R Notebook

Install Packages and Prepare the two dataset and merge them

# install.packages("lmtest")
# install.packages("sandwich")
# rm(list=ls())
# #setRepositories()
# # devtools::install_github("r-lib/conflicted")
# install.packages("mirt")
# install.packages("tidyverse")
# install.packages("ggplot2", dependencies = TRUE, update = TRUE)
# install.packages("lavaan")


library(tidyverse)
library(mirt)
library(lavaan)
library(survey)
library(lattice)
library(lmtest)
library(sandwich)

#reading in data
data_O <- read.csv("E:/Shreya Work in ERO/ECD Study 2023-20230927T042929Z-001/ECD Study 2023/Data/Cleaned data/ELDS2023_final.csv")



dat <- data_O %>% filter(Check == "1") #remove absentees 
# nrow(dat)
dat <- dat %>% filter(is.na(Sampling_error_delete)) #remove sampling errors
dat1<-dat


# nrow(dat)
dat <- dat %>% select(1, 5, 7, 8, 19, 22, 24,25, 27, 40, 41:83) #retain only relevant columns
# nrow(dat)
dat <- dat %>% mutate(across(17:52, ~ recode(.x, "999" = "0", 
                                    "0" = "0", 
                                    "1" ="0.5", 
                                    "2"= "1"))) #convert 999 to 0


####add age levels based on target age group####
dat$Agelevel <- ifelse(dat$Age_months>=39&dat$Age_months<=60,'Below 5 years',
                       ifelse(dat$Age_months>=61&dat$Age_months<=72,'5 years (61-72 m)',
                          ifelse(dat$Age_months>=73&dat$Age_months<=84, '6 years (73-84 m)',
                             ifelse(dat$Age_months>85&dat$Age_months<=96, '7 years (85-96 m)', "Above 7 years"))))


dat <- dplyr::mutate_at(dat, c(17:52), as.numeric)

dat$overall <- rowMeans(dat[, 17:52], na.rm = TRUE) #% of tasks performed correctly & partially correctly

#domain scores
dat$Physical <- rowMeans(dat[ ,c(34:39)], na.rm = TRUE)
dat$LanguageScore <- rowMeans(dat[ ,c(22:24,27:33)], na.rm = TRUE)
dat$Cognitive <- rowMeans(dat[ ,c(18:21,25:26, 40:44)], na.rm = TRUE)
dat$SE <- rowMeans(dat[ ,c(17,45:52)], na.rm = TRUE)
dat$composite <- rowMeans(dat[ ,c(56:59)], na.rm = TRUE)

fiveyr_cutoff <- function(score) {
  compLevel <- ifelse(score <0.34,
                      'Struggling',
                      ifelse(score < 0.74,
                             'Progressing',
                             'On Track')
  )
  return(compLevel)
}

#applying the cut-off

dat$CompLevel <- fiveyr_cutoff(dat$composite)

dat$PhysLevel <- ifelse(dat$Physical <0.28, 'Struggling',
                        ifelse(dat$Physical < 0.74,'Progressing','On Track'))

dat$LangLevel <- ifelse(dat$LanguageScore <0.41, 'Struggling',
                        ifelse(dat$LanguageScore < 0.87,'Progressing','On Track'))

dat$CogLevel <- ifelse(dat$Cognitive <0.29, 'Struggling',
                       ifelse(dat$Cognitive < 0.66,'Progressing','On Track'))

dat$SELevel <- ifelse(dat$SE <0.39, 'Struggling',
                      ifelse(dat$SE < 0.70,'Progressing','On Track'))

merging the data belowa

file_path <- "E:/Shreya Work in ERO/ECD Study 2023-20230927T042929Z-002/ECD Study 2023/Data/Cleaned data/ECEDBackground_final.csv"
data <- read_csv(file_path, show_col_types = FALSE) #249

New names:
• `` -> `...2`
• `` -> `...3`

mergedtest <- merge(dat, data,  by="Code", all.x= TRUE) #2720 
# view(mergedtest)
# 
names(mergedtest)[names(mergedtest) == "index.y"] <- "index"

ECEDBackground_final <- merge(mergedtest, dat1, by="index", all.x=TRUE)

standardize the data (Mean 0 and SD 1)

