Statistics Assignment deadline ASAP

Assignment 4: Bivariate statistics

To be submitted electronically

Quantitative methods for conflict studies and human rights, ECH3360

1. Amartya Sen famously wrote that “No famine has ever taken place in the history of the world in a func- tioning democracy”.1 In this exercise you will undertake to examine the link between democracy and child malnutrition, to shed empirical light on Sen’s statement. The file democracy underweight.csv provides data at the country level on two variables: (1) the proportion of underweight children 0-5 years old in each country. This variable is divided into three categories: Low: 0 to 14% of children in the country are underweight; Medium: 14 to 28% of children underweight; High: 28 to 42% of children underweight,2 and (2) whether the country is a democracy (TRUE/FALSE).3

(a) Make a cross-tabulation that shows the number of countries that take on each level for the two variables (i.e., how many countries are highly democratic and have a medium proportion of mal- nourished children, etc.). (Hint: the table should columns and rows with one variable (democracy, malnutrition) in each – see below. You may find Excel’s PivotTable function useful.) Make sure your table is well-labeled and clear.

Democracy Malnutrition True False Low - - Med - - High - -

Figure 1: Example of a cross-tabulation

(b) Conduct a χ2 test to test whether there is a relationship between democracy and child malnutri- tion. Show your calculations. Interpret the findings.

(c) Does this provide evidence that democracy causes improvements children’s nutrition? Use the ”four hurdles” framework from Kellstedt and Whitten to structure your answer.

2. In a recent study, Banerjee et al. (2015) provide evidence from a randomized controlled trial on how a multifaceted program can help to improve the lives of the very poor.4 The file banerjee data.csv includes the data for one country analyzed by Banerjee - Ethiopia. The variable id is a unique identifier number for each household. The variable treatment indicates whether the household was provided an income support program (1) or not (0). Because this was a randomized controlled trial, the treatment status of the household was randomly assigned by Banerjee et al. (2015) as part of the experiment. The variables foodsecurity bsl and foodsecurity end are indices that measures five components of food security.5 The food security indices are numeric, and are constructed so that a score of 0 indicates a household is at the mean food security level for all the households included in the sample, a positive score indicates the household is more food secure than the mean household in the sample, and vice-versa for a negative score. The suffix bsl refers to the measure of food security before the program was implemented, and the suffix end refers to the same measure 3 years after the program was started.

1Sen, Amartya, 1999, Democracy as Freedom, Knopf. 2Data come from the World Bank. 3Data come from the PolityIV database. A country is considered a democracy if it’s democracy score in the Polity database

is greater than or equal to 8 out of 10. 4Banerjee, Abhijit, et al. “A multifaceted program causes lasting progress for the very poor: Evidence from six countries.”

Science 348.6236 (2015): 1260799. The program provides selected very poor households with a productive asset (usually goats), weekly income support for a few months to a year, training, and a savings account.

5The food security indices are measured based on answers to several questions: (1) Everyone gets enough food every day, (2) no adult skips meal, (3) no one went a whole day without food, (4) no child skipped meal, (5) everyone regularly eats two meals a day.

1

(a) Before the program was initiated, was there any difference in mean food security between house- holds that were eventually to receive the treatment compared to those that did not? Is the difference statistically significant (i.e., are you at least 95% sure there’s a difference)? Why do you think this is?

(b) Is the program associated with a change in mean food security for treated households relative to untreated households (to determine the change in security, subtract the baseline value from the endline value)? How big was it? How confident are you that the program is associated with a change in food security?

(c) Does this provide evidence that the program caused a change in food security for treated house- holds?

3. Pfizer and BioNTech announced the results of Phase III trials of their experimental COVID-19 vaccine in November 2020. 43,000 participants were randomly divided into two equal groups, with half given a placebo and half given a vaccine. 162 of the participants in the placebo group became sick, and 8 participants in the treatment group. How confident can we be that the vaccine is effective (i.e., that it reduces sickness relative to the placebo group)? Data to answer this question is in covid vaccine.csv.

