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Data Project Relationship Between Gun Ownership And Ethnicity Groups.html

Data Project: Relationship Between Gun Ownership And
Ethnicity Groups
Introduction:
The purpose of this project is to investigate if there is a relationship between gun ownership in the households of US citizens aged 18 or older and ethnicity groups. A clearer way to state the research question is “are people belonging to particular ethnicity groups more likely to own a gun in their households?” Widespread gun ownership is the subject of many debates on crime rate in the US. In that respect this study could also provide useful insights into indentifying whether people belonging to a particular ethnicity group feel they are not sufficiently protected by police force.

Data:
The study uses American National Elections Study (ANES) data for the year 2012. ANES is a survey of voters in the United States, conducted before and after every presidential election. For the year 2012 the data were collected in 2 different modes (Internet mode and Face-to-face mode), using 2 separate samples.
The global sample is composed of 5914 cases (2.054 face-to-face mode and 3.860 Internet mode).
The observations are US citizens aged 18 or older.
For the Internet mode, all study participants were members of the Knowledge Panel, a panel of regular survey participants administered by GfK (formerly Knowledge Networks). Panelists were recruited using two probability sampling methods: address-based sampling (ABS) and random-digit dialing (RDD). A sample of
Knowledge Panelists received invitations to take the ANES Time Series survey. This sample was limited to
U.S. citizens who would be at least 18 years old by Election Day, November 6, 2012, and was limited to one person per household.
For the face-to-face mode, all sampled persons were interviewed in person. The sample includes a nationally-representative main sample and two oversamples: one of blacks and one of Hispanics. The first stage of sampling consisted of stratifying the 48 contiguous states and the District of Columbia into nine regions corresponding to Census Divisions. These Census Divisions constituted the study’s strata. Within each region, a number of census tracts was then randomly selected. The number of tracts selected per region was proportional to the region’s proportion of the U.S. adult population. The second stage of sampling consisted of the random selection of residential addresses within each tract. Addresses for the black and Hispanic oversamples were selected from tracts with relatively high proportions of one or both of these populations. The third and final stage of sampling was the selection of one eligible person per household. It is important to underline that the data come from a survey and not from an experiment (the researchers did not assign different groups of subjects to various treatments), consequently the study can be characterized as observational. For this reason, it can establish only correlation between the variables of interest and not causation. However, since the sample design criteria included: probability sampling, stratified sampling and random sampling, the study’s findings can be generalized to the entire population of interest (US citizens aged 18 or older). One last note on the scope of inference is that one potential source of bias might be represented by privacy concerns on respondents’ answers. In order to limit its effects, for a portion of the face-to-face interview respondents were allowed to answer questions privately.
The study uses two variables chosen from those collected by ANES survey: file:///C:/Documents%20and%20Settings/Administrator/Documenti/Courses/Data%20Analysis%20and%20Statistical%20Inference/Lab/Project/Data%20Pro… 1/7

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Data Project Relationship Between Gun Ownership And Ethnicity Groups.html

1. Respondent’s race and ethnicity group (code name: “dem_raceeth”): it is a categorical variable whose values are: “White-Non Hispanic”, “Black-Non Hispanic”, “Hispanic”, “Other-Non Hispanic”;
2. Gun ownership in the respondent’s household (code name: “owngun_owngun”): it is a categorical variable whose values are " Yes“;”No“.

Exploratory data analysis:
Before exploring the data, we create a dataset with the two variables of interest and we give them a clearer label. mvr < c1417 yas - (1,1)

poetdt < ae[yas rjc_aa - nsmvr]

clae(rjc_aa < c"tnct.ru""u.wesi" onmspoetdt) - (EhiiyGop,GnOnrhp)

There are some observations with missing values. Filtering them out brings the number of observations to
5704. The sample size remains significant for the study. poetdt =poetdt[opeecsspoetdt)] rjc_aa rjc_aacmlt.ae(rjc_aa,

no(rjc_aa rwpoetdt) # []50
# 1 74

The traditional way to explore a categorical value is through a frequency table. We can easily compute the number (and the proportion) of respondents who own a gun in their households. tbepoetdt$u.wesi) al(rjc_aaGnOnrhp

#
#
# Ys N
# e o # 11 39
# 84 80

tbepoetdt$u.wesi)50 al(rjc_aaGnOnrhp/74 #
#
#
#
Ys e N o # 0382406176
# .102 .897

We are now able to describe graphically the distribution of this categorical variable. brlttbepoetdt$u.wesi)50,an"u Onrhp) apo(al(rjc_aaGnOnrhp/74mi=Gn wesi"

file:///C:/Documents%20and%20Settings/Administrator/Documenti/Courses/Data%20Analysis%20and%20Statistical%20Inference/Lab/Project/Data%20Pro… 2/7

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Data Project Relationship Between Gun Ownership And Ethnicity Groups.html