As suggested by Kenji

ECEDBackground_final <- ECEDBackground_final %>%
  mutate(
    SE_standardized = scale(SE),
    Cognitive_standardized = scale(Cognitive),
    LanguageScore_standardized = scale(LanguageScore),
    Physical_standardized = scale(Physical),
    Composite_standardized = scale(composite)
  )


learning_columns <- c("TC6_A", "TC6_B", "TC6_C", "TC6_D", "TC6_E", "TC6_F", "TC6_G")
# view(ECEDBackground_final)
ECEDBackground_final <- ECEDBackground_final %>%
  mutate(
    EMISCode = Code.x,
    Age_months = Age_months.x, #ifelse(Age_months.x >= 12 & Age_months.x <= 24, 1, 0),
    Gender_Male = ifelse(A8 == 2, 1, 0),  #  A8 is the gender column, छात्र २ | Boy-> 
    Primary_language_instruction = ifelse(TC1_A>1, 1, 0),  #  TC1_A is the language column, 1 is nepali,2 is english,  we are checking for language other than nepali and 
    ECED_Attendance_Yes = ifelse(A12.x >=1, 1, 0),  # A12 is the ECED attendance column
    School_Type_Community = ifelse(PI_Type == "Community", 1, 0),  # How does Community school affect the Score
    Urbanicity_Urban = ifelse(Urbanicity.x == "Urban", 1, 0),  # Urban only 
    Teachers_Qualification_Grade_10_only = ifelse(Teacher_Qualification_TI5 ==3, 1, 0),  # We check for grade 10 and grade 12 to see the relative affect. ; 3-> 10; 4->12
    Pre_Service_Training_Received = ifelse(Preservice_TI6_A == 1, 1, 0),  # Preservice training yes only
    In_Service_Training_Received = ifelse(Inservice_Number_TI7_A>0, 1, 0),  # In service training yes only,
    Availability_of_Reading_Learning_Areas = if_else(TC6_A!=0,1, 0),  
    Availability_of_Mathematics_Learning_Areas = if_else(TC6_B!=0,1, 0),  
    Availability_of_RolePlay_Learning_Areas = if_else(TC6_C!=0,1, 0),  
    Availability_of_Science_Learning_Areas = if_else(TC6_D!=0,1, 0),  
    Availability_of_Creativity_Learning_Areas = if_else(TC6_E!=0,1, 0),  
    Availability_of_Constructions_Learning_Areas = if_else(TC6_F!=0,1, 0),  

 Availability_of_Caretaker_Yes =  ifelse(rowSums(select(.,starts_with("Aaya_BI11_F")))>0, 1, 0),  # if sum of caretakers is greater than 1 
#Urbanicity.x == "Rural" & 
    Usage_of_textbook_Yes = ifelse(TC16 >0, 1, 0),  # Changed to textbook || Exclude No only, no need to replace 98
    Usage_of_curriculum_Yes = ifelse(TC7 ==1, 1, 0),  # Useing curriculam yes only
    Usage_of_ELDS_Yes = ifelse(TC8 ==1, 1, 0)
#    homework_week_daily_yes = ifelse(TC9>=1, 1, 0)    # removed becaise the variable has no major variance, as 92% have said they give homeowkr, multiple regression could not estimate in such case. 
# ELDS report cards yes only
  ) %>%
  mutate(
    Weighted_Students = rowSums(across(starts_with("Student_number_BI11_D"), ~ replace_na(.x, 0) * school_weight)),
    Weighted_Teachers = rowSums(across(starts_with("Teachers_BI11_E"), ~ replace_na(.x, 0) * school_weight))
  ) %>%
  # Calculating the  weighted student-to-teacher ratio, makin sure avoiding division by zero
  mutate(Weighted_Student_Teacher_Ratio = ifelse(Weighted_Teachers > 0, Weighted_Students / Weighted_Teachers, NA))

Function to fir the model

# Function to fit OLS and use cluster-robust SEs with coeftest  //StackExchange

fit_ols_with_robust_se <- function(formula, data, cluster_var) {
  # Fit the OLS model
  model <- lm(formula, data = data)
  
