Introduction

Given the extraordinary surge in migration during the recent years, it is interesting to find out if there is a particular change in the demographics of those groups. The data presented here does not account for refugees or population outflows, but it does provide the opportunity to explore some macro trends of migration, which in this case will be gender.

The guiding research questions is: Is there convincing evidence that the world has seen a change in its gender proportion of migrants between 1990 and 2019?

In order to address this question, we postulate the following hypothesis:

\[Ho: The \ gender \ proportion \ has \ not\ changed\ (p_{1990} = p_{2019} \rightarrow p_{2019} - p_{1990}=0 \rightarrow p_{diff} = 0) \] \[Ha: The \ gender \ proportion \ has \ changed\ (p_{1990} \neq p_{2019} \rightarrow p_{2019} - p_{1990}\neq0 \rightarrow p_{diff} \neq 0) \]

Environment Setup

Load required libraries

library(tidyverse) #readr, dplyr, tidyr, stringr, tibble, ggplot2
library(knitr)
library(kableExtra)
library(readxl)
library(scales)
library(countrycode)

A helper function for displaying tables

showtable <- function(data, title) {
  kable(data, caption = title) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"))
}

Data

Data Description

We are looking at data collected by the United Nations found here.

In particular, we are looking at Table 1.

The data is collected by the United Nations and the estimates are based on official statistics of foreign-born populations. The data is collected every year, but only 5 year increments as well as the current year (2019) are given.

Each case represents an estimate of a country’s international migrant population by gender, for a particular country and year. There are 3216 observations in the data set.

The response variable is the count of migrant population which is discrete and numerical. We will boil it down into the gender proportion of migrants which is continuous and bounded between 0 and 1.

The independent variables are Year which is a quantitative discretization of time and Gender which is qualitative. We should note that Year can be a different type of variable depending on how it is used. While in this context it makes sense to think of it as numerical time series, it does not make sense to apply numerical operations to it like for example to taking the average of two years or adding two years.

This study is observational because the data collectors had no control over the variables.

Regarding generalizability, the collected data represents the entire population of migrants so there was no random sampling. However, we will be randomly sampling the data to be able to generalize. In this study there is notion of causality since there is no random assignment.

Data Import

The document consists of multiple tabs of data. We will focus on Table 1 which contains International migrant stock at mid-year by sex and by major area, region, country or area, 1990-2019. We will look at the non-aggregated data for each country for both males and females to see what trends we can derive from this dataset.

untidy <- read_xlsx("UN_MigrantStockTotal_2019.xlsx", sheet = "Table 1")

Here is a quick look at the data. There are rows for every country as well as for aggregations by region. We can only find data by year and gender for the range 1990-2019.

Raw Data

Data Transormation/Preparation

We start by selecting the rows and columns of interest. We will ignore the aggregated data and select the country rows and the and the migrant stock data for the individual sexes

# Select the rows and columns of interest.
clean <- untidy %>% 
  select(2,`United Nations`,13:26) %>% 
  slice(33:294) %>% 
  filter(!is.na(`United Nations`)) %>% 
  select(-`United Nations`)

years <- untidy %>% 
  select(2, 13:26) %>% 
  slice(11)

# rename columns
names(clean) <- as.character(years)
names(clean)[1] <- "Country"

# transform the data into long format
cleaner_m <- clean[1:8]
cleaner_f <- clean[c(1,9:15)]
tidy_m <- cleaner_m %>% 
  gather("1990":"2019", key = Year, value = MigrantCount) %>%  
  mutate(Sex = "Male")
tidy_f <- cleaner_f %>% 
  gather("1990":"2019", key = Year, value = MigrantCount) %>%  
  mutate(Sex = "Female")
migrants <- rbind(tidy_m, tidy_f)
migrants["MigrantCount"] <- apply(migrants["MigrantCount"], 2, function(x) as.numeric(x))
migrants <- drop_na(migrants)

Let’s take a look at 15 random oberservations from this tidy data table.

showtable(sample_n(migrants, 10),"Long Format")

