Togruta-Kaminoan            -4.300000e+01 -139.6003126  53.600313 0.9940958
## Toong-Kaminoan              -5.800000e+01 -154.6003126  38.600313 0.8348414
## Toydarian-Kaminoan          -8.400000e+01 -180.6003126  12.600313 0.1753678
## Trandoshan-Kaminoan         -3.100000e+01 -127.6003126  65.600313 0.9999846
## Twi'lek-Kaminoan            -4.200000e+01 -120.8738250  36.873825 0.9445817
## Vulptereen-Kaminoan         -1.270000e+02 -223.6003126 -30.399687 0.0012500
## Wookiee-Kaminoan             1.000000e+01  -68.8738250  88.873825 1.0000000
## Xexto-Kaminoan              -9.900000e+01 -195.6003126  -2.399687 0.0384228
## Yoda's species-Kaminoan     -1.550000e+02 -251.6003126 -58.399687 0.0000300
## Zabrak-Kaminoan             -4.800000e+01 -126.8738250  30.873825 0.8169191
## Mirialan-Kel Dor            -2.000000e+01 -116.6003126  76.600313 1.0000000
## Mon Calamari-Kel Dor        -8.000000e+00 -119.5444330 103.544433 1.0000000
## Muun-Kel Dor                 3.000000e+00 -108.5444330 114.544433 1.0000000
## Nautolan-Kel Dor             8.000000e+00 -103.5444330 119.544433 1.0000000
## Neimodian-Kel Dor            3.000000e+00 -108.5444330 114.544433 1.0000000
## Pau'an-Kel Dor               1.800000e+01  -93.5444330 129.544433 1.0000000
## Quermian-Kel Dor             7.600000e+01  -35.5444330 187.544433 0.6254897
## Rodian-Kel Dor              -1.500000e+01 -126.5444330  96.544433 1.0000000
## Skakoan-Kel Dor              5.000000e+00 -106.5444330 116.544433 1.0000000
## Sullustan-Kel Dor           -2.800000e+01 -139.5444330  83.544433 1.0000000
## Tholothian-Kel Dor          -4.000000e+00 -115.5444330 107.544433 1.0000000
## Togruta-Kel Dor             -1.000000e+01 -121.5444330 101.544433 1.0000000
## Toong-Kel Dor               -2.500000e+01 -136.5444330  86.544433 1.0000000
## Toydarian-Kel Dor           -5.100000e+01 -162.5444330  60.544433 0.9913517
## Trandoshan-Kel Dor           2.000000e+00 -109.5444330 113.544433 1.0000000
## Twi'lek-Kel Dor             -9.000000e+00 -105.6003126  87.600313 1.0000000
## Vulptereen-Kel Dor          -9.400000e+01 -205.5444330  17.544433 0.2198230
## Wookiee-Kel Dor              4.300000e+01  -53.6003126 139.600313 0.9940958
## Xexto-Kel Dor               -6.600000e+01 -177.5444330  45.544433 0.8529483
## Yoda's species-Kel Dor      -1.220000e+02 -233.5444330 -10.455567 0.0179317
## Zabrak-Kel Dor              -1.500000e+01 -111.6003126  81.600313 1.0000000
## Mon Calamari-Mirialan        1.200000e+01  -84.6003126 108.600313 1.0000000
## Muun-Mirialan                2.300000e+01  -73.6003126 119.600313 1.0000000
## Nautolan-Mirialan            2.800000e+01  -68.6003126 124.600313 0.9999985
## Neimodian-Mirialan           2.300000e+01  -73.6003126 119.600313 1.0000000
## Pau'an-Mirialan              3.800000e+01  -58.6003126 134.600313 0.9991794
## Quermian-Mirialan            9.600000e+01   -0.6003126 192.600313 0.0533487
## Rodian-Mirialan              5.000000e+00  -91.6003126 101.600313 1.0000000
## Skakoan-Mirialan             2.500000e+01  -71.6003126 121.600313 0.9999999
## Sullustan-Mirialan          -8.000000e+00 -104.6003126  88.600313 1.0000000
## Tholothian-Mirialan          1.600000e+01  -80.6003126 112.600313 1.0000000
## Togruta-Mirialan             