Investigating The Difference in Olympic Figure Skating Scores Throughout the Years

ANOVA
Post Hoc Comparisons
Using ANOVA to explore differences in mean scores throughout the years of Winter Olympic Figure Skating
Authors
Affiliation

Faith Rhinehart

St. Lawrence University

Jessica Chapman

St. Lawrence University

Ivan Ramler

St. Lawrence University

Published

June 27, 2025

Source: https://www.nytimes.com/interactive/2022/02/10/sports/olympics/nathan-chen-jumps.html

Background to Figure Skating Video

If you are unfamiliar with Figure Skating Scoring, please watch this video:

Introduction to Module

Figure skating is a sport where athletes perform choreographed routines on ice to music, combining athletic skill with artistic expression. Skaters compete in different categories like men’s singles, women’s singles, pairs (a man and a woman skating together), and ice dance (which focuses more on rhythm and movement). Each skater or team performs two routines: the short program and the free skate. The short program is a shorter routine with a list of required moves that every skater must include. Judges rate how well each move is done and how smoothly everything fits with the music. The free skate routine is longer and gives skaters more freedom to show their personal style and creativity. They still need to include certain types of moves, but they can choose how to put them together. Judges give scores for both routines based on how difficult the moves are, how well they’re done, and how artistic the performance is. The scores from both routines are added together, and the skater or team with the highest total wins.

The MensFigureSkating dataset features data from male skaters in the winter Olympics since 2006. Variables include characteristics such as Name, Nation, Year. Other variables included the 3 types of scoring: Free Skate, Short Program, and Total Points. The relevant variables for this specific module are Total Points and Year.

For the sake of this module, the data set was tidied so that it excluded any skater who did not advance to the Free Skate round.

Learning Objectives:

  1. Students will learn when and how to use One-Way ANOVA

  2. Students will learn how to perform a pair wise comparison such as Post Hoc Tukey Test

  3. Students will gain a further understanding of interpreting graphs and outputs

Intended as a reinforcement module, students should be exposed to ANOVA prior to the module. In particular, students are expected to have been exposed to the concept of hypothesis forming, rejecting hypothesis, confidence intervals and interpreting output. Students are also expected to now how to construct basic plots, fit ANOVA models, and use software (such as R or Minita) to produce said results.

This activity would be suitable for an in-class activity or as an out-of-class assignment taking approximately one class period.

For this activity, students will need to a statistical software capable of producing ANOVA output with Tukey’s HSD. Materials are provided both for using R as well as a a handout that is software agnostic.

Data

The MensFigureSkating.csv data contains scores from skaters in the Winter Olympics since 2006.

Download data: MensFigureSkating.csv

Variable Descriptions
Variable Description
Rank Rank of the skater
Name Name of the skater
Nation Country skater represents
TP Total points scored (SP + FS)
SP Short Program score
FS Free Skate Score
Year Year of Olympics

Additional details related to the data are available on the SCORE Data Repository

Materials

Class Handout

Solutions

Students should gain an understanding of how the process of One-way ANOVA and Pair-wise Comparisons (such as Post Hoc Tukey test) works.