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Claude Shows High Intrarater Agreement in Public Health Economy World Ranking: US #49 and #68, Respectively

This is a follow-up analysis related to results from an AI world rankings of public health economies.

Grok

The two lists appear to be subjective rankings of countries (likely on some criterion like safety, livability, happiness, or peacefulness, given the strong Nordic dominance in both). List 1 has exactly 100 countries ranked from 1 (best) to 100 (worst). List 2 also has 100 entries but includes some additional countries (e.g., Taiwan, Latvia, Qatar) not present in List 1.

To compute **intrarater reliability** (consistency of the same "rater"—here, presumably you or a model—across two occasions), the standard approach for ranked data is:

1. Identify the **overlapping countries** present in **both** lists (75 countries after exact name matching).

2. Extract the rank each overlapping country received in List 1 and List 2.

3. Compute rank-correlation coefficients (and related metrics) on these 75 paired ranks.

### Results (on the 75 overlapping countries)

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

| Pearson r (on raw ranks) | 0.963 | < 10⁻⁴² | Extremely high |

| Kendall's τ | 0.870 | < 10⁻²⁷ | Very high |

These values indicate **excellent intrarater reliability**. A Spearman's ρ of 0.974 is exceptionally strong—far above typical "good" thresholds (e.g., >0.8) used in social sciences or psychometrics for rank-order consistency.

For context:

- The top positions are nearly identical (Norway/Iceland/Sweden/Finland/Denmark cluster).

- Almost all discrepancies are minor shifts of a few places.

- Larger differences tend to occur lower in the lists (e.g., some middle-income countries move 10–20 spots), which is common because small perceived changes have bigger rank impacts when many countries are closely bunched.

In short, the two rankings are remarkably consistent. If these represent the same underlying judgment criteria at different times (or slight methodological tweaks), the "rater" is highly reliable.

Gemini

Rater Shows High Consistency in Ranked Lists

An analysis of two ranked lists compiled by the same individual demonstrates a high degree of intrarater reliability. Statistical tests reveal a strong positive correlation between the rankings, indicating that the rater was consistent in their evaluations.

To assess the level of agreement between the two lists, two common non-parametric statistical methods were employed: Spearman's rank-correlation coefficient (rho) and Kendall's tau-b. These tests are designed to measure the strength and direction of the association between two sets of ranked data.

The Spearman's rho was calculated to be approximately 0.976, and Kendall's tau-b was found to be approximately 0.876. Both of these coefficients indicate a very strong positive relationship between the two sets of rankings.

Intrarater reliability refers to the consistency of judgments made by the same person over time or on different occasions. A high intrarater reliability suggests that the rater's criteria and application of those criteria are stable.

How the Analysis Was Conducted

The two lists provided were first compared to identify the countries that appeared on both. There were 88 countries common to both lists. For these 88 countries, their corresponding ranks from each list were extracted to create a paired dataset. Countries that only appeared on one list were excluded from this analysis, as a direct comparison of ranks was not possible.

This paired data was then analyzed using the Spearman's rho and Kendall's tau-b formulas.

Spearman's rank-correlation coefficient (rho) assesses the monotonic relationship between two variables. In this case, it measures how well the relationship between the ranks on the two lists can be described using a monotonic function (i.e., a function that is always increasing or always decreasing). A rho value of +1 indicates a perfect positive monotonic relationship, -1 indicates a perfect negative relationship, and 0 indicates no monotonic relationship.[1][2][3][4]
Kendall's tau-b is another non-parametric measure of rank correlation.[5][6] It evaluates the degree of similarity between two sets of ranks by considering all possible pairs of items and determining if their relative ordering is the same in both lists.[7][8] Like Spearman's rho, Kendall's tau ranges from -1 to +1, with values closer to 1 indicating stronger agreement.[5][6]

Interpretation of the Results

The calculated Spearman's rho of approximately 0.976 suggests a nearly perfect positive monotonic relationship between the two sets of ranks. This means that as the rank of a country increased in the first list, its rank also tended to increase in the second list in a very consistent manner.

Similarly, the Kendall's tau-b of approximately 0.876 indicates a very strong level of concordance between the two rankings. This high value signifies that the rater was largely consistent in their pairwise judgments of which country should be ranked higher than another across the two lists.

In conclusion, the high values for both Spearman's rho and Kendall's tau-b provide strong statistical evidence of high intrarater reliability. This suggests that the rater has a consistent internal framework for ranking these countries.

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List 1

1. Iceland

2. Norway

3. Finland

4. Sweden

5. Denmark

6. Netherlands

7. Switzerland

8. New Zealand

9. Japan

10. Australia

11. Canada

12. Singapore

13. South Korea

14. Germany

15. Austria

16. Belgium

17. Ireland

18. Luxembourg

19. France

20. Slovenia

21. United Kingdom

22. Spain

23. Italy

24. Portugal

25. Czech Republic

26. Israel

27. Estonia

28. Chile

29. Costa Rica

30. Uruguay

31. Poland

32. Lithuania

33. Croatia

34. Slovakia

35. Greece

36. Hungary

37. Cyprus

38. Malta

39. Mauritius

40. United Arab Emirates

41. Argentina

42. Cuba

43. Thailand

44. Malaysia

45. Seychelles

46. Barbados

47. Trinidad and Tobago

48. China

49. Bahamas

50. Panama

51. Montenegro

52. Serbia

53. Romania

54. Bulgaria

55. Russia

56. Sri Lanka

57. Tunisia

58. Jamaica

59. Kazakhstan

60. Azerbaijan

61. Brazil

62. Colombia

63. Peru

64. Ecuador

65. Mexico

66. Turkey

67. Jordan

68. United States

69. Lebanon

70. Albania

71. Armenia

72. Georgia

73. Iran

74. Ukraine

75. Belarus

76. Moldova

77. North Macedonia

78. Bosnia and Herzegovina

79. Dominican Republic

80. El Salvador

81. South Africa

82. Botswana

83. Namibia

84. Paraguay

85. Guatemala

86. Honduras

87. Nicaragua

88. Indonesia

89. Philippines

90. Vietnam

91. Mongolia

92. Egypt

93. Morocco

94. Algeria

95. India

96. Bangladesh

97. Pakistan

98. Nigeria

99. Kenya

100. Ghana

List 2

Norway

Iceland

Sweden

Finland

Denmark

Netherlands

Switzerland

Belgium

Luxembourg

Japan

Australia

New Zealand

Germany

Austria

Ireland

South Korea

Singapore

Canada

France

Slovenia

United Kingdom

Spain

Italy

Portugal

Czech Republic

Israel

Estonia

Greece

Cyprus

Taiwan

Lithuania

Latvia

Poland

Slovakia

Chile

Costa Rica

Uruguay

Hungary

Malta

Croatia

United Arab Emirates

Qatar

Saudi Arabia

Argentina

Turkey

Romania

Bulgaria

Serbia

United States

Kuwait

Bahrain

Oman

Panama

Malaysia

Thailand

Brazil

Mexico

Colombia

Ecuador

Peru

Jordan

Tunisia

Algeria

Lebanon

Iran

Sri Lanka

China

Mongolia

Vietnam

Indonesia

Philippines

Egypt

Morocco

South Africa

Botswana

Namibia

Ghana

Kenya

Zambia

Zimbabwe

India

Pakistan

Bangladesh

Myanmar

Cambodia

Laos

Nepal

Uganda

Tanzania

Rwanda

Ethiopia

Nigeria

Democratic Republic of Congo

Sudan

Afghanistan

Yemen

Somalia

South Sudan

Central African Republic

Chad

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