1.000000e+01  -86.6003126 106.600313 1.0000000
## Toong-Mirialan              -5.000000e+00 -101.6003126  91.600313 1.0000000
## Toydarian-Mirialan          -3.100000e+01 -127.6003126  65.600313 0.9999846
## Trandoshan-Mirialan          2.200000e+01  -74.6003126 118.600313 1.0000000
## Twi'lek-Mirialan             1.100000e+01  -67.8738250  89.873825 1.0000000
## Vulptereen-Mirialan         -7.400000e+01 -170.6003126  22.600313 0.3883596
## Wookiee-Mirialan             6.300000e+01  -15.8738250 141.873825 0.3091594
## Xexto-Mirialan              -4.600000e+01 -142.6003126  50.600313 0.9850430
## Yoda's species-Mirialan     -1.020000e+02 -198.6003126  -5.399687 0.0273992
## Zabrak-Mirialan              5.000000e+00  -73.8738250  83.873825 1.0000000
## Muun-Mon Calamari            1.100000e+01 -100.5444330 122.544433 1.0000000
## Nautolan-Mon Calamari        1.600000e+01  -95.5444330 127.544433 1.0000000
## Neimodian-Mon Calamari       1.100000e+01 -100.5444330 122.544433 1.0000000
## Pau'an-Mon Calamari          2.600000e+01  -85.5444330 137.544433 1.0000000
## Quermian-Mon Calamari        8.400000e+01  -27.5444330 195.544433 0.4224067
## Rodian-Mon Calamari         -7.000000e+00 -118.5444330 104.544433 1.0000000
## Skakoan-Mon Calamari         1.300000e+01  -98.5444330 124.544433 1.0000000
## Sullustan-Mon Calamari      -2.000000e+01 -131.5444330  91.544433 1.0000000
## Tholothian-Mon Calamari      4.000000e+00 -107.5444330 115.544433 1.0000000
## Togruta-Mon Calamari        -2.000000e+00 -113.5444330 109.544433 1.0000000
## Toong-Mon Calamari          -1.700000e+01 -128.5444330  94.544433 1.0000000
## Toydarian-Mon Calamari      -4.300000e+01 -154.5444330  68.544433 0.9994249
## Trandoshan-Mon Calamari      1.000000e+01 -101.5444330 121.544433 1.0000000
## Twi'lek-Mon Calamari        -1.000000e+00  -97.6003126  95.600313 1.0000000
## Vulptereen-Mon Calamari     -8.600000e+01 -197.5444330  25.544433 0.3757375
## Wookiee-Mon Calamari         5.100000e+01  -45.6003126 147.600313 0.9493702
## Xexto-Mon Calamari          -5.800000e+01 -169.5444330  53.544433 0.9570515
## Yoda's species-Mon Calamari -1.140000e+02 -225.5444330  -2.455567 0.0396050
## Zabrak-Mon Calamari         -7.000000e+00 -103.6003126  89.600313 1.0000000
## Nautolan-Muun                5.000000e+00 -106.5444330 116.544433 1.0000000
## Neimodian-Muun               2.842171e-14 -111.5444330 111.544433 1.0000000
## Pau'an-Muun                  1.500000e+01  -96.5444330 126.544433 1.0000000
## Quermian-Muun                7.300000e+01  -38.5444330 184.544433 0.7012157
## Rodian-Muun                 -1.800000e+01 -129.5444330  93.544433 1.0000000
## Skakoan-Muun                 2.000000e+00 -109.5444330 113.544433 1.0000000
## Sullustan-Muun              -3.100000e+01 -142.5444330  80.544433 0.9999994
## Tholothian-Muun             -7.000000e+00 -118.5444330 104.544433 1.0000000
## Togruta-Muun                -1.300000e+01 -124.5444330  98.544433 1.0000000
## Toong-Muun                  -2.800000e+01 -139.5444330  83.544433 1.0000000
## Toydarian-Muun              -5.400000e+01 -165.5444330  57.544433 0.9815208
## Trandoshan-Muun             -1.000000e+00 -112.5444330 110.544433 1.0000000
## Twi'lek-Muun                -1.200000e+01 -108.6003126  