Roberson P K, Shema S J, Mundfrom D J, Holmes T M
Department of Pediatrics, University of Arkansas for Medical Sciences, Little Rock, USA.
Fam Med. 1995 Nov-Dec;27(10):671-5.
Likert scale data present unique analysis concerns that are often not recognized by nonstatistical researchers. Mean responses to a single question are frequently compared among two or more groups of moderate sample size using normal theory methods (t test, ANOVA). These tests are designed for continuous normally distributed data, but Likert responses are categorical, ordinal, and not normally distributed. The problems are further complicated when the paired nature of pre/post- or preference questioning is ignored.
Simulated data for a single five-point Likert scale question was used to illustrate the differing conclusions that may arise from single-question Likert scale data depending on whether pairing is modeled appropriately and which statistical procedure was applied (two sample: t test or Wilcoxon rank sum; paired samples; t test, Wilcoxon signed rank, or sign test).
Cases are shown for which the paired responses are significantly different (indicated by the sign test), although the group mean responses to the two questions are identical (leading to nonsignificance with both paired t and signed rank tests). The sign test is shown to be appropriate and simple to apply in typical pre/post- or preference situations.
Correctly identifying the question of interest is critical to selecting the appropriate statistical methodology.
李克特量表数据存在独特的分析问题，非统计专业的研究人员常常认识不到这些问题。对于中等样本量的两组或多组数据，人们经常使用正态理论方法（t检验、方差分析）比较单个问题的平均回答。这些检验是为连续正态分布数据设计的，但李克特回答是分类的、有序的，且并非正态分布。当忽略前后或偏好问题的配对性质时，问题会变得更加复杂。
使用单个五点李克特量表问题的模拟数据来说明，根据配对是否得到恰当建模以及应用了哪种统计程序（两组样本：t检验或威尔科克森秩和检验；配对样本：t检验、威尔科克森符号秩检验或符号检验），单问题李克特量表数据可能得出不同的结论。
展示了这样的案例，即配对回答存在显著差异（通过符号检验表明），尽管两组对两个问题的平均回答相同（导致配对t检验和符号秩检验均无显著性）。结果表明，符号检验在典型的前后或偏好情形中适用且易于应用。
正确识别感兴趣的问题对于选择合适的统计方法至关重要。
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