Analysis Aira 2

Packages

library(tidyverse) # load tidiverse library

Dataset and cleaning

df <- read_csv("https://docs.google.com/spreadsheets/d/e/2PACX-1vStv7Pr69DtRKv6Nw6gVBep8hbT3pEeO6B1vNwxK_1DUHgpoTgbuRpZ4SvgtHFQnBZJVGeeQVyRuXZl/pub?gid=20675042&single=true&output=csv") # load the dataset from google drive

Parsed with column specification:
cols(
  `Merijumu punkts` = col_character(),
  Virsmas = col_character(),
  `1_1` = col_integer(),
  `1_2` = col_integer(),
  `1_3` = col_integer(),
  `1_4` = col_integer(),
  `1_5` = col_integer(),
  `1_6` = col_integer(),
  `1_7` = col_integer(),
  `1_8` = col_integer(),
  `1_9` = col_integer(),
  `1_10` = col_integer(),
  Measurement = col_character()
)

head(df) # explore the dataset

summary(df) # view a summary of dataset

 Mērījumu punkts      Virsmas               1_1              1_2              1_3              1_4              1_5              1_6        
 Length:180         Length:180         Min.   :-60.00   Min.   :-90.00   Min.   :-90.00   Min.   :-90.00   Min.   :-90.00   Min.   :-60.00  
 Class :character   Class :character   1st Qu.: 52.50   1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00  
 Mode  :character   Mode  :character   Median : 90.00   Median : 30.00   Median : 30.00   Median : 30.00   Median : 30.00   Median : 30.00  
                                       Mean   : 80.33   Mean   : 31.28   Mean   : 35.44   Mean   : 37.67   Mean   : 34.67   Mean   : 38.78  
                                       3rd Qu.:120.00   3rd Qu.: 60.00   3rd Qu.: 60.00   3rd Qu.: 60.00   3rd Qu.: 60.00   3rd Qu.: 60.00  
                                       Max.   :200.00   Max.   :200.00   Max.   :200.00   Max.   :250.00   Max.   :250.00   Max.   :250.00  
                                       NA's   :120                                                                                          
      1_7              1_8              1_9              1_10        Measurement       
 Min.   :-90.00   Min.   :-90.00   Min.   :-60.00   Min.   :-60.00   Length:180        
 1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00   Class :character  
 Median : 30.00   Median : 30.00   Median : 30.00   Median :  0.00   Mode  :character  
 Mean   : 38.17   Mean   : 38.94   Mean   : 31.72   Mean   : 25.17                     
 3rd Qu.: 60.00   3rd Qu.: 60.00   3rd Qu.: 30.00   3rd Qu.: 30.00                     
 Max.   :250.00   Max.   :250.00   Max.   :250.00   Max.   :250.00                     
                                                                                       

df <- janitor::clean_names(df) # normalize names, requires janitor library

df <-  df %>%                                             # create a new df, replacing the old one
  gather(key = "comparison", value = "value", x1_1:x1_10 ) # gathering the columns x1_1 to X1-10. The titles will be in a new colum named "comparison" and the values to a column "value"

summary(df)

 merijumu_punkts      virsmas          measurement         comparison            value       
 Length:1800        Length:1800        Length:1800        Length:1800        Min.   :-90.00  
 Class :character   Class :character   Class :character   Class :character   1st Qu.:  0.00  
 Mode  :character   Mode  :character   Mode  :character   Mode  :character   Median : 30.00  
                                                                             Mean   : 36.28  
                                                                             3rd Qu.: 60.00  
                                                                             Max.   :250.00  
                                                                             NA's   :120     

df <- df %>% # create a new df, replacing the old one
  select(-merijumu_punkts)  # without the merijumu column, since we will not use it 

df$value <- abs(df$value) # change all the values to absolute, to eliminate negative values

Ready for analysis

Tables and graphs

io and eo

Comparison

df %>% 
  filter(measurement == "extraoral" | measurement == "intraoral")%>% # filter excluiding the intra_vs_extra  level
  # filter(comparison != "x1_1") %>% 
  group_by(comparison) %>%  # group by
  summarise(Mean = mean(value), # create a column for each summary 
            sd = sd(value), 
            Min = min(value), 
            Max = max(value), 
            Q25 = quantile(value, na.rm = T, probs = .25), 
            Median = quantile(value, na.rm = T, probs = .5),
            Q75 = quantile(value, na.rm = T, probs = .75)) 

df %>% 
  filter(measurement == "extraoral" | measurement == "intraoral") %>% # filter excluiding the intra_vs_extra  level
  ggplot(aes(x =fct_reorder(comparison, value), y = value)) + 
  geom_boxplot() + 
  theme_minimal()

df_i_e <- df %>% 
  filter(measurement == "extraoral" | measurement == "intraoral") # create a new df with only i and e

ANOVA comparison

aov(value ~ comparison, data = df_i_e)

Call:
   aov(formula = value ~ comparison, data = df_i_e)

Terms:
                comparison Residuals
Sum of Squares      3296.7  336502.5
Deg. of Freedom          8      1071

Residual standard error: 17.72554
Estimated effects may be unbalanced
120 observations deleted due to missingness

summary(aov(value ~ comparison, data = df_i_e))

