Stats_challenge
D. Rerio
9/17/2020
Last updated: 2020-09-18
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Knit directory: myproject/
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Loading the data
# read data
library(utils)
#read the Dataset sheet into “R”. The dataset will be called "data".
data <- read.csv("https://opendata.ecdc.europa.eu/covid19/casedistribution/csv", na.strings = "", fileEncoding = "UTF-8-BOM")
# the code below shows how you may recode the country name's
#first letter to a numeric alphabetic position.
data1 <- data[(data$dateRep=="11/08/2020"), ]
CountryAb <- as.integer((nchar(data1$countriesAndTerritories)))
# build a linear model for the relationship between Cumulative_number_for_14_days_of_COVID.19_ca
model1<- lm(Cumulative_number_for_14_days_of_COVID.19_cases_per_100000~CountryAb, data=data1)
summary(model1)
Call:
lm(formula = Cumulative_number_for_14_days_of_COVID.19_cases_per_100000 ~
CountryAb, data = data1)
Residuals:
Min 1Q Median 3Q Max
-54.10 -46.82 -34.45 9.62 432.80
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 46.582 10.757 4.330 2.32e-05 ***
CountryAb 0.258 1.002 0.257 0.797
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 78.78 on 207 degrees of freedom
Multiple R-squared: 0.00032, Adjusted R-squared: -0.004509
F-statistic: 0.06626 on 1 and 207 DF, p-value: 0.7971# On 8/11/2020, we did not find a significant relationship
# between alphabetic order of country name and COVID-19 cases.
#But what if we keep looking at other dates?Testing for significance
Lets do a for loop to do the stats test for this:
dates = levels(as.factor(data$dateRep)) ##all unique dates we have data on
for (i in seq(1,length(dates))){
#print(i)
data1 = data %>% filter(dateRep ==dates[i]) %>%
na.omit()
if(nrow(data1) > 1){
#CountryAb <- as.integer(as.factor(substr(data1$countriesAndTerritories,1,1)))
data1 = data1 %>% mutate(CountryAb= as.integer(as.factor(nchar((data1$countriesAndTerritories)))))
alphabet = data1 %>% group_by(CountryAb)
means = alphabet %>% summarise(mean = mean(Cumulative_number_for_14_days_of_COVID.19_cases_per_100000))
iqr = alphabet %>% summarise(IQR = IQR(Cumulative_number_for_14_days_of_COVID.19_cases_per_100000))
quant1 = alphabet %>%
summarise(quant1= quantile(Cumulative_number_for_14_days_of_COVID.19_cases_per_100000)[2])
quant3 = alphabet %>%
summarise(quant3= quantile(Cumulative_number_for_14_days_of_COVID.19_cases_per_100000)[4])
##filter out the outliers
data1 = data1 %>% left_join(means, ., by=c("CountryAb"="CountryAb")) %>%
left_join(iqr, ., by=c("CountryAb"="CountryAb")) %>%
left_join(quant1, ., by=c("CountryAb"="CountryAb")) %>%
left_join(quant3, ., by=c("CountryAb"="CountryAb")) %>%
filter(Cumulative_number_for_14_days_of_COVID.19_cases_per_100000 > quant1 - IQR*1.5 |Cumulative_number_for_14_days_of_COVID.19_cases_per_100000 < quant3 + IQR*1.5 )
model1 <- lm(Cumulative_number_for_14_days_of_COVID.19_cases_per_100000~CountryAb, data=data1)
sum = summary(model1)
if(sum$coefficients[2,4] < 0.05){
print(paste("CountryAb p-value:",sum$coefficients[2,4]),quote = F)
print("Significant!")
print(dates[i])
sig_date = (dates[i])
p_val = sum$coefficients[2,4]
}
}
}[1] CountryAb p-value: 0.00748299725523194
[1] "Significant!"
[1] "24/03/2020"
[1] CountryAb p-value: 0.00687706604930121
[1] "Significant!"
[1] "25/03/2020"
[1] CountryAb p-value: 0.00976040945291237
[1] "Significant!"
[1] "26/03/2020"
[1] CountryAb p-value: 0.0131030442323662
[1] "Significant!"
[1] "27/03/2020"Visualizing our result
Plotting the data as a scatterplot, we can see that the correlation between country name length and covid cases is likely due to a large number of short-named countries having very few cases. There certainly is no causal reason for COVID cases to be higher in counties with shorter names, as the country name does not incluence factors like mask-wearing, social distancing, international travel, or ACE2 expression. While intuitively name length has no connection to variables known to control for covid spread, it could be plausible that there is a correlation, due to counties from certain regions having similarities in language and therefore name length, as well as closeness geographically leading to more frequent travel, and therefore, virus presence being similar amongst these nations. To verify that we have indeed hacked the p-value through excessive testing of combinations of variables rather than detecting a correlation we plotted the country name length and COVID cases by country. It is apparent that there is no underlying correlation in country name and COVID spread. Additionally, out of the 263 dates tested, we found 4 significant dates. This is well within the expected number of false positive results and when considering potential corrections, like Bonferroni, we see for the 4 dates in question the p-values shift from (0.00748, 0.00687, 0.00976, 0.01310) to (1, 1, 1, 1).