2

banerjee_data.csv

id	treatment	index_foodsecurity_bsl	index_foodsecurity_end
11001	1	-0.38842574	0.7090705
11002	0	-1.7528449	-2.2018483
11003	1	-1.0291989	0.7090705
11004	1	0.17005141	0.7090705
11005	1	0.74893624	0.7090705
11006	1	1.3448595	0.7090705
11007	0	-1.0291989	-0.4520842
11008	1	-0.38842574	0.7090705
11009	0	1.3448595	-0.27394557
11010	1	-0.38842574	-1.2188321
11011	0	0.74893624	0.7090705
11012	1	-0.5535947	0.7090705
11013	1	1.3448595	0.7090705
11014	1	-1.7528449	-2.5894449
11015	0	-0.38842574	-0.4520842
11016	1	1.3448595	0.7090705
11017	0	-1.7528449	-0.4520842
11018	1	0.74893624	0.7090705
11019	1	0.17005141	-0.4520842
11020	0	-1.0291989	-3.1730053
11022	0	-1.7528449	0.7090705
11023	1	0.19045909	0.7090705
11024	0	-1.0291989	-1.2188321
11025	1	-1.0291989	0.7090705
11026	1	0.025290107	0.7090705
11027	0	-1.7528449	-1.2188321
11028	1	-0.38842574	0.7090705
11029	0	-0.38842574	0.7090705
11030	0	-1.0291989	0.1255101
11031	0	-0.38842574	0.7090705
11032	1	-0.38842574	0.7090705
11033	0	-1.7528449	-2.2018483
11034	1	0.74893624	0.7090705
11035	0	1.3448595	-0.4520842
11036	0	0.76597464	-0.4520842
11037	1	-1.0291989	-2.2018483
11039	1	-1.1943679	-0.4520842
11040	1	-0.4707217	0.7090705
11041	1	-0.38842574	0.7090705
11042	1	-0.4707217	0.7090705
11043	0	-0.4707217	0.7090705
11045	0	1.3448595	-0.26208645
11046	0	-0.38842574	-1.2188321
11047	1	-1.0291989	0.13147624
11048	1	0.76597464	-0.4520842
11049	0	-0.38842574	-0.4520842
11051	1	0.20749749	0.7090705
11052	1	-0.38842574	0.7090705
11053	1	0.7863823	0.7090705
11054	0	0.7863823	-1.2188321
11055	1	0.17005141	0.7090705
11056	1	-1.0291989	-0.26208645
11057	1	1.3448595	-0.4520842
11058	0	-1.0291989	0.7090705
11059	1	-1.1120719	0.7090705
11060	0	0.17005141	0.7090705
11061	0	-0.4707217	0.7090705
11062	0	-1.7528449	0.7090705
11063	1	-1.0291989	0.7090705
11064	0	0.74893624	-1.4351003
11065	0	-1.0291989	-1.8226968
11066	1	-0.4707217	-0.4520842
11067	0	-1.1120719	0.7090705
11068	1	1.3448595	0.7090705
11069	1	1.3448595	0.7090705
11070	1	0.74893624	-0.4520842
11071	1	-0.38842574	0.13147624
11073	0	-1.0291989	-2.2018483
11074	1	-1.0291989	-0.4520842
11075	1	-1.7528449	0.7090705
11077	0	0.74893624	0.7090705
11078	0	-1.7528449	0.1255101
11079	0	0.19045909	-0.4520842
11081	1	1.3448595	0.7090705
11082	0	-0.38842574	0.7090705
11083	0	-0.38842574	-1.2188321
11084	0	1.3448595	-1.2188321
11085	1	1.3448595	-0.4520842
11086	1	0.74893624	0.7090705
11087	0	-1.0291989	-0.4520842
11088	1	-1.0291989	0.7090705
11089	0	-1.7528449	-1.6182878
11090	0	0.7863823	0.7090705
11091	1	-0.38842574	0.7090705
11092	1	-0.4707217	0.7090705
11093	1	1.3448595	0.7090705
11094	0	0.20749749	0.1255101