              Df Sum Sq Mean Sq F value Pr(>F)
comparison     8   3297   412.1   1.312  0.234
Residuals   1071 336502   314.2               
120 observations deleted due to missingness

virsmas

df %>% 
  filter(measurement == "extraoral" | measurement == "intraoral") %>% # filter excluiding the intra_vs_extra  level
  # filter(comparison != "x1_1") %>% 
  group_by(virsmas) %>%  # group by
  summarise(Mean = mean(value, na.rm=TRUE), # create a column for each summary 
            sd = sd(value, na.rm=TRUE), 
            Min = min(value, na.rm=TRUE), 
            Max = max(value, na.rm=TRUE), 
            Q25 = quantile(value, na.rm = T, probs = .25), 
            Median = quantile(value, na.rm = T, probs = .5),
            Q75 = quantile(value, na.rm = T, probs = .75)) 

df %>% 
  filter(measurement == "extraoral" | measurement == "intraoral") %>% # filter excluiding the intra_vs_extra  level
  ggplot(aes(x =fct_reorder(virsmas, value), y = value)) + 
  geom_boxplot() + 
  theme_minimal()

ANOVA virsmas

aov(value ~ virsmas, data = df_i_e)

Call:
   aov(formula = value ~ virsmas, data = df_i_e)

Terms:
                 virsmas Residuals
Sum of Squares    2313.2  337486.0
Deg. of Freedom        3      1076

Residual standard error: 17.71013
Estimated effects may be unbalanced
120 observations deleted due to missingness

summary(aov(value ~ virsmas, data = df_i_e))

              Df Sum Sq Mean Sq F value Pr(>F)  
virsmas        3   2313   771.1   2.458 0.0614 .
Residuals   1076 337486   313.6                 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
120 observations deleted due to missingness

measurement

df %>% 
  filter(measurement == "extraoral" | measurement == "intraoral") %>% 
  group_by(measurement) %>%  # group by
  summarise(Mean = mean(value, na.rm=TRUE), # create a column for each summary 
            sd = sd(value, na.rm=TRUE), 
            Min = min(value, na.rm=TRUE), 
            Max = max(value, na.rm=TRUE), 
            Q25 = quantile(value, na.rm = T, probs = .25), 
            Median = quantile(value, na.rm = T, probs = .5),
            Q75 = quantile(value, na.rm = T, probs = .75)) 

df %>% 
  filter(measurement == "extraoral" | measurement == "intraoral") %>% # filter excluiding the intra_vs_extra  level
  ggplot(aes(x =fct_reorder(measurement, value), y = value)) + 
  geom_boxplot() + 
  theme_minimal()

ANOVA measurement

aov(value ~ measurement, data = df_i_e)

Call:
   aov(formula = value ~ measurement, data = df_i_e)

Terms:
                measurement Residuals
Sum of Squares     47600.83 292198.33
Deg. of Freedom           1      1078

Residual standard error: 16.46378
Estimated effects may be unbalanced
120 observations deleted due to missingness

summary(aov(value ~ measurement, data = df_i_e))

              Df Sum Sq Mean Sq F value Pr(>F)    
measurement    1  47601   47601   175.6 <2e-16 ***
Residuals   1078 292198     271                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
120 observations deleted due to missingness

intraoral vs extraoral

Comparison

df %>% 
  filter(measurement == "intra_vs_extra") %>% 
  group_by(comparison) %>%  # group by
  summarise(Mean = mean(value, na.rm=TRUE), # create a column for each summary 
            sd = sd(value, na.rm=TRUE), 
            Min = min(value, na.rm=TRUE), 
            Max = max(value, na.rm=TRUE), 
            Q25 = quantile(value, na.rm = T, probs = .25), 
            Median = quantile(value, na.rm = T, probs = .5),
            Q75 = quantile(value, na.rm = T, probs = .75)) 

df %>% 
  filter(measurement == "intra_vs_extra") %>%
  ggplot(aes(x = comparison, y = value)) + 
  geom_boxplot() + 
  theme_minimal()

ANOVA intraveextra comparison

df_intravsextra <- df %>% 
  filter(measurement == "intra_vs_extra")

aov(value ~ comparison, data = df_intravsextra)

Call:
   aov(formula = value ~ comparison, data = df_intravsextra)

Terms:
                comparison Residuals
Sum of Squares     31107.3 1712100.0
Deg. of Freedom          9       590

Residual standard error: 53.86896
Estimated effects may be unbalanced

summary(aov(value ~ comparison, data = df_intravsextra))

             Df  Sum Sq Mean Sq F value Pr(>F)
comparison    9   31107    3456   1.191  0.298
Residuals   590 1712100    2902               

virsmas

df %>% 
  filter(measurement == "intra_vs_extra") %>% 
  group_by(virsmas) %>%  # group by
  summarise(Mean = mean(value, na.rm=TRUE), # create a column for each summary 
            sd = sd(value, na.rm=TRUE), 
            Min = min(value, na.rm=TRUE), 
            Max = max(value, na.rm=TRUE), 
            Q25 = quantile(value, na.rm = T, probs = .25), 
            Median = quantile(value, na.rm = T, probs = .5),
            Q75 = quantile(value, na.rm = T, probs = .75)) 

df %>% 
  filter(measurement == "intra_vs_extra") %>%
  ggplot(aes(x = fct_reorder(virsmas, value),  y = value)) + 
  geom_boxplot() + 
  theme_minimal()

ANOVA intraveextra virsmas

df_intravsextra <- df %>% 
  filter(measurement == "intra_vs_extra")

aov(value ~ virsmas, data = df_intravsextra)

Call:
   aov(formula = value ~ virsmas, data = df_intravsextra)

Terms:
                  virsmas Residuals
Sum of Squares   663971.4 1079235.9
Deg. of Freedom         3       596

Residual standard error: 42.55348
Estimated effects may be unbalanced

summary(aov(value ~ virsmas, data = df_intravsextra))

             Df  Sum Sq Mean Sq F value Pr(>F)    
virsmas       3  663971  221324   122.2 <2e-16 ***
Residuals   596 1079236    1811                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1