df = subset(data, data$dateRep == sig_date)
data2 <- data[(data$dateRep==sig_date), ]
CountryAb <- as.integer((nchar(data2$countriesAndTerritories)))
df = df %>% mutate( CountryAb = CountryAb )
plot_1 = ggplot(df, aes_string(x = "CountryAb", y = "Cumulative_number_for_14_days_of_COVID.19_cases_per_100000")) + geom_point() + labs( x = "Number of letters in country name", y = "Covid Cases [cumulative for 14 days]", title = "Correlation between Country name length and COVID Cases") + theme_cowplot()
fit = lm(Cumulative_number_for_14_days_of_COVID.19_cases_per_100000 ~ CountryAb, df)
summary(fit)
Call:
lm(formula = Cumulative_number_for_14_days_of_COVID.19_cases_per_100000 ~
CountryAb, data = df)
Residuals:
Min 1Q Median 3Q Max
-44.60 -24.17 -21.68 -8.53 411.14
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 19.1747 13.2098 1.452 0.149
CountryAb 0.7964 1.4200 0.561 0.576
Residual standard error: 64.45 on 114 degrees of freedom
(78 observations deleted due to missingness)
Multiple R-squared: 0.002751, Adjusted R-squared: -0.005996
F-statistic: 0.3145 on 1 and 114 DF, p-value: 0.576p_val_label = paste0("Date: ", sig_date, " p value: ", p_val)
plot_1_label = paste0("y=", substr((coef(fit)[2]),1,6), "x+", substr((coef(fit)[1]),1,6))
plot_1_label_2 = paste0(" R2=", summary(fit)$r.squared)
plot_1 = plot_1 + geom_abline(color = "dodgerblue", linetype = "dashed", intercept = coef(fit)[1], slope = coef(fit)[2]) + annotate(geom="text", x=25, y=350, label=plot_1_label, color="dodgerblue") + annotate(geom="text", x=25, y=325, label=plot_1_label_2, color="dodgerblue") + annotate(geom="text", x=25, y=300, label=p_val_label, color="orange") + geom_text_repel(mapping = aes_string(label = "countriesAndTerritories"), size = 2.5, color = "gray")
print(plot_1)Warning: Removed 78 rows containing missing values (geom_point).Warning: Removed 78 rows containing missing values (geom_text_repel).
plot_2_A = ggplot(df, aes(x = as.factor(continentExp), y = CountryAb, color = continentExp)) + geom_boxplot(na.rm = TRUE) + labs( x = "Continent", y = "Number Letters", title = "Country name length") + theme_cowplot()
print(plot_2_A)
plot_2_B = ggplot(df, aes(x = as.factor(continentExp), y = Cumulative_number_for_14_days_of_COVID.19_cases_per_100000, color = continentExp)) + geom_boxplot(na.rm = TRUE) + labs( x = "Continent", y = "Covid Cases [cumulative for 14 days]", title = "COVID cases") + theme_cowplot()
print(plot_2_B)
sessionInfo()R version 4.0.2 (2020-06-22)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 18363)
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.1252
[2] LC_CTYPE=English_United States.1252
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] ggrepel_0.8.2 cowplot_1.1.0 forcats_0.5.0 stringr_1.4.0
[5] purrr_0.3.4 readr_1.3.1 tidyr_1.1.2 tibble_3.0.3
[9] ggplot2_3.3.2 tidyverse_1.3.0 dplyr_1.0.2 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] tidyselect_1.1.0 xfun_0.17 haven_2.3.1 colorspace_1.4-1
[5] vctrs_0.3.4 generics_0.0.2 htmltools_0.5.0 yaml_2.2.1
[9] blob_1.2.1 rlang_0.4.7 later_1.1.0.1 pillar_1.4.6
[13] withr_2.2.0 glue_1.4.2 DBI_1.1.0 dbplyr_1.4.4
[17] modelr_0.1.8 readxl_1.3.1 lifecycle_0.2.0 munsell_0.5.0
[21] gtable_0.3.0 cellranger_1.1.0 rvest_0.3.6 evaluate_0.14
[25] labeling_0.3 knitr_1.29 httpuv_1.5.4 fansi_0.4.1
[29] broom_0.7.0 Rcpp_1.0.4.6 promises_1.1.1 backports_1.1.9
[33] scales_1.1.1 jsonlite_1.7.1 farver_2.0.3 fs_1.5.0
[37] hms_0.5.3 digest_0.6.25 stringi_1.5.3 rprojroot_1.3-2
[41] grid_4.0.2 cli_2.0.2 tools_4.0.2 magrittr_1.5
[45] crayon_1.3.4 whisker_0.4 pkgconfig_2.0.3 ellipsis_0.3.1
[49] xml2_1.3.2 reprex_0.3.0 lubridate_1.7.9 assertthat_0.2.1
[53] rmarkdown_2.3 httr_1.4.2 rstudioapi_0.11 R6_2.4.1
[57] git2r_0.27.1 compiler_4.0.2