  # Calculate the clustered variance-covariance matrix
  clustered_vcov <- vcovCL(model, cluster = data[[cluster_var]])
  
  # Apply coeftst to return robust standard erors
  robust_results <- coeftest(model, vcov. = clustered_vcov)
  
  return(robust_results)
}

Building the model

# ECEDBackground_final <- ECEDBackground_final %>%  #already done abobve
#   mutate(
#     SE_standardized = scale(SE),
#     Cognitive_standardized = scale(Cognitive),
#     LanguageScore_standardized = scale(LanguageScore),
#     Physical_standardized = scale(Physical),
#     Composite_standardized = scale(composite)
#   )

# view(ECEDBackground_final$Code.x)

model_SE <- fit_ols_with_robust_se(
  SE_standardized ~ Age_months + Gender_Male + Primary_language_instruction + ECED_Attendance_Yes +
    School_Type_Community + Urbanicity_Urban + Teachers_Qualification_Grade_10_only +
    Pre_Service_Training_Received + In_Service_Training_Received + Availability_of_Reading_Learning_Areas +
    Availability_of_Mathematics_Learning_Areas + Availability_of_RolePlay_Learning_Areas +
    Availability_of_Science_Learning_Areas + Availability_of_Creativity_Learning_Areas +
    Availability_of_Constructions_Learning_Areas + Availability_of_Caretaker_Yes +
    Weighted_Student_Teacher_Ratio + Usage_of_textbook_Yes + Usage_of_curriculum_Yes + Usage_of_ELDS_Yes,
  data = ECEDBackground_final,
  cluster_var = "EMISCode"
)

# view(ECEDBackground_final$Code.x)

model_Cognitive <- fit_ols_with_robust_se(
  Cognitive_standardized ~ Age_months + Gender_Male + Primary_language_instruction + ECED_Attendance_Yes +
    School_Type_Community + Urbanicity_Urban + Teachers_Qualification_Grade_10_only +
    Pre_Service_Training_Received + In_Service_Training_Received + Availability_of_Reading_Learning_Areas +
    Availability_of_Mathematics_Learning_Areas + Availability_of_RolePlay_Learning_Areas +
    Availability_of_Science_Learning_Areas + Availability_of_Creativity_Learning_Areas +
    Availability_of_Constructions_Learning_Areas + Availability_of_Caretaker_Yes +
    Weighted_Student_Teacher_Ratio + Usage_of_textbook_Yes + Usage_of_curriculum_Yes + Usage_of_ELDS_Yes,
  data = ECEDBackground_final,
  cluster_var = "EMISCode"
)

model_Language <- fit_ols_with_robust_se(
  LanguageScore_standardized ~ Age_months + Gender_Male + Primary_language_instruction + ECED_Attendance_Yes +
    School_Type_Community + Urbanicity_Urban + Teachers_Qualification_Grade_10_only +
    Pre_Service_Training_Received + In_Service_Training_Received + Availability_of_Reading_Learning_Areas +
    Availability_of_Mathematics_Learning_Areas + Availability_of_RolePlay_Learning_Areas +
    Availability_of_Science_Learning_Areas + Availability_of_Creativity_Learning_Areas +
    Availability_of_Constructions_Learning_Areas + Availability_of_Caretaker_Yes +
    Weighted_Student_Teacher_Ratio + Usage_of_textbook_Yes + Usage_of_curriculum_Yes + Usage_of_ELDS_Yes,
  data = ECEDBackground_final,
  cluster_var = "EMISCode"
)

model_Physical <- fit_ols_with_robust_se(
  Physical_standardized ~ Age_months + Gender_Male + Primary_language_instruction + ECED_Attendance_Yes +
    School_Type_Community + Urbanicity_Urban + Teachers_Qualification_Grade_10_only +
    Pre_Service_Training_Received + In_Service_Training_Received + Availability_of_Reading_Learning_Areas +
    Availability_of_Mathematics_Learning_Areas + Availability_of_RolePlay_Learning_Areas +
    Availability_of_Science_Learning_Areas + Availability_of_Creativity_Learning_Areas +
    Availability_of_Constructions_Learning_Areas + Availability_of_Caretaker_Yes +
    Weighted_Student_Teacher_Ratio + Usage_of_textbook_Yes + Usage_of_curriculum_Yes + Usage_of_ELDS_Yes,
  data = ECEDBackground_final,
  cluster_var ="EMISCode"
)

