A Misuse of Statistical Reasoning: The Statistical Arguments Offered by Texas to the Supreme Court in an Attempt to Overturn the Results of the 2020 Election

Figures & data

Table 1 Z-scores in the four battleground states.

	Biden 2020 versus Clinton 2016		Early versus Late in 2020
	Total votes	Percentage of votes	Percentage for Biden
Georgia	396.3	108.7	1891
Pennsylvania	290.4	90.7	736
Wisconsin	198.5	77	1271
Michigan	333.1	107.4	586

Source: Adapted from Table 2 of the expert’s original declaration.

Table 2 Comparison of the opponents’ percentages of the popular votes in the first and second elections when U.S. Presidents Ran for Reelection.

President	Opponent%	Opponent%	Difference %
	in first	in second
McKinley (1896, 1900)	45.8	45.5	−0.3
Roosevelt (1904, 1912)	37.6	41.8	4.2
Wilson (1912, 1916)	27.4*	46.1	18.7
Hoover (1928,1932)	40.8	57.4	16.6
Roosevelt (1932, 1936)	39.6	36.5	−3.1
Roosevelt (1936, 1940)	36.5	44.8	8.3
Roosevelt (1940, 1944)	44.8	45.9	1.1
Eisenhower (1952, 1956)	44.4	42.0	−2.4
Nixon (1968, 1972)	42.7	37.5	−5.2
Carter (1976, 1980)	48.0	50.7	2.7
Reagan (1980, 1984)	41.0	40.6	−0.4
Bush (1988, 1992)	45.6	43.0	−2.6
Clinton (1992, 1996)	37.4	40.7	3.3
Bush (2000, 2004)	48.4	48.3	−0.1
Obama (2008, 2012)	45.7	47.2	1.5
Trump (2016, 2020)	48.2	51.3	3.1

Source: https://www.presidency.ucsb.edu/statistics/elections/2020. The 1912 election has an * because it was unusual and the difference in the last column is an outlier. There were three main candidates. Wilson won with 41.8% of the vote; T. Roosevelt received 27.4% and Taft received 23.2%.

Table A1 Clinton versus Biden comparison.