Long Format
Country	Year	MigrantCount	Sex
Brunei Darussalam	1995	47832	Male
Norway	2005	176444	Male
British Virgin Islands	1995	5012	Female
Lebanon	2019	967998	Female
North Macedonia	1995	45581	Male
Indonesia	1990	229885	Male
Morocco	2005	27543	Male
Liberia	2005	36005	Female
Senegal	2010	135879	Male
Seychelles	2010	7804	Male

migrants_wide <- migrants %>% spread(Year, MigrantCount)
showtable(sample_n(migrants_wide, 10),"Wide Format")

Wide Format
Country	Sex	1990	1995	2000	2005	2010	2015	2019
Uzbekistan	Male	723618	657490	606163	589690	558379	545721	545048
Cambodia	Male	19084	45361	71638	57511	43385	39854	42379
Uganda	Male	283337	308281	290859	292130	241903	415845	836620
United States Virgin Islands	Female	27146	28481	29881	29921	29962	29993	30005
Rwanda	Female	79261	105952	171335	209908	212853	258320	270015
Nauru	Female	1309	1210	1111	1045	530	819	908
Mauritania	Female	54081	42547	26203	25531	36074	72482	75221
Guadeloupe	Male	32718	36248	39778	41273	42768	43858	44537
Slovenia	Female	88563	84164	99736	100477	112501	103156	110496
Bahrain	Male	122730	144227	165344	288614	475905	508966	535728

We perform a series of transformations for downstream analysis.

grouped_total <- migrants %>% 
  group_by(Year, Sex)  %>% 
  summarize(Total=sum(MigrantCount)) %>% 
  mutate("Total_m" = round(Total/1000000,1))

proportions_by_year <- grouped_total %>% 
  select(-Total_m) %>%
  spread(Sex, Total) %>% 
  mutate(Total = Female + Male, Female = round(Female/Total,4), Male = round(Male/Total,4))  %>%
  select(Year, Female, Male) %>%
  gather("Female":"Male", key = Sex, value = Proportion)

showtable(proportions_by_year, "")


Year	Sex	Proportion
1990	Female	0.4924
1995	Female	0.4936
2000	Female	0.4929
2005	Female	0.4893
2010	Female	0.4834
2015	Female	0.4822
2019	Female	0.4791
1990	Male	0.5076
1995	Male	0.5064
2000	Male	0.5071
2005	Male	0.5107
2010	Male	0.5166
2015	Male	0.5178
2019	Male	0.5209

diff <- migrants %>% 
  spread(Sex, MigrantCount) %>%
  select(1:2, Male, Female) %>%
  mutate(Delta = Male - Female, Delta_m = Delta/1000000, Total = round(Male + Female,4), Prop = round(Male/Total,4))

showtable(sample_n(diff, 10),"")


Country	Year	Male	Female	Delta	Delta_m	Total	Prop
Costa Rica	2000	156798	154148	2650	0.002650	310946	0.5043
Belarus	1990	572021	676956	-104935	-0.104935	1248977	0.4580
Tajikistan	2019	118207	155864	-37657	-0.037657	274071	0.4313
Nauru	2000	1283	1111	172	0.000172	2394	0.5359
Saint Lucia	2000	4960	4911	49	0.000049	9871	0.5025
Eswatini	1990	39905	35086	4819	0.004819	74991	0.5321
Burundi	1990	163267	169843	-6576	-0.006576	333110	0.4901
Barbados	2000	12405	16019	-3614	-0.003614	28424	0.4364
Samoa	2015	2148	2104	44	0.000044	4252	0.5052
Bosnia and Herzegovina	1990	26538	29462	-2924	-0.002924	56000	0.4739

Here we randomly sample around 9% of the observations that we will use in our statistical analysis. We choose 9% to respect the condition for inference stated below. The two following tables show an example of the randomly selected countries for 1990 and 2019.

set.seed(606)
# determine number of observations
n <- length(clean$Country)
# sample 9%
y1990 <- diff %>% filter(Year == "1990") %>% sample_n(round(0.09*n))
y2019 <- diff %>% filter(Year == "2019") %>% sample_n(round(0.09*n))

showtable(y1990, "Sampled Data for 1990")