84.600313 1.0000000
## Vulptereen-Muun             -9.700000e+01 -208.5444330  14.544433 0.1752977
## Wookiee-Muun                 4.000000e+01  -56.6003126 136.600313 0.9980593
## Xexto-Muun                  -6.900000e+01 -180.5444330  42.544433 0.7936672
## Yoda's species-Muun         -1.250000e+02 -236.5444330 -13.455567 0.0131720
## Zabrak-Muun                 -1.800000e+01 -114.6003126  78.600313 1.0000000
## Neimodian-Nautolan          -5.000000e+00 -116.5444330 106.544433 1.0000000
## Pau'an-Nautolan              1.000000e+01 -101.5444330 121.544433 1.0000000
## Quermian-Nautolan            6.800000e+01  -43.5444330 179.544433 0.8145320
## Rodian-Nautolan             -2.300000e+01 -134.5444330  88.544433 1.0000000
## Skakoan-Nautolan            -3.000000e+00 -114.5444330 108.544433 1.0000000
## Sullustan-Nautolan          -3.600000e+01 -147.5444330  75.544433 0.9999826
## Tholothian-Nautolan         -1.200000e+01 -123.5444330  99.544433 1.0000000
## Togruta-Nautolan            -1.800000e+01 -129.5444330  93.544433 1.0000000
## Toong-Nautolan              -3.300000e+01 -144.5444330  78.544433 0.9999975
## Toydarian-Nautolan          -5.900000e+01 -170.5444330  52.544433 0.9483549
## Trandoshan-Nautolan         -6.000000e+00 -117.5444330 105.544433 1.0000000
## Twi'lek-Nautolan            -1.700000e+01 -113.6003126  79.600313 1.0000000
## Vulptereen-Nautolan         -1.020000e+02 -213.5444330   9.544433 0.1170356
## Wookiee-Nautolan             3.500000e+01  -61.6003126 131.600313 0.9998171
## Xexto-Nautolan              -7.400000e+01 -185.5444330  37.544433 0.6763866
## Yoda's species-Nautolan     -1.300000e+02 -241.5444330 -18.455567 0.0077867
## Zabrak-Nautolan             -2.300000e+01 -119.6003126  73.600313 1.0000000
## Pau'an-Neimodian             1.500000e+01  -96.5444330 126.544433 1.0000000
## Quermian-Neimodian           7.300000e+01  -38.5444330 184.544433 0.7012157
## Rodian-Neimodian            -1.800000e+01 -129.5444330  93.544433 1.0000000
## Skakoan-Neimodian            2.000000e+00 -109.5444330 113.544433 1.0000000
## Sullustan-Neimodian         -3.100000e+01 -142.5444330  80.544433 0.9999994
## Tholothian-Neimodian        -7.000000e+00 -118.5444330 104.544433 1.0000000
## Togruta-Neimodian           -1.300000e+01 -124.5444330  98.544433 1.0000000
## Toong-Neimodian             -2.800000e+01 -139.5444330  83.544433 1.0000000
## Toydarian-Neimodian         -5.400000e+01 -165.5444330  57.544433 0.9815208
## Trandoshan-Neimodian        -1.000000e+00 -112.5444330 110.544433 1.0000000
## Twi'lek-Neimodian           -1.200000e+01 -108.6003126  84.600313 1.0000000
## Vulptereen-Neimodian        -9.700000e+01 -208.5444330  14.544433 0.1752977
## Wookiee-Neimodian            4.000000e+01  -56.6003126 136.600313 0.9980593
## Xexto-Neimodian             -6.900000e+01 -180.5444330  42.544433 0.7936672
## Yoda's species-Neimodian    -1.250000e+02 -236.5444330 -13.455567 0.0131720
## Zabrak-Neimodian            -1.800000e+01 -114.6003126  78.600313 1.0000000
## Quermian-Pau'an              5.800000e+01  -53.5444330 169.544433 0.9570515
## Rodian-Pau'an               -3.300000e+01 -144.5444330  78.544433 0.9999975
## Skakoan-Pau'an              -1.300000e+01 -124.5444330  98.544433 1.0000000