11095	0	-0.38842574	0.7090705
11096	0	0.17005141	-1.4232411
11097	0	-1.0291989	0.7090705
11098	0	-1.0291989	-0.4520842
11099	0	0.76597464	0.7090705
11100	0	1.3448595	0.7090705
11101	0	-1.0291989	-0.4520842
11102	0	0.74893624	0.13147624
11103	0	1.3448595	-0.6352717
11105	1	-1.7528449	-1.4351003
11106	1	0.74893624	0.7090705
11107	0	-1.1120719	-0.4520842
11108	1	1.3448595	-0.4520842
11109	1	0.19045909	-2.189989
11110	1	-1.0291989	0.7090705
11111	1	1.3448595	-2.189989
11112	1	1.3448595	-0.4520842
11113	0	-1.0291989	0.7090705
11114	0	1.3448595	0.7090705
11115	0	-0.38842574	-1.2188321
11116	0	-1.7528449	-2.2018483
11118	1	-1.1120719	-0.26208645
11119	1	-1.0291989	0.13147624
11120	1	0.74893624	0.7090705
11121	1	-1.1120719	0.7090705
11122	0	1.3448595	-0.4520842
11123	1	-1.0291989	-3.1730053
11124	0	0.76597464	0.7090705
11126	1	0.12520152	-2.4062574
11127	1	-1.1943679	0.7090705
11128	1	0.74893624	0.7090705
11129	0	-1.7528449	-1.2188321
11130	0	1.3448595	-0.4520842
11131	1	-0.38842574	0.7090705
11132	1	0.20749749	0.1255101
11133	0	-0.38842574	-3.1730053
11134	0	0.20749749	-0.4520842
11135	1	-0.38842574	0.7090705
11137	0	0.20749749	0.7090705
11138	0	-0.38842574	-1.4232411
11139	1	1.3448595	-0.4520842
11140	0	0.19045909	0.7090705
11143	0	1.3448595	0.7090705
11144	0	-0.38842574	-2.2018483
11145	0	0.74893624	0.7090705
11146	0	1.3448595	0.7090705
11147	1	1.3448595	0.7090705
11149	0	1.3448595	-1.2188321
11150	0	0.74893624	-1.2188321
11151	0	0.19045909	-0.4520842
11152	0	0.6212133	0.7090705
11153	0	1.3448595	0.7090705
11154	1	1.3448595	0.7090705
11155	1	1.3448595	0.13147624
11156	1	-1.7528449	-1.4351003
11157	1	1.3448595	-1.4351003
11158	1	0.17005141	-0.4520842
11159	1	-1.0291989	-1.2188321
11160	0	0.17005141	0.7090705
11161	0	1.3448595	0.13147624
11162	1	-0.38842574	-0.4520842
11163	0	-0.38842574	0.7090705
11164	0	0.17005141	0.7090705
11165	1	-0.38842574	0.7090705
11166	0	1.3448595	0.7090705
11167	0	-0.5535947	-1.4232411
11168	0	0.74893624	0.7090705
11169	0	1.3448595	0.7090705
11170	1	-1.0291989	-1.4351003
11172	1	-1.1120719	0.7090705
11173	1	1.3448595	0.7090705
11174	0	-0.4707217	-0.8396808
11175	1	-0.4707217	0.7090705
11176	0	-1.1943679	0.1255101
11177	0	-0.38842574	-1.4351003
11178	1	1.3448595	-0.4520842
11179	1	-1.7528449	0.13147624
11180	1	0.76597464	0.7090705
11181	0	1.3448595	0.13147624
11182	0	1.3448595	-0.4520842
11183	0	-0.38842574	0.62410754
11184	0	1.3448595	0.7090705
11186	1	-0.38842574	0.7090705
11187	0	-0.38842574	-2.2018483
11188	1	-0.38842574	-2.2018483
11189	1	0.10816312	0.13147624
11190	1	-1.0291989	-2.189989
11191	0	-0.38842574	-0.4520842
11192	0	0.7040863	0.7090705
11193	0	-1.7528449	0.7090705