Sampled Data for 1990
Country	Year	Male	Female	Delta	Delta_m	Total	Prop
Grenada	1990	2106	2157	-51	-0.000051	4263	0.4940
Armenia	1990	270535	388254	-117719	-0.117719	658789	0.4107
Algeria	1990	150234	123720	26514	0.026514	273954	0.5484
Afghanistan	1990	32558	25128	7430	0.007430	57686	0.5644
Anguilla	1990	1258	1312	-54	-0.000054	2570	0.4895
Samoa	1990	1771	1586	185	0.000185	3357	0.5276
El Salvador	1990	22218	25142	-2924	-0.002924	47360	0.4691
Finland	1990	31682	31573	109	0.000109	63255	0.5009
Saint Helena	1990	110	68	42	0.000042	178	0.6180
Turkmenistan	1990	134174	172326	-38152	-0.038152	306500	0.4378
Gibraltar	1990	4528	4181	347	0.000347	8709	0.5199
Haiti	1990	10606	8478	2128	0.002128	19084	0.5558
Portugal	1990	209922	225860	-15938	-0.015938	435782	0.4817
Syrian Arab Republic	1990	364077	350063	14014	0.014014	714140	0.5098
Lebanon	1990	267922	255771	12151	0.012151	523693	0.5116
Cyprus	1990	20463	23342	-2879	-0.002879	43805	0.4671
Kuwait	1990	654878	419513	235365	0.235365	1074391	0.6095
Georgia	1990	133285	171185	-37900	-0.037900	304470	0.4378
Sweden	1990	383085	405682	-22597	-0.022597	788767	0.4857
Serbia	1990	46712	52557	-5845	-0.005845	99269	0.4706
Zimbabwe	1990	356240	278381	77859	0.077859	634621	0.5613

showtable(y2019, "Sampled Data for 2019")

Sampled Data for 2019
Country	Year	Male	Female	Delta	Delta_m	Total	Prop
Serbia	2019	361216	459096	-97880	-0.097880	820312	0.4403
Guadeloupe	2019	44537	55493	-10956	-0.010956	100030	0.4452
Mali	2019	237428	230802	6626	0.006626	468230	0.5071
Slovenia	2019	142626	110496	32130	0.032130	253122	0.5635
Belize	2019	30180	29818	362	0.000362	59998	0.5030
Seychelles	2019	9049	3877	5172	0.005172	12926	0.7001
Timor-Leste	2019	5086	3331	1755	0.001755	8417	0.6043
Niue	2019	319	269	50	0.000050	588	0.5425
Haiti	2019	10426	8330	2096	0.002096	18756	0.5559
Colombia	2019	575805	566514	9291	0.009291	1142319	0.5041
Cook Islands	2019	1748	1743	5	0.000005	3491	0.5007
Malawi	2019	117932	129720	-11788	-0.011788	247652	0.4762
Venezuela (Bolivarian Republic of)	2019	685975	689715	-3740	-0.003740	1375690	0.4986
Tokelau	2019	242	262	-20	-0.000020	504	0.4802
Algeria	2019	131596	117479	14117	0.014117	249075	0.5283
Anguilla	2019	2694	2985	-291	-0.000291	5679	0.4744
Benin	2019	183593	206519	-22926	-0.022926	390112	0.4706
Burkina Faso	2019	341830	376508	-34678	-0.034678	718338	0.4759
Iraq	2019	214288	153774	60514	0.060514	368062	0.5822
India	2019	2640513	2514224	126289	0.126289	5154737	0.5122
Bulgaria	2019	82718	85798	-3080	-0.003080	168516	0.4909

Exploratory Data Analysis

Population

The following analysis is based on the true population data.