	Clinton	Biden		Trump			% Voted for others
State	2016	2020	DiffD	2016	2020	DiffR	2016	2020	DiffO
AK	37.7%	43.0%	$-5.3\%$	52.9%	53.1%	$-0.23\%$	9.4%	3.9%	5.5%
AL	34.6%	36.7%	$-2.1\%$	62.9%	62.2%	0.65%	2.6%	1.1%	1.5%
AR	33.8%	34.8%	$-1.0\%$	60.4%	62.4%	$-1.96\%$	5.8%	2.8%	3.0%
AZ	45.4%	49.4%	$-4.0\%$	49.5%	49.1%	0.42%	5.1%	1.5%	3.6%
CA	61.6%	63.5%	$-1.9\%$	32.8%	34.3%	$-1.57\%$	5.7%	2.2%	3.5%
CO	47.2%	55.4%	$-8.2\%$	44.4%	41.9%	2.52%	8.4%	2.7%	5.7%
CT	54.5%	59.3%	$-4.8\%$	41.2%	39.2%	1.94%	4.4%	1.5%	2.8%
DC	92.8%	92.9%	$-0.1\%$	4.1%	5.5%	$-1.37\%$	3.0%	1.6%	1.5%
DE	53.4%	58.8%	$-5.4\%$	41.9%	39.8%	2.12%	4.7%	1.4%	3.3%
FL	47.8%	47.9%	$-0.1\%$	49.1%	51.2%	$-2.16\%$	3.1%	0.9%	2.2%
GA	45.6%	49.5%	$-3.9\%$	51.3%	49.3%	2.08%	3.1%	1.2%	1.8%
HI	62.3%	63.7%	$-1.4\%$	30.1%	34.3%	$-4.17\%$	7.6%	2.0%	5.6%
IA	42.2%	45.0%	$-2.8\%$	51.8%	53.2%	$-1.44\%$	6.0%	1.8%	4.3%
ID	27.6%	33.1%	$-5.5\%$	59.2%	63.9%	$-4.72\%$	13.3%	3.0%	10.3%
IL	55.4%	57.5%	$-2.1\%$	39.4%	40.6%	$-1.14\%$	5.2%	1.9%	3.3%
IN	37.9%	41.0%	$-3.1\%$	57.2%	57.1%	0.11%	4.9%	2.0%	3.0%
KS	36.2%	41.6%	$-5.4\%$	57.2%	56.2%	1.01%	6.7%	2.2%	4.4%
KY	32.7%	36.1%	$-3.5\%$	62.5%	62.1%	0.46%	4.8%	1.8%	3.0%
LA	38.4%	39.9%	$-1.4\%$	58.1%	58.5%	$-0.37\%$	3.5%	1.7%	1.8%
MA	60.8%	65.9%	$-5.1\%$	33.5%	32.2%	1.27%	5.7%	1.8%	3.9%
MD	60.5%	65.8%	$-5.3\%$	35.3%	32.4%	2.94%	4.2%	1.8%	2.3%
ME	47.9%	53.1%	$-5.3\%$	45.2%	44.0%	1.14%	7.0%	2.9%	4.1%
MI	47.3%	50.6%	$-3.3\%$	47.6%	47.8%	$-0.26\%$	5.1%	1.5%	3.5%
MN	46.9%	52.6%	$-5.7\%$	45.4%	45.4%	$-0.07\%$	7.8%	2.0%	5.8%
MO	38.0%	41.4%	$-3.4\%$	57.1%	56.8%	0.37%	4.8%	1.8%	3.1%
MS	39.7%	41.1%	$-1.3\%$	58.3%	57.6%	0.74%	1.9%	1.3%	0.6%
MT	36.0%	40.6%	$-4.7\%$	56.5%	56.8%	$-0.33\%$	7.5%	2.5%	5.0%
NC	46.7%	48.7%	$-2.0\%$	50.5%	50.1%	0.48%	2.8%	1.2%	1.5%
ND	27.8%	31.9%	$-4.2\%$	64.1%	65.4%	$-1.27\%$	8.1%	2.6%	5.5%
NE	34.0%	39.4%	$-5.4\%$	60.3%	58.5%	1.82%	5.7%	2.1%	3.6%
NH	47.6%	52.9%	$-5.3\%$	47.2%	45.5%	1.73%	5.2%	1.6%	3.5%
NJ	55.0%	57.3%	$-2.3\%$	41.8%	41.4%	0.39%	3.2%	1.3%	1.9%
NM	48.3%	54.2%	$-6.0\%$	40.0%	43.5%	$-3.50\%$	11.7%	2.2%	9.5%
NV	47.9%	50.1%	$-2.2\%$	45.5%	47.7%	$-2.13\%$	6.6%	2.3%	4.3%
NY	58.8%	60.9%	$-2.1\%$	37.5%	37.7%	$-0.27\%$	3.7%	1.3%	2.4%
OH	43.5%	45.3%	$-1.7\%$	52.1%	53.3%	$-1.24\%$	4.4%	1.5%	3.0%
OK	28.9%	32.3%	$-3.4\%$	65.3%	65.4%	$-0.05\%$	5.7%	2.3%	3.4%
OR	51.7%	56.9%	$-5.2\%$	41.1%	40.7%	0.40%	7.3%	2.5%	4.8%
PA	47.6%	50.0%	$-2.4\%$	48.8%	48.8%	$-0.05\%$	3.6%	1.1%	2.4%
RI	55.4%	59.6%	$-4.2\%$	39.8%	38.9%	0.89%	4.8%	1.5%	3.3%
SC	40.8%	43.4%	$-2.7\%$	54.9%	55.1%	$-0.23\%$	4.4%	1.5%	2.9%
SD	31.7%	35.6%	$-3.9\%$	61.5%	61.8%	$-0.24\%$	6.7%	2.6%	4.1%
TN	34.9%	37.5%	$-2.6\%$	61.1%	60.7%	0.39%	4.0%	1.9%	2.2%
TX	43.4%	46.5%	$-3.1\%$	52.6%	52.1%	0.50%	4.0%	1.4%	2.6%
UT	27.8%	37.6%	$-9.8\%$	45.9%	58.1%	$-12.2\%$	26.3%	4.3%	21.9%
VA	49.9%	54.3%	$-4.5\%$	45.0%	44.2%	0.84%	5.1%	1.5%	3.6%
VT	61.1%	66.4%	$-5.3\%$	32.6%	30.8%	1.78%	6.2%	2.7%	3.5%
WA	54.4%	58.2%	$-3.8\%$	38.2%	38.9%	$-0.76\%$	7.4%	2.8%	4.5%
WI	46.9%	49.6%	$-2.6\%$	47.9%	48.9%	$-1.08\%$	5.2%	1.5%	3.7%
WV	26.5%	29.7%	$-3.2\%$	68.7%	68.6%	0.02%	4.9%	1.7%	3.2%
WY	22.5%	26.7%	$-4.2\%$	70.1%	70.4%	$-0.33\%$	7.5%	2.9%	4.6%