11194	0	1.3448595	0.7090705
11195	0	1.3448595	-1.4351003
11196	1	-0.38842574	0.13147624
11197	1	-0.38842574	0.13147624
11198	0	-1.1120719	-1.2188321
11199	1	0.76597464	0.7090705
11200	1	-1.7528449	-0.4520842
11201	0	-0.38842574	-1.4351003
11202	0	1.3448595	0.7090705
11203	1	1.3448595	0.7090705
11204	0	1.3448595	0.7090705
11205	0	-0.38842574	0.1255101
11206	1	1.3448595	0.7090705
11207	1	0.0423285	0.7090705
11208	1	-1.0291989	-0.26208645
11209	1	-0.38842574	0.7090705
11210	0	-1.0291989	0.7090705
11211	0	0.17005141	0.7090705
11212	1	-1.0291989	0.7090705
11213	1	1.3448595	-0.4520842
11214	0	-0.38842574	0.7090705
11215	1	-1.0291989	-3.1730053
11216	1	-0.38842574	-0.4520842
11217	1	-1.7528449	0.7090705
11218	1	-0.38842574	0.7090705
11219	1	-1.0291989	0.7090705
11220	1	0.17005141	-3.1730053
11221	1	1.3448595	-1.2188321
11222	0	0.76597464	-0.4520842
11223	0	-1.0291989	-1.2188321
11224	1	0.20749749	0.7090705
11225	0	-0.43327564	-0.4520842
11226	1	-0.38842574	-1.2188321
11227	1	1.3448595	0.7090705
11228	1	0.74893624	0.7090705
11229	1	-0.38842574	0.7090705
11230	0	0.17005141	0.7090705
11231	1	-1.1120719	0.7090705
11232	1	1.3448595	0.7090705
11233	1	-0.38842574	0.7090705
11234	1	0.20749749	-0.4520842
11235	1	-0.38842574	0.7090705
11236	1	0.74893624	-1.2188321
11237	1	1.3448595	0.7090705
11238	1	0.17005141	0.7090705
11239	1	1.3448595	0.7090705
11240	0	-0.38842574	-1.2188321
11241	0	-0.38842574	-0.4520842
11242	0	-1.0291989	-3.1730053
11243	1	1.3448595	-0.4520842
11244	1	1.3448595	-0.4520842
11245	0	1.3448595	0.7090705
11246	1	-1.1120719	0.7090705
11247	1	0.17005141	0.13147624
11248	0	-0.38842574	-0.4520842
11249	1	0.74893624	0.7090705
11250	0	0.17005141	0.7090705
11251	0	1.3448595	-0.4520842
11252	1	1.3448595	0.7090705
11253	0	0.17005141	-0.4520842
11254	0	-0.4707217	-0.4520842
11255	0	1.3448595	0.7090705
11256	1	-1.1120719	0.1255101
11257	1	1.3448595	-0.4520842
11258	1	1.3448595	-0.4520842
11259	1	1.3448595	-1.839049
11260	1	-0.4707217	0.7090705
11261	0	-1.7528449	0.7090705
11262	0	1.3448595	0.7090705
11263	0	-0.38842574	0.7090705
11264	0	-0.5331871	-0.6352717
11265	1	-1.0291989	-1.4351003
11266	0	1.3448595	0.7090705
11267	1	-0.38842574	0.7090705
11268	0	-1.0291989	-1.2188321
11269	0	-1.0291989	-1.2188321
11270	0	1.3448595	0.7090705
11271	0	0.74893624	-1.4351003
11272	0	-0.38842574	0.7090705
11273	0	-0.5331871	0.7090705
11274	1	1.3448595	0.7090705
11275	0	1.3448595	0.7090705
11277	1	1.3448595	0.7090705
11278	1	-1.7528449	-0.4520842
11279	0	-1.7528449	-1.4351003
11280	1	1.3448595	0.7090705
11281	0	-1.0291989	0.7090705
11282	0	-1.0291989	0.1255101
11283	0	0.20749749	0.7090705
11284	0	-1.7528449	-2.189989
11285	0	-0.38842574	0.13147624