Below is a summary of the data. We see in particular that the greatest net positive of female migrants was ~1.7m while it is nearly 4.9m for men. In terms of proportion, the parameter of interest (proportion of males) was as high as 87% and as low as 29%. The summary statistics just stated are from all observations, meaning here that these numbers are individual observations so they could be from any country or any year.

summary(diff)

##    Country              Year                Male         
##  Length:1608        Length:1608        Min.   :      61  
##  Class :character   Class :character   1st Qu.:   13160  
##  Mode  :character   Mode  :character   Median :   63032  
##                                        Mean   :  453763  
##                                        3rd Qu.:  286557  
##                                        Max.   :24488382  
##      Female             Delta             Delta_m         
##  Min.   :      47   Min.   :-1684385   Min.   :-1.684385  
##  1st Qu.:   12203   1st Qu.:   -5937   1st Qu.:-0.005937  
##  Median :   61813   Median :     224   Median : 0.000224  
##  Mean   :  429830   Mean   :   23933   Mean   : 0.023933  
##  3rd Qu.:  279594   3rd Qu.:    6722   3rd Qu.: 0.006722  
##  Max.   :26172767   Max.   : 4880026   Max.   : 4.880026  
##      Total               Prop       
##  Min.   :     108   Min.   :0.2930  
##  1st Qu.:   26197   1st Qu.:0.4800  
##  Median :  125646   Median :0.5079  
##  Mean   :  883593   Mean   :0.5163  
##  3rd Qu.:  588974   3rd Qu.:0.5392  
##  Max.   :50661149   Max.   :0.8767

The plots below reveals that the total population of migrants is increasing over time. We notice that the difference between the number of male and female migrants is increasing. Also shown is the change in the gender proportion over time.

Here we see how the difference between male and female migrant population is dsitributed over time. We can identify the max and min observations from the summary above in 2019.

As seen below, there is averall increase in the proportion of male migrants.

The side-by-side plot shown below looks at the cases of interest for the statistical study.

ggplot(pop, aes(Sex, Proportion)) + geom_bar(stat="identity") + facet_wrap(~Year) +
  geom_text(aes(label=Proportion), vjust=-1, size=3) +
  ggtitle("Migrant Gender Proportions from True Population 1990:2019")

By looking at the population data, we can say that there has been an increase in the number of male migrants relative to females.

Sampled Data

This side-by-side plot below shows the proportions from the sampled data. We observe very minor change from 1990 to 2019.

summary(y1990)

##    Country              Year                Male            Female      
##  Length:21          Length:21          Min.   :   110   Min.   :    68  
##  Class :character   Class :character   1st Qu.: 10606   1st Qu.:  8478  
##  Mode  :character   Mode  :character   Median : 46712   Median : 52557  
##                                        Mean   :147541   Mean   :141251  
##                                        3rd Qu.:267922   3rd Qu.:255771  
##                                        Max.   :654878   Max.   :419513  
##      Delta            Delta_m              Total              Prop       
##  Min.   :-117719   Min.   :-0.117719   Min.   :    178   Min.   :0.4107  
##  1st Qu.:  -5845   1st Qu.:-0.005845   1st Qu.:  19084   1st Qu.:0.4706  
##  Median :     42   Median : 0.000042   Median :  99269   Median :0.5009  
##  Mean   :   6290   Mean   : 0.006290   Mean   : 288792   Mean   :0.5082  
##  3rd Qu.:   7430   3rd Qu.: 0.007430   3rd Qu.: 523693   3rd Qu.:0.5484  
##  Max.   : 235365   Max.   : 0.235365   Max.   :1074391   Max.   :0.6180

summary(y2019)

##    Country              Year                Male             Female       
##  Length:21          Length:21          Min.   :    242   Min.   :    262  
##  Class :character   Class :character   1st Qu.:   9049   1st Qu.:   3877  
##  Mode  :character   Mode  :character   Median : 117932   Median : 110496  
##                                        Mean   : 277133   Mean   : 273655  
##                                        3rd Qu.: 237428   3rd Qu.: 230802  
##                                        Max.   :2640513   Max.   :2514224  
##      Delta           Delta_m              Total              Prop       
##  Min.   :-97880   Min.   :-0.097880   Min.   :    504   Min.   :0.4403  
##  1st Qu.: -3740   1st Qu.:-0.003740   1st Qu.:  12926   1st Qu.:0.4762  
##  Median :    50   Median : 0.000050   Median : 247652   Median :0.5030  
##  Mean   :  3478   Mean   : 0.003478   Mean   : 550788   Mean   :0.5170  
##  3rd Qu.:  6626   3rd Qu.: 0.006626   3rd Qu.: 468230   3rd Qu.:0.5425  
##  Max.   :126289   Max.   : 0.126289   Max.   :5154737   Max.   :0.7001

Inference

Methodology

The distribution of the sample proportion is described by the following:

\(\hat{p} \sim N \left( mean = p, SE = \sqrt{\frac{p(1-p)}{n}} \right)\)

The confidence interval is described by the following:

\(confidence\ interval = \hat{p} \pm z*SE\)

In this study, we will be using a 95% significance level.