Source: https://www.270towin.com/2020-election-results-live/state/ and https://www.politico.com/2016-election/results/map/president/.

Table A2 Voter Turnout rates for 2020 and 2016.

State	2016	2020	Diff
United State	59.2%	66.7%	$-7.5\%$
AK	61.0%	68.8%	$-7.8\%$
AL	58.8%	63.1%	$-4.3\%$
AR	52.8%	56.1%	$-3.3\%$
AZ	54.9%	65.9%	$-11.0\%$
CA	56.5%	68.5%	$-12.0\%$
CO	70.0%	76.4%	$-6.4\%$
CT	63.7%	71.5%	$-7.8\%$
DC	60.4%	64.1%	$-3.7\%$
DE	64.2%	70.7%	$-6.5\%$
FL	64.5%	71.7%	$-7.2\%$
GA	59.1%	67.7%	$-8.6\%$
HI	42.3%	57.5%	$-15.2\%$
IA	68.4%	73.2%	$-4.8\%$
ID	59.2%	68.0%	$-8.8\%$
IL	62.2%	67.0%	$-4.8\%$
IN	56.4%	61.4%	$-5.0\%$
KS	57.7%	65.9%	$-8.2\%$
KY	58.6%	64.9%	$-6.3\%$
LA	60.0%	64.6%	$-4.6\%$
MA	67.2%	72.1%	$-4.9\%$
MD	66.4%	71.1%	$-4.7\%$
ME	70.7%	76.3%	$-5.6\%$
MI	64.7%	73.9%	$-9.2\%$
MN	74.1%	80.0%	$-5.9\%$
MO	62.2%	65.7%	$-3.5\%$
MS	55.2%	60.2%	$-5.0\%$
MT	61.8%	73.1%	$-11.3\%$
NC	64.5%	71.5%	$-7.0\%$
ND	60.8%	64.5%	$-3.7\%$
NE	62.8%	69.9%	$-7.1\%$
NH	71.4%	75.5%	$-4.1\%$
NJ	64.4%	75.3%	$-10.9\%$
NM	54.4%	61.3%	$-6.9\%$
NV	57.4%	65.4%	$-8.0\%$
NY	56.8%	63.4%	$-6.6\%$
OH	62.9%	67.4%	$-4.5\%$
OK	52.3%	55.0%	$-2.7\%$
OR	66.2%	75.5%	$-9.3\%$
PA	63.6%	71.0%	$-7.4\%$
RI	59.1%	65.7%	$-6.6\%$
SC	56.7%	64.5%	$-7.8\%$
SD	58.6%	66.0%	$-7.4\%$
TN	51.1%	59.8%	$-8.7\%$
TX	51.4%	60.4%	$-9.0\%$
UT	56.8%	69.2%	$-12.4\%$
VA	66.1%	73.0%	$-6.9\%$
VT	63.7%	74.2%	$-10.5\%$
WA	64.7%	75.7%	$-11.0\%$
WI	69.5%	75.8%	$-6.3\%$
WV	50.2%	57.6%	$-7.4\%$
WY	59.5%	64.6%	$-5.1\%$

