The Pairs Skating competition at the 2002 Winter Olympics in Salt Lake City was contentious. It resulted in the awarding of Gold Medals to both a Russian and a Canadian pair, after the French judge admitted to awarding biased scores. Multidimensionality, differential item functioning, and item bias are all manifestations of disparate subdimensions within the data. In judged competitions, judge behavior can introduce unwanted subdimensions.

 

The data comprise 4 facets: skaters + judges + program + skill → rating

 

For this analysis, each pair is allowed to have a different skill level, i.e., different measure, on each skill of each performance. The judges are modeled to maintain their leniencies across all performances.

 

In this judge-focused analysis: (judges = columns) + (skaters + program + skill = rows) → rating

 

The control file and data are in exam15.txt.

 

; This control file is EXAM15.TXT

Title  = "Pairs Skating: Winter Olympics, SLC 2002"

Item   = Judge

Person = Pair

NI     = 9  ; the judges

Item1  = 14  ; the leading blank of the first rating

Xwide  = 3  ; Observations are 3 CHARACTERS WIDE for convenience

NAME1  = 1  ; start of person identification

NAMELENGTH = 13 ; 13 characters identifiers

 

; CODES NEXT LINE HAS ALL OBSERVED RATING SCORES

CODES= " 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44+

      + 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60"

 

STEPKEEP=YES  ; maintain missing intermediate rating scores in the scoring structure

@order = 1-2  ; order number at finish of competition in person label columns 1-2

DIF = @order  ; judge "DIF" across skating pairs

tfile=*

30   ; produce Table 30 for judge "DIF"

*

&END

1 Rus ;Mrs. Marina SANAIA : RUSSIA

2 Chn ;Mr. Jiasheng YANG : CHINA

3 USA ;Mrs. Lucy BRENNAN : USA

4 Fra ;Miss Marie Reine LE GOUGNE : FRANCE

5 Pol ;Mrs. Anna SIEROCKA : POLAND

6 Can ;Mr. Benoit LAVOIE : CANADA

7 Ukr ;Mr. Vladislav PETUKHOV : UKRAINE

8 Ger ;Mrs. Sissy KRICK : GERMANY

9 Jap ;Mr. Hideo SUGITA : JAPAN

 

; Description of Person Identifiers

; Cols.  Description

; 1-2  Order immediately after competition (@order)

; 4-5  Skaters' initials

; 7-9  Nationality

; 11   Program: S=Short  F=Free

; 13   Skill: T=Technical Merit, A=Artistic Impression

END LABELS

1 BS-Rus S T 58 58 57 58 58 58 58 58 57 ;  1 BEREZHNAYA Elena / SIKHARULIDZE Anton : RUS

1 BS-Rus S A 58 58 58 58 59 58 58 58 58 ;  2 BEREZHNAYA Elena / SIKHARULIDZE Anton : RUS

1 BS-Rus F T 58 58 57 58 57 57 58 58 57 ;  3 BEREZHNAYA Elena / SIKHARULIDZE Anton : RUS

1 BS-Rus F A 59 59 59 59 59 58 59 58 59 ;  4 BEREZHNAYA Elena / SIKHARULIDZE Anton : RUS

2 SP-Can S T 57 57 56 57 58 58 57 58 56 ;  5 SALE Jamie / PELLETIER David : CAN

2 SP-Can S A 58 59 58 58 58 59 58 59 58 ;  6 SALE Jamie / PELLETIER David : CAN

2 SP-Can F T 58 59 58 58 58 59 58 59 58 ;  7 SALE Jamie / PELLETIER David : CAN

2 SP-Can F A 58 58 59 58 58 59 58 59 59 ;  8 SALE Jamie / PELLETIER David : CAN

3 SZ-Chn S T 57 58 56 57 57 57 56 57 56 ;  9 SHEN Xue / ZHAO Hongbo : CHN

.....

 

From this data file, estimate judge severity. In my run this took 738 iterations, because the data are so thin, and the rating scale is so long.

 

Here is some of the output of Table 30, for Judge DIF, i.e., Judge Bias by skater pair order number, @order = $S1W2.

 

+-------------------------------------------------------------------------+

| Pair    DIF   DIF  Pair   DIF   DIF     DIF    JOINT       Judge        |

| CLASS  ADDED  S.E. CLASS  ADDED  S.E. CONTRAST  S.E.   t   Number  Name |

|-------------------------------------------------------------------------|

| 13      -.93   .40 18      1.50   .39    -2.43   .56 -4.35      9 9 Jap |

| 14     -1.08   .36 18      1.50   .39    -2.58   .53 -4.83      9 9 Jap |

+-------------------------------------------------------------------------+

 

The most significant statistical bias is by the Japanese judge on skater pairs 13 and 14 vs. 18. These pairs are low in the final order, and so of little interest.

 

Table 23, the principal components/contrast analysis of Judge residuals is more interesting. Note that Judge 4, the French judge, is at the top with the largest contrast loading. The actual distortion in the measurement framework is small, but crucial to the awarding of the Gold Medal!

 

STANDARDIZED RESIDUAL CONTRAST PLOT

      -1                                0                                1

      ++--------------------------------+--------------------------------++

   .6 +                       4         |                                 +

      |                                 |                                 |

   .5 +                                 | 5      7                        +

C     |                                 |                                 |

O  .4 +                      1          |                                 +

N     |                                 |                                 |

T  .3 +                                 |                                 +

R     |                                 |                                 |

A  .2 +                                 |                                 +

S     |                                 |                                 |

T  .1 +                                 |                                 +

      |                                 |                                 |

1  .0 +---------------------------------|---------------------------------+

      |                  2              |                                 |

L -.1 +                                 |                                 +

O     |                                 |                                 |

A -.2 +                                 |                                 +

D     |                                 |                                 |

I -.3 +                                 |                                 +

N     |                                 |  9                              |

G -.4 +                                 |         8                       +

      |                                 |        6                        |

  -.5 +                                 |  3                              +

      |                                 |                                 |

      ++--------------------------------+--------------------------------++

      -1                                0                                1

Judge MEASURE