11286	0	-0.38842574	0.7090705
11287	0	-0.38842574	-2.189989
11288	0	-1.0291989	0.7090705
11289	1	-0.38842574	0.7090705
11290	0	1.3448595	-1.2188321
11291	1	1.3448595	0.1255101
11292	1	-1.0291989	0.7090705
11293	1	-1.7528449	0.7090705
11294	0	0.17005141	-0.26208645
11295	1	1.3448595	0.7090705
11296	0	1.3448595	0.7090705
11297	0	0.20749749	0.7090705
11298	0	1.3448595	-0.4520842
11299	0	1.3448595	0.7090705
11300	0	-1.7528449	0.7090705
11302	1	-0.38842574	0.7090705
11306	1	1.3448595	0.13147624
11314	0	-1.1120719	0.7090705
11315	0	-0.38842574	0.7090705
11316	0	0.17005141	0.7090705
11317	0	0.17005141	0.7090705
11319	1	1.3448595	0.7090705
11321	1	0.7863823	0.7090705
11322	0	0.74893624	-0.4520842
11325	0	1.3448595	0.7090705
11328	0	-0.4707217	0.7090705
11329	0	-0.38842574	-0.8396808
11331	0	0.7863823	0.7090705
11332	0	0.7040863	0.7090705
11333	1	1.3448595	0.7090705
11336	0	1.3448595	0.7090705
11338	0	0.025290107	0.7090705
11339	0	-1.7528449	0.7090705
11340	0	0.17005141	0.7090705
11342	0	1.3448595	0.1255101
11344	1	-1.0291989	0.7090705
11346	1	1.3448595	-0.26208645
11347	0	1.3448595	-0.26208645
11348	0	0.17005141	-1.2188321
11349	1	-1.1120719	0.7090705
11351	0	1.3448595	0.7090705
11352	0	0.76597464	-0.4520842
11353	1	-0.38842574	0.7090705
11355	0	-1.1943679	-3.1730053
11356	1	-0.5161486	0.7090705
11357	0	-1.1943679	-0.4520842
11358	1	1.3448595	-0.4520842
11359	0	-1.1120719	0.7090705
11360	1	-0.38842574	-1.4351003
11361	1	-0.38842574	0.7090705
11362	1	-1.7528449	0.7090705
11364	0	1.3448595	-0.4520842
11365	1	-1.0291989	0.7090705
11371	1	-0.38842574	-2.4062574
11372	1	-1.1120719	0.7090705
11373	1	0.17005141	0.13147624
11374	0	0.17005141	0.7090705
11375	0	-1.1120719	0.13147624
11376	0	-0.38842574	-1.2188321
11378	1	0.20749749	-1.4232411
11379	1	-0.38842574	-1.839049
11382	0	0.17005141	-0.26208645
11383	1	-0.38842574	0.13147624
11384	0	0.17005141	0.13147624
11385	0	1.3448595	0.13147624
11387	1	1.3448595	0.7090705
11388	1	0.17005141	-0.8396808
11391	1	-1.7528449	0.7090705
11392	1	0.17005141	0.7090705
11393	0	-0.5535947	0.7090705
11394	1	-1.0291989	0.7090705
11395	1	1.3448595	0.7090705
11397	1	-1.0291989	0.7090705
11398	0	1.3448595	-1.2188321
11399	0	-0.38842574	-2.2018483
11400	1	-0.5535947	0.13147624
11401	0	1.3448595	-0.4520842
11402	1	-1.7528449	-1.2188321
11403	0	-1.7528449	0.7090705
11404	0	1.3448595	0.7090705
11405	1	-1.7528449	-1.2188321
11406	1	-0.43327564	0.7090705
11407	0	-0.38842574	-3.1730053
11408	0	1.3448595	-1.2188321
11409	1	-1.1120719	0.7090705
11410	0	0.20749749	-1.2188321
11411	1	1.3448595	0.7090705
11412	0	1.3448595	0.7090705
11413	1	0.20749749	0.7090705
11414	0	1.3448595	0.7090705
