Analysis of Continuous Data
Victoria Sparandera
Research Question
Is there a statistically significant difference between the mean feeling towards feminism in females and males?
Variables
Independent Variable
gender
This variable will be separated into two groups: “Female” and “Male”.
Dependent Variable
ft_fem_2017
Respondents rated their feeling towards feminism using a 0-100 scale; 100 indicates absolute positive feeling, 50 indicates neutral feeling, and 0 implies absolutely negative feeling.
Data Prep
library(readr)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)
Voter_Dataset<- read_csv("Abbreviated Voter Dataset Labeled.csv")##
## ── Column specification ─────────────────────────────────────────────────────────
## cols(
## .default = col_character(),
## NumChildren = col_double(),
## Immigr_Economy_GiveTake = col_double(),
## ft_fem_2017 = col_double(),
## ft_immig_2017 = col_double(),
## ft_police_2017 = col_double(),
## ft_dem_2017 = col_double(),
## ft_rep_2017 = col_double(),
## ft_evang_2017 = col_double(),
## ft_muslim_2017 = col_double(),
## ft_jew_2017 = col_double(),
## ft_christ_2017 = col_double(),
## ft_gays_2017 = col_double(),
## ft_unions_2017 = col_double(),
## ft_altright_2017 = col_double(),
## ft_black_2017 = col_double(),
## ft_white_2017 = col_double(),
## ft_hisp_2017 = col_double()
## )
## ℹ Use `spec()` for the full column specifications.head(Voter_Dataset)## # A tibble: 6 x 53
## gender race education familyincome children region urbancity Vote2012
## <chr> <chr> <chr> <chr> <chr> <chr> <chr> <chr>
## 1 Female White 4-year Prefer not … No West Suburb Barack …
## 2 Female White Some Col… $60K-$69,999 No West Rural Ar… Mitt Ro…
## 3 Male White High Sch… $50K-$59,999 No Midwe… City Mitt Ro…
## 4 Male White Some Col… $70K-$79,999 No South City Barack …
## 5 Male White 4-year $40K-$49,999 No South Suburb Mitt Ro…
## 6 Female White 2-year $30K-$39,999 No West Suburb Barack …
## # … with 45 more variables: Vote2016 <chr>, TrumpSanders <chr>,
## # PartyRegistration <chr>, PartyIdentification <chr>,
## # PartyIdentification2 <chr>, PartyIdentification3 <chr>,
## # NewsPublicAffairs <chr>, DemPrimary <chr>, RepPrimary <chr>,
## # ImmigrantContributions <chr>, ImmigrantNaturalization <chr>,
## # ImmigrationShouldBe <chr>, Abortion <chr>, GayMarriage <chr>,
## # DeathPenalty <chr>, DeathPenaltyFreq <chr>, TaxWealthy <chr>,
## # Healthcare <chr>, GlobWarmExist <chr>, GlobWarmingSerious <chr>,
## # AffirmativeAction <chr>, Religion <chr>, ReligiousImportance <chr>,
## # ChurchAttendance <chr>, PrayerFrequency <chr>, NumChildren <dbl>,
## # areatype <chr>, GunOwnership <chr>, EconomyBetterWorse <chr>,
## # Immigr_Economy_GiveTake <dbl>, ft_fem_2017 <dbl>, ft_immig_2017 <dbl>,
## # ft_police_2017 <dbl>, ft_dem_2017 <dbl>, ft_rep_2017 <dbl>,
## # ft_evang_2017 <dbl>, ft_muslim_2017 <dbl>, ft_jew_2017 <dbl>,
## # ft_christ_2017 <dbl>, ft_gays_2017 <dbl>, ft_unions_2017 <dbl>,
## # ft_altright_2017 <dbl>, ft_black_2017 <dbl>, ft_white_2017 <dbl>,
## # ft_hisp_2017 <dbl>gen_fem<-Voter_Dataset%>%
select(gender,ft_fem_2017)%>%
filter(!is.na(ft_fem_2017))Comparison of Means
Table
Null Hypothesis
gen_fem%>%
summarise(avg_ft_fem=mean(ft_fem_2017))## # A tibble: 1 x 1
## avg_ft_fem
## <dbl>
## 1 52.1If a person’s gender does not make a difference in their feeling toward feminism, it is expected that the group-wise averages for both “Females” and “Males” are near 52.1.
Actual Observations
gen_fem%>%
group_by(gender)%>%
summarise(avg_ft_fem=mean(ft_fem_2017))## `summarise()` ungrouping output (override with `.groups` argument)## # A tibble: 2 x 2
## gender avg_ft_fem
## <chr> <dbl>
## 1 Female 58.3
## 2 Male 45.3Visualization
gen_fem%>%
group_by(gender)%>%
summarise(avg_ft_fem=mean(ft_fem_2017))%>%
ggplot()+geom_col(aes(x=gender,y=avg_ft_fem,fill=gender))## `summarise()` ungrouping output (override with `.groups` argument)
Interpretation
As shown by the actual observations table and the chart above, the group-wise mean feeling towards feminism for females and males are almost the same distance from 52.1, in opposite directions. Therefore, the conclusion that there is no difference in the mean between groups cannot be made.
Comparison of Distributions
Visualization
gen_fem%>%
ggplot()+ geom_histogram(aes(x=ft_fem_2017,fill=gender))+facet_wrap(~gender)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Interpretation
The sampling distributions of the females and males in this study differ in their skew. The sampling distribution of female respondents is right skewed when it comes to their feeling towards feminism. However, that of male respondents is skewed more to the left.
Sampling Distribution
Females
F_gen_fem<-gen_fem%>%
filter(gender=="Female")
mean(F_gen_fem$ft_fem_2017)## [1] 58.34626replicate(10000,
sample(F_gen_fem$ft_fem_2017,40)%>%
mean(na.rm=TRUE))%>%
data.frame()%>%
rename("mean"=1)%>%
ggplot()+geom_histogram(aes(x=mean),fill="salmon")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Males
M_gen_fem<-gen_fem%>%
filter(gender=="Male")
mean(M_gen_fem$ft_fem_2017)## [1] 45.34614replicate(10000,
sample(M_gen_fem$ft_fem_2017,40)%>%
mean(na.rm=TRUE))%>%
data.frame()%>%
rename("mean"=1)%>%
ggplot()+geom_histogram(aes(x=mean),fill="turquoise3")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
T-test
options(scipen = 999)
t.test(ft_fem_2017~gender,data=gen_fem)##
## Welch Two Sample t-test
##
## data: ft_fem_2017 by gender
## t = 13.787, df = 4682.9, p-value < 0.00000000000000022
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 11.15155 14.84871
## sample estimates:
## mean in group Female mean in group Male
## 58.34626 45.34614The t-test produced a p-value of less than 0.05. Therefore, there is a statistically significant difference between the mean feeling towards feminism of females and males.