WEEK3
Heleine Fouda
2023-07-28
The research question:
Is the difference observed in life expectancy between Africa and Europe between 1952 and 1977 statistically significant?
1. Data Exploration
First let’s take a broad look at the data frame
glimpse(gapminder)## Rows: 1,704
## Columns: 6
## $ country <fct> "Afghanistan", "Afghanistan", "Afghanistan", "Afghanistan", …
## $ continent <fct> Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, …
## $ year <int> 1952, 1957, 1962, 1967, 1972, 1977, 1982, 1987, 1992, 1997, …
## $ lifeExp <dbl> 28.801, 30.332, 31.997, 34.020, 36.088, 38.438, 39.854, 40.8…
## $ pop <int> 8425333, 9240934, 10267083, 11537966, 13079460, 14880372, 12…
## $ gdpPercap <dbl> 779.4453, 820.8530, 853.1007, 836.1971, 739.9811, 786.1134, …Let’s also check the names, types,nature and structure of the variables contained in the data frame.
head(gapminder)## # A tibble: 6 × 6
## country continent year lifeExp pop gdpPercap
## <fct> <fct> <int> <dbl> <int> <dbl>
## 1 Afghanistan Asia 1952 28.8 8425333 779.
## 2 Afghanistan Asia 1957 30.3 9240934 821.
## 3 Afghanistan Asia 1962 32.0 10267083 853.
## 4 Afghanistan Asia 1967 34.0 11537966 836.
## 5 Afghanistan Asia 1972 36.1 13079460 740.
## 6 Afghanistan Asia 1977 38.4 14880372 786.names(gapminder)## [1] "country" "continent" "year" "lifeExp" "pop" "gdpPercap"str(gapminder)## tibble [1,704 × 6] (S3: tbl_df/tbl/data.frame)
## $ country : Factor w/ 142 levels "Afghanistan",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ continent: Factor w/ 5 levels "Africa","Americas",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ year : int [1:1704] 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 ...
## $ lifeExp : num [1:1704] 28.8 30.3 32 34 36.1 ...
## $ pop : int [1:1704] 8425333 9240934 10267083 11537966 13079460 14880372 12881816 13867957 16317921 22227415 ...
## $ gdpPercap: num [1:1704] 779 821 853 836 740 ...The structure function reveals the presence of two numerical variables: lifeExp and gdpPercap; two integers:pop and year variables; two factors: country and continent variables. Let’s visualize the numerical variables
class(gapminder$lifeExp)## [1] "numeric"class(gapminder$gdpPercap)## [1] "numeric"class(gapminder$pop)## [1] "integer"class(gapminder$pop)## [1] "integer"2. Descriptive statistics
summary(gapminder)## country continent year lifeExp
## Afghanistan: 12 Africa :624 Min. :1952 Min. :23.60
## Albania : 12 Americas:300 1st Qu.:1966 1st Qu.:48.20
## Algeria : 12 Asia :396 Median :1980 Median :60.71
## Angola : 12 Europe :360 Mean :1980 Mean :59.47
## Argentina : 12 Oceania : 24 3rd Qu.:1993 3rd Qu.:70.85
## Australia : 12 Max. :2007 Max. :82.60
## (Other) :1632
## pop gdpPercap
## Min. :6.001e+04 Min. : 241.2
## 1st Qu.:2.794e+06 1st Qu.: 1202.1
## Median :7.024e+06 Median : 3531.8
## Mean :2.960e+07 Mean : 7215.3
## 3rd Qu.:1.959e+07 3rd Qu.: 9325.5
## Max. :1.319e+09 Max. :113523.1
## var(gapminder$lifeExp,gapminder$gdpPercap, na.rm= TRUE)## [1] 74323.22a. First, Examining the general correlation between lifeExp and gdpPercap across time and space:
Below, a correlation test, a plot and a boxplot all reveal a statistically significant correlation between lifeExp and gdpPercap across continents at a 95% level of confidence. The higher the gdpPercap, the longer the lifeExp and vice versa.
cor.test(gapminder$lifeExp,gapminder$gdpPercap)##
## Pearson's product-moment correlation
##
## data: gapminder$lifeExp and gapminder$gdpPercap
## t = 29.658, df = 1702, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.5515065 0.6141690
## sample estimates:
## cor
## 0.5837062plot(gapminder$lifeExp~gapminder$gdpPercap)
boxplot(gapminder$lifeExp~gapminder$gdpPercap)
There is a correlation across time between GDP per capita and life expectancy as shown in the boplot for 2007 and 1952
plot(lifeExp ~ gdpPercap, gapminder, subset = year == 2007, log = "x")
plot(lifeExp ~ gdpPercap, gapminder, subset = year == 1952, log = "x")
hist(gapminder$gdpPercap)
hist(gapminder$lifeExp)
library (gapminder)
lifeExp<- c(gapminder$lifeExp)
aggregate(lifeExp~continent,gapminder, median)## continent lifeExp
## 1 Africa 47.7920
## 2 Americas 67.0480
## 3 Asia 61.7915
## 4 Europe 72.2410
## 5 Oceania 73.66502b. Second, Examining the correlation between lifeExp and gdpPercap between Africa and Europe
METHOD:
Creating a subset of the main data frame with new columns names.