11415	0	-1.1120719	0.7090705
11416	1	-1.0291989	-0.4520842
11417	0	1.3448595	0.7090705
11418	1	-0.45031404	-0.4520842
11419	0	0.12520152	0.7090705
11420	1	-1.1739601	0.7090705
11421	0	-0.38842574	-1.839049
11422	1	-0.38842574	0.7090705
11423	0	0.7863823	0.7090705
11424	1	0.76597464	-0.4520842
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11901	1	-0.38842574	0.7090705
11902	1	1.3448595	0.7090705
11904	1	1.3448595	0.7090705
11905	1	0.74893624	-1.2188321
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11908	0	0.17005141	0.7090705
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11910	1	-0.38842574	0.7090705
11911	1	1.3448595	0.7090705
11912	1	1.3448595	0.7090705
11913	0	-0.38842574	0.7090705
11914	1	1.3448595	0.7090705
11915	1	0.19045909	0.7090705
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11920	1	0.19045909	0.7090705
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11922	1	-1.0291989	-0.4520842
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11924	0	0.17005141	-0.27394557
11925	0	0.17005141	0.7090705
11926	1	-1.0291989	-0.4520842
11927	1	0.17005141	0.1255101
11928	0	1.3448595	-0.4520842
11929	1	-0.4707217	0.7090705
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11938	0	0.7863823	-0.4520842
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11945	0	1.3448595	0.7090705
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11947	1	1.3448595	-0.8456469
11948	0	1.3448595	0.7090705
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11962	0	1.3448595	0.7090705
11963	0	1.3448595	0.7090705
11964	1	1.3448595	0.7090705
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11966	1	0.20749749	0.7090705
11967	1	1.3448595	0.7090705
11968	0	-1.0291989	0.7090705
11969	1	0.17005141	0.7090705
11970	0	0.19045909	0.7090705
11971	1	1.3448595	-1.2188321
11972	0	1.3448595	0.7090705
11973	0	0.12520152	-2.2018483
11974	1	1.3448595	0.7090705
11975	0	1.3448595	0.7090705
11977	1	-0.38842574	-1.2188321
11978	1	0.74893624	-1.2188321
11979	1	-0.38842574	0.7090705
11980	1	-1.0291989	0.7090705
11981	0	1.3448595	0.7090705
11982	1	0.17005141	0.7090705
11983	0	-1.0291989	-0.4520842
11984	0	1.3448595	0.7090705
11985	0	0.19045909	0.7090705
11986	1	-0.38842574	0.7090705
11987	0	1.3448595	0.7090705
11988	1	1.3448595	0.7090705
11989	1	-0.38842574	0.7090705
11990	0	1.3448595	0.7090705
11991	0	-0.38842574	-0.4520842
11992	0	-0.38842574	0.7090705
11993	1	0.17005141	0.7090705
11995	1	-0.38842574	0.7090705
11996	0	0.74893624	0.7090705
11997	1	0.17005141	-0.4520842
11998	1	-0.38842574	0.7090705
11999	0	1.3448595	0.7090705
12000	0	0.19045909	0.7090705
12001	0	1.3448595	0.7090705
12002	1	-0.38842574	-0.4520842