## Sullustan-Pau'an            -4.600000e+01 -157.5444330  65.544433 0.9981838
## Tholothian-Pau'an           -2.200000e+01 -133.5444330  89.544433 1.0000000
## Togruta-Pau'an              -2.800000e+01 -139.5444330  83.544433 1.0000000
## Toong-Pau'an                -4.300000e+01 -154.5444330  68.544433 0.9994249
## Toydarian-Pau'an            -6.900000e+01 -180.5444330  42.544433 0.7936672
## Trandoshan-Pau'an           -1.600000e+01 -127.5444330  95.544433 1.0000000
## Twi'lek-Pau'an              -2.700000e+01 -123.6003126  69.600313 0.9999994
## Vulptereen-Pau'an           -1.120000e+02 -223.5444330  -0.455567 0.0479032
## Wookiee-Pau'an               2.500000e+01  -71.6003126 121.600313 0.9999999
## Xexto-Pau'an                -8.400000e+01 -195.5444330  27.544433 0.4224067
## Yoda's species-Pau'an       -1.400000e+02 -251.5444330 -28.455567 0.0026265
## Zabrak-Pau'an               -3.300000e+01 -129.6003126  63.600313 0.9999428
## Rodian-Quermian             -9.100000e+01 -202.5444330  20.544433 0.2720296
## Skakoan-Quermian            -7.100000e+01 -182.5444330  40.544433 0.7490383
## Sullustan-Quermian          -1.040000e+02 -215.5444330   7.544433 0.0987228
## Tholothian-Quermian         -8.000000e+01 -191.5444330  31.544433 0.5220973
## Togruta-Quermian            -8.600000e+01 -197.5444330  25.544433 0.3757375
## Toong-Quermian              -1.010000e+02 -212.5444330  10.544433 0.1272042
## Toydarian-Quermian          -1.270000e+02 -238.5444330 -15.455567 0.0106916
## Trandoshan-Quermian         -7.400000e+01 -185.5444330  37.544433 0.6763866
## Twi'lek-Quermian            -8.500000e+01 -181.6003126  11.600313 0.1602051
## Vulptereen-Quermian         -1.700000e+02 -281.5444330 -58.455567 0.0000854
## Wookiee-Quermian            -3.300000e+01 -129.6003126  63.600313 0.9999428
## Xexto-Quermian              -1.420000e+02 -253.5444330 -30.455567 0.0021036
## Yoda's species-Quermian     -1.980000e+02 -309.5444330 -86.455567 0.0000033
## Zabrak-Quermian             -9.100000e+01 -187.6003126   5.600313 0.0899037
## Skakoan-Rodian               2.000000e+01  -91.5444330 131.544433 1.0000000
## Sullustan-Rodian            -1.300000e+01 -124.5444330  98.544433 1.0000000
## Tholothian-Rodian            1.100000e+01 -100.5444330 122.544433 1.0000000
## Togruta-Rodian               5.000000e+00 -106.5444330 116.544433 1.0000000
## Toong-Rodian                -1.000000e+01 -121.5444330 101.544433 1.0000000
## Toydarian-Rodian            -3.600000e+01 -147.5444330  75.544433 0.9999826
## Trandoshan-Rodian            1.700000e+01  -94.5444330 128.544433 1.0000000
## Twi'lek-Rodian               6.000000e+00  -90.6003126 102.600313 1.0000000
## Vulptereen-Rodian           -7.900000e+01 -190.5444330  32.544433 0.5478549
## Wookiee-Rodian               5.800000e+01  -38.6003126 154.600313 0.8348414
## Xexto-Rodian                -5.100000e+01 -162.5444330  60.544433 0.9913517
## Yoda's species-Rodian       -1.070000e+02 -218.5444330   4.544433 0.0758474
## Zabrak-Rodian               -5.684342e-14  -96.6003126  96.600313 1.0000000
## Sullustan-Skakoan           -3.300000e+01 -144.5444330  78.544433 0.9999975
## Tholothian-Skakoan          -9.000000e+00 -120.5444330 102.544433 1.0000000
## Togruta-Skakoan             -1.500000e+01 -126.5444330  96.544433 1.0000000
## Toong-Skakoan               -3.000000e+01 -141.5444330  81.544433 0.9999997
## Toydarian-Skakoan           -5.600000e+01 -167.5444330  55.544433 0.9711956
## Trandoshan-Skakoan          -3.000000e+00 -114.5444330 108.544433 1.0000000
## Twi'lek-Skakoan             -1.400000e+01 -110.6003126  82.600313 1.0000000
## Vulptereen-Skakoan          -9.900000e+01 -210.5444330  12.544433 0.1497133
## Wookiee-Skakoan              3.800000e+01  -58.6003126 134.600313 0.9991794
## Xexto-Skakoan               -7.100000e+01 -182.5444330  40.544433 0.7490383
## Yoda's species-Skakoan      -1.270000e+02 -238.5444330 -15.455567 0.0106916
## Zabrak-Skakoan              -2.000000e+01 -116.6003126  76.600313 1.0000000
## Tholothian-Sullustan         2.400000e+01  -87.5444330 135.544433 1.0000000
## Togruta-Sullustan            1.800000e+01  -93.5444330 129.544433 1.0000000
## Toong-Sullustan              3.000000e+00 -108.5444330 114.544433 1.0000000
## Toydarian-Sullustan         -2.300000e+01 -134.5444330  88.544433 1.0000000
## Trandoshan-Sullustan         3.000000e+01  -81.5444330 141.544433 0.9999997
## Twi'lek-Sullustan            1.900000e+01  -77.6003126 115.600313 1.0000000
## Vulptereen-Sullustan        -6.600000e+01 -177.5444330  45.544433 0.8529483
## Wookiee-Sullustan            7.100000e+01  -25.6003126 167.600313 0.4718062
## Xexto-Sullustan             -3.800000e+01 -149.5444330  73.544433 0.9999459
## Yoda's species-Sullustan    -9.400000e+01 -205.5444330  17.544433 0.2198230
## Zabrak-Sullustan             1.300000e+01  -83.6003126 109.600313 1.0000000
## Togruta-Tholothian          -6.000000e+00 -117.5444330 105.544433 1.0000000
## Toong-Tholothian            -2.100000e+01 -132.5444330  90.544433 1.0000000
## Toydarian-Tholothian        -4.700000e+01 -158.5444330  64.544433 0.9974348
## Trandoshan-Tholothian        6.000000e+00 -105.5444330 117.544433 1.0000000
## Twi'lek-Tholothian          -5.000000e+00 -101.6003126  91.600313 1.0000000
## Vulptereen-Tholothian       -9.000000e+01 -201.5444330  21.544433 0.2911454
## Wookiee-Tholothian           4.700000e+01  -49.6003126 143.600313 0.9803213
## Xexto-Tholothian            -6.200000e+01 -173.5444330  49.544433 0.9150665
## Yoda's species-Tholothian   -1.180000e+02 -229.5444330  -6.455567 0.0268073
## Zabrak-Tholothian           -1.100000e+01 -107.6003126  85.600313 1.0000000
## Toong-Togruta               -1.500000e+01 -126.5444330  96.544433 1.0000000
## Toydarian-Togruta           -4.100000e+01 -152.5444330  70.544433 0.9997596
## Trandoshan-Togruta           1.200000e+01  -99.5444330 123.544433 1.0000000
## Twi'lek-Togruta              1.000000e+00  -95.6003126  97.600313 1.0000000
## Vulptereen-Togruta          -8.400000e+01 -195.5444330  27.544433 0.4224067
## Wookiee-Togruta              5.300000e+01  -43.6003126 149.600313 0.9250498
## Xexto-Togruta               -5.600000e+01 -167.5444330  55.544433 0.9711956
## Yoda's species-Togruta      -1.120000e+02 -223.5444330  -0.455567 0.0479032
## Zabrak-Togruta              -5.000000e+00 -101.6003126  91.600313 1.0000000
## Toydarian-Toong             -2.600000e+01 -137.5444330  85.544433 1.0000000
## Trandoshan-Toong             2.700000e+01  -84.5444330 138.544433 