The subset will show data for only Europe and Africa. LifeExp and gdpPercap will also be renamed as a second step
library(dplyr)
library(ggplot2)
library(tidyverse)
library(gapminder)
data_subset <- gapminder[13:48,2:6]
summary(data_subset)## continent year lifeExp pop gdpPercap
## Africa :24 Min. :1952 Min. :30.02 Min. : 1282697 Min. :1601
## Americas: 0 1st Qu.:1966 1st Qu.:40.88 1st Qu.: 3402653 1st Qu.:2725
## Asia : 0 Median :1980 Median :56.62 Median : 6589530 Median :3527
## Europe :12 Mean :1980 Mean :55.12 Mean : 9921682 Mean :3763
## Oceania : 0 3rd Qu.:1993 3rd Qu.:68.99 3rd Qu.:12505482 3rd Qu.:4826
## Max. :2007 Max. :76.42 Max. :33333216 Max. :62233. Renaming LifeExp and gdpPercap to Life_Expectancy and GDP
data_subset = data("gapminder")
gapminder %>%
select(continent,lifeExp,gdpPercap) %>%
filter(continent%in%
c("Africa","Europe"))%>%
rename(Life_Expectancy=lifeExp,
GDP=gdpPercap,) %>%
arrange()## # A tibble: 984 × 3
## continent Life_Expectancy GDP
## <fct> <dbl> <dbl>
## 1 Europe 55.2 1601.
## 2 Europe 59.3 1942.
## 3 Europe 64.8 2313.
## 4 Europe 66.2 2760.
## 5 Europe 67.7 3313.
## 6 Europe 68.9 3533.
## 7 Europe 70.4 3631.
## 8 Europe 72 3739.
## 9 Europe 71.6 2497.
## 10 Europe 73.0 3193.
## # ℹ 974 more rowsdata_subset = data("gapminder")
gapminder %>%
select(continent,lifeExp,gdpPercap) %>%
filter(continent%in%
c("Africa","Europe"))%>%
rename(Life_Expectancy=lifeExp,
GDP=gdpPercap,) %>%
names()## [1] "continent" "Life_Expectancy" "GDP"4. Samples Findings:
4a. Statical significance
How statistically significant are the sample findings? Assuming (H0), against the samples findings, that there is absolutely no difference between the life expectancy in Africa and the life expectancy in Europe, how likely is it that one can randomly come across a sample showing a difference of the magnetude seen in the data sets findings?
4b. Samples summaries from both the main and the subset data frames reveal an average of 25 to 30 years of difference in life expectancy between Europe and Africa.
4c. Conducting a Two sample t-test
data("gapminder")
gapminder %>%
filter(continent %in% c("Africa","Europe")) %>%
t.test(lifeExp~continent,data =.,
alternative= "two.sided",
paired=FALSE)##
## Welch Two Sample t-test
##
## data: lifeExp by continent
## t = -49.551, df = 981.2, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group Africa and group Europe is not equal to 0
## 95 percent confidence interval:
## -23.95076 -22.12595
## sample estimates:
## mean in group Africa mean in group Europe
## 48.86533 71.903695. Results of the t-test
5a, The t-test results reveal (within a 95 percent confidence interval) that a true, statistically significant difference in life expectancy existed between Africa and Europe from 1952 to 1977.
One must therefore rejects the null hypothesis of zero difference and accept the alternative idea that there is, in truth,a difference and that life expectancy is a function of the gdp per capita.
6. Visualizing the findings
library(ggplot2)
gapminder %>%
filter(gdpPercap < 50000) %>%
ggplot(aes(x=log(gdpPercap), y=lifeExp))+
geom_point()
7. Regression/Linear modeling
library(ggplot2)
library(tidyverse)
library(gapminder)
lm(gapminder$lifeExp~gapminder$gdpPercap)##
## Call:
## lm(formula = gapminder$lifeExp ~ gapminder$gdpPercap)
##
## Coefficients:
## (Intercept) gapminder$gdpPercap
## 5.396e+01 7.649e-04library(ggplot2)
library(tidyverse)
library(gapminder)
summary(lm(gapminder$lifeExp~gapminder$gdpPercap))##
## Call:
## lm(formula = gapminder$lifeExp ~ gapminder$gdpPercap)
##
## Residuals:
## Min 1Q Median 3Q Max
## -82.754 -7.758 2.176 8.225 18.426
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.396e+01 3.150e-01 171.29 <2e-16 ***
## gapminder$gdpPercap 7.649e-04 2.579e-05 29.66 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.49 on 1702 degrees of freedom
## Multiple R-squared: 0.3407, Adjusted R-squared: 0.3403
## F-statistic: 879.6 on 1 and 1702 DF, p-value: < 2.2e-16library(ggplot2)
library(tidyverse)
library(gapminder)
summary(lm(gapminder$lifeExp~gapminder$gdpPercap +gapminder$pop))##
## Call:
## lm(formula = gapminder$lifeExp ~ gapminder$gdpPercap + gapminder$pop)
##
## Residuals:
## Min 1Q Median 3Q Max
## -82.754 -7.745 2.055 8.212 18.534
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.365e+01 3.225e-01 166.36 < 2e-16 ***
## gapminder$gdpPercap 7.676e-04 2.568e-05 29.89 < 2e-16 ***
## gapminder$pop 9.728e-09 2.385e-09 4.08 4.72e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.44 on 1701 degrees of freedom
## Multiple R-squared: 0.3471, Adjusted R-squared: 0.3463
## F-statistic: 452.2 on 2 and 1701 DF, p-value: < 2.2e-16