model_composite <- fit_ols_with_robust_se(
  Composite_standardized ~ Age_months + Gender_Male + Primary_language_instruction + ECED_Attendance_Yes +
    School_Type_Community + Urbanicity_Urban + Teachers_Qualification_Grade_10_only +
    Pre_Service_Training_Received + In_Service_Training_Received + Availability_of_Reading_Learning_Areas +
    Availability_of_Mathematics_Learning_Areas + Availability_of_RolePlay_Learning_Areas +
    Availability_of_Science_Learning_Areas + Availability_of_Creativity_Learning_Areas +
    Availability_of_Constructions_Learning_Areas + Availability_of_Caretaker_Yes +
    Weighted_Student_Teacher_Ratio + Usage_of_textbook_Yes + Usage_of_curriculum_Yes + Usage_of_ELDS_Yes,
  data = ECEDBackground_final,
  cluster_var = "EMISCode"
)

Just a list of models for easy recalling

models <- list(
  SE = model_SE,
  Cognitive = model_Cognitive,
  Language = model_Language,
  Physical = model_Physical, 
  composite = model_composite
)

Extract Coefficients, and Significance

raw scores, justto cehck adn confirm

print(models)

$SE

t test of coefficients:

                                               Estimate Std. Error t value  Pr(>|t|)    
(Intercept)                                   0.8556416  0.8045903  1.0635  0.288588    
Age_months                                    0.0092047  0.0042623  2.1596  0.031741 *  
Gender_Male                                  -0.2122895  0.4828820 -0.4396  0.660579    
Primary_language_instruction                 -0.4800951  0.5279415 -0.9094  0.364016    
ECED_Attendance_Yes                          -0.5652008  0.2442828 -2.3137  0.021482 *  
School_Type_Community                        -0.5728832  0.4622755 -1.2393  0.216390    
Urbanicity_Urban                              1.0338997  0.3872672  2.6697  0.008081 ** 
Teachers_Qualification_Grade_10_only         -1.5165349  0.6620800 -2.2906  0.022809 *  
Pre_Service_Training_Received                 0.4247265  0.5079113  0.8362  0.403816    
In_Service_Training_Received                  0.0026245  0.3608394  0.0073  0.994202    
Availability_of_Reading_Learning_Areas       -0.5734329  0.7096227 -0.8081  0.419800    
Availability_of_Mathematics_Learning_Areas    0.2166686  0.2647358  0.8184  0.413877    
Availability_of_RolePlay_Learning_Areas       0.3905955  0.9582187  0.4076  0.683891    
Availability_of_Science_Learning_Areas        0.4335475  0.7287614  0.5949  0.552433    
Availability_of_Creativity_Learning_Areas    -1.6439521  0.5720228 -2.8739  0.004397 ** 
Availability_of_Constructions_Learning_Areas  1.3723579  0.9659765  1.4207  0.156632    
Availability_of_Caretaker_Yes                -2.4255139  0.4989687 -4.8611 2.047e-06 ***
Weighted_Student_Teacher_Ratio                0.0142970  0.0101896  1.4031  0.161808    
Usage_of_textbook_Yes                         0.0749074  0.5047407  0.1484  0.882139    
Usage_of_curriculum_Yes                      -0.0421430  0.5855151 -0.0720  0.942678    
Usage_of_ELDS_Yes                             0.0629852  0.5171663  0.1218  0.903162    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


$Cognitive

t test of coefficients:

                                               Estimate Std. Error t value  Pr(>|t|)    
(Intercept)                                  -0.2246610  0.5261649 -0.4270 0.6697568    
Age_months                                    0.0075503  0.0045007  1.6776 0.0946600 .  
Gender_Male                                  -0.7163217  0.3393584 -2.1108 0.0357660 *  
Primary_language_instruction                 -0.1998520  0.3287157 -0.6080 0.5437451    
ECED_Attendance_Yes                          -0.6562482  0.1895019 -3.4630 0.0006267 ***
School_Type_Community                        -0.2757081  0.2973116 -0.9273 0.3546319    
Urbanicity_Urban                              0.4849977  0.2379874  2.0379 0.0425948 *  
Teachers_Qualification_Grade_10_only         -1.1494056  0.5130622 -2.2403 0.0259375 *  
Pre_Service_Training_Received                 0.5926027  0.3327694  1.7808 0.0761368 .  
In_Service_Training_Received                 -0.1160293  0.2708635 -0.4284 0.6687460    
Availability_of_Reading_Learning_Areas        0.0345459  0.4555192  0.0758 0.9396073    
Availability_of_Mathematics_Learning_Areas    1.0546702  0.2149260  4.9071 1.653e-06 ***
Availability_of_RolePlay_Learning_Areas       1.5630986  0.7564982  2.0662 0.0398207 *  
Availability_of_Science_Learning_Areas        0.3371825  0.4638423  0.7269 0.4679362    
Availability_of_Creativity_Learning_Areas    -2.0519473  0.4896398 -4.1907 3.841e-05 ***
Availability_of_Constructions_Learning_Areas  0.0031873  0.7381248  0.0043 0.9965580    
Availability_of_Caretaker_Yes                -2.4904530  0.4244102 -5.8680 1.371e-08 ***
Weighted_Student_Teacher_Ratio                0.0179913  0.0061369  2.9317 0.0036789 ** 
Usage_of_textbook_Yes                         1.2607315  0.3253654  3.8748 0.0001359 ***
Usage_of_curriculum_Yes                       0.6496497  0.4365983  1.4880 0.1379965    
Usage_of_ELDS_Yes                            -1.0153391  0.3414475 -2.9736 0.0032260 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


$Language

t test of coefficients:

                                               Estimate Std. Error t value  Pr(>|t|)    
(Intercept)                                   0.5160944  0.5395497  0.9565 0.3397150    
Age_months                                    0.0026612  0.0039864  0.6676 0.5050202    
Gender_Male                                  -0.5040239  0.3190266 -1.5799 0.1153787    
Primary_language_instruction                 -0.5194648  0.3167547 -1.6400 0.1022515    
ECED_Attendance_Yes                          -0.5474689  0.2536540 -2.1583 0.0318395 *  
School_Type_Community                        -0.5652276  0.3404858 -1.6601 0.0981360 .  
Urbanicity_Urban                              0.5693176  0.2499387  2.2778 0.0235681 *  
Teachers_Qualification_Grade_10_only         -1.2241148  0.4609277 -2.6558 0.0084135 ** 
Pre_Service_Training_Received                 1.0639061  0.3346915  3.1788 0.0016624 ** 
In_Service_Training_Received                  0.1790612  0.2920928  0.6130 0.5404059    
Availability_of_Reading_Learning_Areas       -0.9077014  0.4480241 -2.0260 0.0438090 *  
Availability_of_Mathematics_Learning_Areas    1.4398584  0.2820624  5.1048 6.499e-07 ***
Availability_of_RolePlay_Learning_Areas       1.5437337  0.8434321  1.8303 0.0683769 .  
Availability_of_Science_Learning_Areas        0.2235743  0.5420240  0.4125 0.6803353    
Availability_of_Creativity_Learning_Areas    -2.7434522  0.5475718 -5.0102 1.019e-06 ***
Availability_of_Constructions_Learning_Areas  0.3427029  0.7753674  0.4420 0.6588742    
Availability_of_Caretaker_Yes                -2.6881957  0.4554219 -5.9026 1.140e-08 ***
Weighted_Student_Teacher_Ratio                0.0184642  0.0061905  2.9827 0.0031354 ** 
Usage_of_textbook_Yes                         1.5419127  0.4025172  3.8307 0.0001611 ***
Usage_of_curriculum_Yes                      -0.0070235  0.4435351 -0.0158 0.9873782    
Usage_of_ELDS_Yes                            -0.9725957  0.3272576 -2.9720 0.0032431 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


$Physical

t test of coefficients:

                                               Estimate Std. Error t value Pr(>|t|)   
(Intercept)                                  -0.6042149  0.6840780 -0.8833 0.377934   
Age_months                                    0.0055298  0.0032444  1.7044 0.089530 . 
Gender_Male                                  -0.3980297  0.2957904 -1.3456 0.179616   
Primary_language_instruction                 -0.1497218  0.6017656 -0.2488 0.803713   
ECED_Attendance_Yes                          -0.2329371  0.2877486 -0.8095 0.418976   
School_Type_Community                        -1.0517809  0.3169765 -3.3182 0.001039 **
Urbanicity_Urban                             -0.1948808  0.2998779 -0.6499 0.516365   
Teachers_Qualification_Grade_10_only         -1.0237623  0.8740336 -1.1713 0.242573   
Pre_Service_Training_Received                 0.4335251  0.5373026  0.8069 0.420505   
In_Service_Training_Received                  0.4344775  0.3971790  1.0939 0.275031   
Availability_of_Reading_Learning_Areas       -0.4025822  0.6897154 -0.5837 0.559945   
Availability_of_Mathematics_Learning_Areas    0.6518367  0.2353286  2.7699 0.006021 **
Availability_of_RolePlay_Learning_Areas       0.8714956  1.0095136  0.8633 0.388796   
Availability_of_Science_Learning_Areas        0.8359995  0.7003819  1.1936 0.233735   
Availability_of_Creativity_Learning_Areas    -1.6922555  0.7365518 -2.2975 0.022402 * 
Availability_of_Constructions_Learning_Areas  0.0756388  0.9849918  0.0768 0.938850   
Availability_of_Caretaker_Yes                -1.5055295  0.6859907 -2.1947 0.029092 * 
Weighted_Student_Teacher_Ratio                0.0201834  0.0081497  2.4766 0.013917 * 
Usage_of_textbook_Yes                         0.6893070  0.3315806  2.0789 0.038635 * 
Usage_of_curriculum_Yes                       0.6853144  0.5452876  1.2568 0.209983   
Usage_of_ELDS_Yes                            -0.7611496  0.5025091 -1.5147 0.131092   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


$composite

t test of coefficients:

                                               Estimate Std. Error t value  Pr(>|t|)    
(Intercept)                                   0.1783044  0.6733649  0.2648 0.7913812    
Age_months                                    0.0076858  0.0039965  1.9231 0.0555851 .  
Gender_Male                                  -0.5537650  0.3801055 -1.4569 0.1463868    
Primary_language_instruction                 -0.4151065  0.4903338 -0.8466 0.3980265    
ECED_Attendance_Yes                          -0.6118443  0.2696329 -2.2692 0.0240968 *  
School_Type_Community                        -0.7566430  0.3614307 -2.0935 0.0372994 *  
Urbanicity_Urban                              0.5873556  0.3186960  1.8430 0.0664947 .  
Teachers_Qualification_Grade_10_only         -1.5083397  0.7157548 -2.1073 0.0360684 *  
Pre_Service_Training_Received                 0.7640436  0.4888869  1.5628 0.1193393    
In_Service_Training_Received                  0.1527797  0.3772038  0.4050 0.6857948    
Availability_of_Reading_Learning_Areas       -0.5691418  0.6394255 -0.8901 0.3742635    
Availability_of_Mathematics_Learning_Areas    1.0139969  0.2375310  4.2689 2.776e-05 ***
Availability_of_RolePlay_Learning_Areas       1.3191443  1.0065974  1.3105 0.1912110    
Availability_of_Science_Learning_Areas        0.5617631  0.6795773  0.8266 0.4092193    
Availability_of_Creativity_Learning_Areas    -2.4774163  0.6512524 -3.8041 0.0001784 ***
Availability_of_Constructions_Learning_Areas  0.5674947  0.9656097  0.5877 0.5572517    
Availability_of_Caretaker_Yes                -2.7850315  0.5978747 -4.6582 5.149e-06 ***
Weighted_Student_Teacher_Ratio                0.0216394  0.0079237  2.7310 0.0067572 ** 
Usage_of_textbook_Yes                         1.0717672  0.3925384  2.7304 0.0067696 ** 
Usage_of_curriculum_Yes                       0.3866621  0.5490799  0.7042 0.4819533    
Usage_of_ELDS_Yes                            -0.8057064  0.4554025 -1.7692 0.0780575 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1