Source: http://www.electproject.org/2016g and http://www.electproject.org/2020g.

Table 3 Georgia votes by type of vote in 2020.

Candidate	Biden	Trump
Total votes (%)	2,474,507 (49.51%)	2,461,837 (49.25%)
Election day	367,205	587,697
Absentee by mail	849,729	451,157
Advanced voting	1,250,509	1,419,161
Provisional	7064	3822

Source: Election results by vote type. The website of the Secretary of State, https://results.enr.clarityelections.com/GA/105369/web.264614/#/detail/5000.

Table A3 Early ballots for 2020 and 2016.

State	2020	2016	2020/2016
Kentucky	1,615,236	126,008	1281.9%
New Jersey	3,658,459	355,771	1028.3%
New York	3,743,745	400,660	934.4%
Pennsylvania	2,504,518	288,996	866.6%
Rhode Island	304,923	41,642	732.2%
Delaware	156,259	(n/a)	627.4%
Virginia	2,744,038	562,547	487.8%
Connecticut	636,000	133,247	477.3%
Alabama	300,402	(n/a)	350.7%
New Hampshire	235,834	75,305	313.2%
Missouri	827,978	287,951	287.5%
Minnesota	1,846,668	683,813	270.1%
South Carolina	1,323,691	503,928	262.7%
Vermont	245,097	95,203	257.4%
Idaho	497,869	202,732	245.6%
Michigan	3,111,414	1,277,405	243.6%
Wisconsin	1,924,838	825,620	233.1%
District of Columbia	282,722	121,858	232.0%
Maryland	2,355,129	1,054,189	223.4%
Hawaii	526,225	237,207	221.8%
Nebraska	510,075	233,052	218.9%
Mississippi	231,031	107,027	215.9%
Illinois	3,798,286	1,817,625	209.0%
South Dakota	216,140	106,415	203.1%
North Dakota	271,960	134,741	201.8%
Massachusetts	2,352,945	1,194,038	197.1%
Maine	508,910	258,370	197.0%
Indiana	1,828,170	952,981	191.8%
Louisiana	985,390	531,555	185.4%
Ohio	3,411,463	1,890,069	180.5%
West Virginia	394,509	223,942	176.2%
Oklahoma	447,051	258,518	172.9%
Wyoming	131,516	80,579	163.2%
Montana	549,832	337,926	162.7%
Georgia	3,957,889	2,438,644	162.3%
Alaska	161,217	102,179	157.8%
Iowa	996,970	647,152	154.1%
Kansas	770,324	520,042	148.1%
Texas	9,693,079	6,564,197	147.7%
New Mexico	777,265	533,215	145.8%
Utah	1,124,206	772,888	145.5%
North Carolina	4,578,269	3,147,210	145.5%
Nevada	1,122,970	780,959	143.8%
California	12,090,543	8,511,992	142.0%
Arkansas	922,661	(n/a)	139.4%
Florida	9,069,761	6,637,731	136.6%
Tennessee	2,280,767	1,690,574	134.9%
Arizona	2,671,783	2,012,841	132.7%
Washington	3,545,289	3,363,452	105.4%
Oregon	2,155,350	2,051,452	105.1%
Colorado	2,893,395	2,855,960	101.3%

Source: https://data.news-leader.com/early-voting-turnout/pennsylvania/. Last accessed in February, 2021.