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Table 3 Comparison of away 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

1.11

1.28

1.11

1.25

0.08

0.938

0.00

19.02

Strong

t = -3.31***

t = 3.47 ***

X

Goals

1.21

1.17

1.19

1.12

0.42

0.678

0.02

17.51

Strong

t = -3.33***

t = 4.16 ***

X

Fouls

15.63

4.41

12.80

3.75

14.82

< 0.001

0.69

0.00

-

t = 13.77 ns

t = 15.87 ***

 

Yellow cards

2.35

1.40

2.25

1.39

1.53

0.125

0.07

5.95

Substantial

t = -1.54 ns

t = 4.61 ***

 

Red cards

0.15

0.42

0.15

0.039

0.13

0.895

0.01

18.91

Strong

t = -10.44***

t = 10.71 ***

X

Offsides

1.92

1.67

1.86

1.52

0.81

0.415

0.04

13.72

Strong

t = -1.87*

t = 3.50 ***

X

Penalties

0.14

0.36

0.17

0.40

-1.45

0.147

-0.07

6.73

Substantial

t = -12.69***

t = 9.79 ***

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)