1.0000000
## Twi'lek-Toong                1.600000e+01  -80.6003126 112.600313 1.0000000
## Vulptereen-Toong            -6.900000e+01 -180.5444330  42.544433 0.7936672
## Wookiee-Toong                6.800000e+01  -28.6003126 164.600313 0.5602827
## Xexto-Toong                 -4.100000e+01 -152.5444330  70.544433 0.9997596
## Yoda's species-Toong        -9.700000e+01 -208.5444330  14.544433 0.1752977
## Zabrak-Toong                 1.000000e+01  -86.6003126 106.600313 1.0000000
## Trandoshan-Toydarian         5.300000e+01  -58.5444330 164.544433 0.9854639
## Twi'lek-Toydarian            4.200000e+01  -54.6003126 138.600313 0.9958349
## Vulptereen-Toydarian        -4.300000e+01 -154.5444330  68.544433 0.9994249
## Wookiee-Toydarian            9.400000e+01   -2.6003126 190.600313 0.0659958
## Xexto-Toydarian             -1.500000e+01 -126.5444330  96.544433 1.0000000
## Yoda's species-Toydarian    -7.100000e+01 -182.5444330  40.544433 0.7490383
## Zabrak-Toydarian             3.600000e+01  -60.6003126 132.600313 0.9996890
## Twi'lek-Trandoshan          -1.100000e+01 -107.6003126  85.600313 1.0000000
## Vulptereen-Trandoshan       -9.600000e+01 -207.5444330  15.544433 0.1893017
## Wookiee-Trandoshan           4.100000e+01  -55.6003126 137.600313 0.9971243
## Xexto-Trandoshan            -6.800000e+01 -179.5444330  43.544433 0.8145320
## Yoda's species-Trandoshan   -1.240000e+02 -235.5444330 -12.455567 0.0146075
## Zabrak-Trandoshan           -1.700000e+01 -113.6003126  79.600313 1.0000000
## Vulptereen-Twi'lek          -8.500000e+01 -181.6003126  11.600313 0.1602051
## Wookiee-Twi'lek              5.200000e+01  -26.8738250 130.873825 0.6878938
## Xexto-Twi'lek               -5.700000e+01 -153.6003126  39.600313 0.8562121
## Yoda's species-Twi'lek      -1.130000e+02 -209.6003126 -16.399687 0.0073975
## Zabrak-Twi'lek              -6.000000e+00  -84.8738250  72.873825 1.0000000
## Wookiee-Vulptereen           1.370000e+02   40.3996874 233.600313 0.0003352
## Xexto-Vulptereen             2.800000e+01  -83.5444330 139.544433 1.0000000
## Yoda's species-Vulptereen   -2.800000e+01 -139.5444330  83.544433 1.0000000
## Zabrak-Vulptereen            7.900000e+01  -17.6003126 175.600313 0.2679134
## Xexto-Wookiee               -1.090000e+02 -205.6003126 -12.399687 0.0120422
## Yoda's species-Wookiee      -1.650000e+02 -261.6003126 -68.399687 0.0000078
## Zabrak-Wookiee              -5.800000e+01 -136.8738250  20.873825 0.4707909
## Yoda's species-Xexto        -5.600000e+01 -167.5444330  55.544433 0.9711956
## Zabrak-Xexto                 5.100000e+01  -45.6003126 147.600313 0.9493702
## Zabrak-Yoda's species        1.070000e+02   10.3996874 203.600313 0.0152959
aov(height~species,data = anova_data) %>% 
  summary()
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## species     36  81843  2273.4   6.299 3.86e-08 ***
## Residuals   40  14437   360.9                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

p<0.05 >> Ho rejected >> difference in mean is not equal.

non parametric test for anova:

kruskall wallis rank sum test

kruskal.test(height~species, data= anova_data) 
## 
##  Kruskal-Wallis rank sum test
## 
## data:  height by species
## Kruskal-Wallis chi-squared = 55.768, df = 36, p-value = 0.01884