The overall rate of gun ownership in the sample is roughly 31.8%. However, what we are really interested in is trying to figure out how this variable is related to the grouping variable:“Ethnicity Group”. We can explore this relation through a contingency table.
Contingency Table (Counts) mtbe< tbepoetdt$u.wesi,rjc_aaEhiiyGop yal - al(rjc_aaGnOnrhppoetdt$tnct.ru)

mtbe yal #
#
#
#
#
#
#
#

Ys e N o WieNnHsai BakNnHsai Hsai OhrNnHsai ht o-ipnc lc o-ipnc ipnc te o-ipnc
16
37
14
6
19
7
14
0
21
09
83
2
80
0
28
4

Contingency Table (Proportions) po.al(yal,2 rptbemtbe )

#
#
#
#
#
#
#
#

WieNnHsai BakNnHsai Hsai OhrNnHsai ht o-ipnc lc o-ipnc ipnc te o-ipnc
Ys
e
04322
.071
0166101236
.610 .889
02555
.944
N
o
05678
.928
0833908764
.389 .110
07445
.055

A graphical representation could be very useful in order to fully understand the scope of these data.

file:///C:/Documents%20and%20Settings/Administrator/Documenti/Courses/Data%20Analysis%20and%20Statistical%20Inference/Lab/Project/Data%20Pro… 3/7

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Data Project Relationship Between Gun Ownership And Ethnicity Groups.html

msipo(rptbemtbe 2,a=,mi=Msi Po GnOnrhpb Ehi oacltpo.al(yal, )ls2 an"oac lt u wesi y tnc iyGop) t ru"

Both the tables and the mosaicplot show that the conditional probabilities vary sensibly depending on race and ethnicity group.
The probability of gun ownership in the household given that the sampled respondent is white non-Hispanic is equal to roughly 40.3%.
The probability of gun ownership in the household given that the sampled respondent is black non-Hispanic is equal to roughly 16.7%.
The probability of gun ownership in the household given that the sampled respondent is Hispanic is equal to roughly 18.3%.
The probability of gun ownership in the household given that the sampled respondent belongs to a different ethnicity group from the ones listed is roughly 29.5%.
This suggests that gun ownership in the household and race or ethnicity are most likely dependent. At this stage of the analysis we are still working with the sample data therefore we can not extend the findings of the study to the population at large. However, the large differences between the conditional probabilities observed in the sample can be interpreted as a strong evidence that there is actually a real difference in the population of interest.

Inference:
The ultimate goal of our study is to establish if there is a real relationship between gun ownership in the households of US citizens aged 18 or older and ethnicity groups. We’re going to use the data we collected to verify if the gun ownership rate varies by ethnicity groups. In order to do so we have to perform a file:///C:/Documents%20and%20Settings/Administrator/Documenti/Courses/Data%20Analysis%20and%20Statistical%20Inference/Lab/Project/Data%20Pro… 4/7

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Data Project Relationship Between Gun Ownership And Ethnicity Groups.html

hypothesis test.
HYPOTHESIS TEST (FRAMEWORK)
In a hypothesis test we set 2 hypotheses: the Null Hypothesis and the Alternative Hypothesis. In the context of this study the hypotheses are:
Null Hypothesis: gun ownership in the households of US citizens aged 18 or older and ethnicity groups are independent of each other. Gun ownership rate does not vary by ethnicity group.
Alternative Hypothesis: gun ownership in the households of US citizens aged 18 or older and ethnicity groups are dependent of each other. Gun ownership rate varies by ethnicity group.
We want to test if gun ownership in the households of US citizens aged 18 or older and ethnicity groups are associated at the 5% significance level.
CHI-SQUARE INDEPENDENCE TEST (CONDITIONS)
Since we are evaluating the relationship between 2 categorical variables and one of which has more than 2 levels we are going to use the Chi-Square Independence Test. This test provides significant results if specific conditions are met. For this reason we must first check for them. The conditions are:
1. Indipendence: ANES data consists in a random sample from less than 10% of the population; each case only contributes to one cell in the table. We can assume that the sampled observations are independent. 2. Sample Size: since the overall gun ownership rate is 31.8% and the sample size is large, each particular scenario has more than 5 expected cases.
CHI-SQUARE INDEPENDENCE TEST (TEST STATISTIC & P-VALUE)
The Chi-Square Independence Test evaluates the hypotheses by quantifying how different the observed counts are from the expected counts. Large Deviations from what we would expect provide strong evidence for the Alternative Hypothesis. Calculations for the Chi-Square test statistic are tedious and error-prone, for this reason we are going to make use of computation. ciqts(yal) hs.etmtbe

#
#
# PasnsCisurdts
# ero' h-qae et
#
#
# dt: mtbe
# aa yal # Xsurd=3296,d =3 pvle