Since we are looking at the distribution of the difference of two independent sample proportions the standard error takes the following form:

\(SE_{(\hat{p}_1 - \hat{p}_2)} = \sqrt{\frac{ \hat{p}_1 (1 - \hat{p}_1)}{n_1} + \frac{ \hat{p}_2 (1 - \hat{p}_2)}{n_2} }\)

Conditions

We then verify the conditions for inference on proportions.

Individual observations should be independent (the sample size should be < 10% of the population if sampling without replacement)

This condition is respected as we sampled 9% of the population.

The sample distribution should be approximately normal.

We are on the border of acceptable with the check below:

\(np = 21 \times 0.5 = 10.5 > 10\)
\(n(1-p) = 21 \times 0.5 = 10.5 > 10\)

Randomness: the data must come from a random sample or a randomized experiment

The data was randomly sampled.

Confidence Intervals

To determine is there is a statistical significance in the different of proportions, we study the overlap of the confidence intervals for the years of interest.

# year 1990
total1990 <- sum(y1990$Male) + sum(y1990$Female)
p1990 <- sum(y1990$Male) / total1990
se1990 <- sqrt((p1990*(1-p1990))/total1990)
me1990 <- qnorm(0.975) * se1990
ci1990 <- c(p1990-me1990,p1990+me1990)

# year 2019
total2019 <- sum(y2019$Male) + sum(y2019$Female)
p2019 <- sum(y2019$Male) / total2019
se2019 <- sqrt((p2019*(1-p2019))/total2019)
me2019 <- qnorm(0.975) * se2019
ci2019 <- c(p2019-me2019,p2019+me2019)

Here is a summary of the analysis. What it reveals is that there is no overlap in the confidence intervals of the male migrant proportion between 1990 and 2019. At a significance level of 95%, we reject the null hypothesis and draw the conclusion that the gender proportion has changed.

summary_df <- data.frame("year" = c(1990,2019),
                      "proportion" = c(p1990,p2019), 
                      "se" = c(se1990,se2019),
                      "ci_lower" = c(ci1990[1],ci2019[1]),
                      "ci_upper" = c(ci1990[2],ci2019[2]))
showtable(summary_df, "Confidence Intervals")

Confidence Intervals
year	proportion	se	ci_lower	ci_upper
1990	0.5108898	0.000203	0.5104919	0.5112876
2019	0.5031577	0.000147	0.5028696	0.5034459

Here we reach the same conclusion differently by looking at the differences in proportion and recognizing that the confidence interval does not contains the null hypothesis value of 0.

p_diff <- p2019-p1990
se <- sqrt((p1990*(1-p1990))/total1990+(p2019*(1-p2019))/total2019)
me <- qnorm(0.975) * se
ci_diff<- c(p_diff-me,p_diff+me)
ci_diff

## [1] -0.008223262 -0.007240805

Conclusion

We return to the research question: Is there convincing evidence that the world has seen a change in its gender proportion of migrants between 1990 and 2019?

From the exploration and analysis above, we conclude that based on our sample, there is enough evidence to reject the null hypothesis and conclude that the gender proportions have changed from 1990 to 2019.

We must note that with our sample size of 21 countries we are on the lower bound of the normality assumption.

A 95% confidence interval tells us that in 95% of the cases, we expect to capture the true population mean. This can be confirmed by simulation.

To improve upon this study we could pursue the following research:

Run a simulation to collect many samples
Instead of overall proportion, we could investigate the number of countries in a sample that have a male proportion greater than 50%
Investigate the average male proportion of the sampled countries instead of the male proportion of the total migrant population of the sample countries.
Investigate the year to year differential instead of the cummulative differences.

Exploring Changes in Migration Trends

Mael Illien

11/25/2019