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Table 2 Comparison of home team’s data in the seasons before and after the introduction of VAR

From: Does video assistant referee technology change the magnitude and direction of home advantages and referee bias? A proof-of-concept study

Variables a

Descriptive statistics

Independent Samples t-test

TOST results for statistical equivalence

H0: (d ≤ − 0.20 U d ≥ 0.20) vs. H1: (-0.20 < d < 0.20)

NO VAR (n: 918)

VAR (n: 920)

M

SD

M

SD

t

p

ES

BF01 (H0/H1) b

Lower bound

Upper bound

Statistical equivalence

Points

1.65

1.33

1.63

1.31

0.47

0.641

0.02

17.13

Strong

t = -2.79**

t = 3.72 ***

X

Goals

1.58

1.30

1.58

1.28

0.02

0.983

0.00

19.07

Strong

t = -3.31***

t = 3.35 ***

X

Fouls

15.64

4.24

13.36

3.81

12.10

< 0.001

0.56

0.00

-

t = 11.03 ns

t = 13.16 ***

 

Yellow cards

2.18

1.36

2.11

1.37

1.07

0.286

0.05

10.86

Strong

t = -2.08*

t = 4.21 ***

X

Red cards

0.12

0.34

0.12

0.36

0.02

0.987

0.00

19.07

Strong

t = -12.21***

t = 12.24 ***

X

Offsides

2.09

1.61

1.99

1.62

1.37

0.170

0.06

7.51

Substantial

t = -1.28 ns

t = 4.02 ***

 

Penalties

0.20

0.44

0.23

0.49

-1.28

0.199

-0.06

8.41

Substantial

t = -10.52***

t = 7.95 ***

X

  1. a All data presented on a per-match basis
  2. b Computed considering a one-sided null hypothesis
  3. M: Mean, SD: Standard Deviation, ES: Cohen’s d effect size, BF01: Bayes Factor
  4. P-values legend: *p <.05; **p <.01, ***p <.001; ns: not significant (p >.05)