t-Test and ANOVA for data with ceiling and/or floor effects

Abstract

Ceiling and floor effects are often observed in social and behavioral science. The current study examines ceiling/floor effects in the context of the t-test and ANOVA, two frequently used statistical methods in experimental studies. Our literature review indicated that most researchers treated ceiling or floor data as if these data were true values, and that some researchers used statistical methods such as discarding ceiling or floor data in conducting the t-test and ANOVA. The current study evaluates the performance of these conventional methods for t-test and ANOVA with ceiling or floor data. Our evaluation also includes censored regression with regard to its capacity for handling ceiling/floor data. Furthermore, we propose an easy-to-use method that handles ceiling or floor data in t-tests and ANOVA by using properties of truncated normal distributions. Simulation studies were conducted to compare the performance of the methods in handling ceiling or floor data for t-test and ANOVA. Overall, the proposed method showed greater accuracy in effect size estimation and better-controlled Type I error rates over other evaluated methods. We developed an easy-to-use software package and web applications to help researchers implement the proposed method. Recommendations and future directions are discussed.

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Notes

  1. 1.

    F* can be systematically smaller than F given large samples with small variances where F is too liberal. F* can be systematically larger than F given large samples with large variances where F is too conservative. Moreover, when cell sample sizes are equal, F and F* are identical, but the denominator degrees of freedom are different. See Maxwell et al., (2018) for more details.

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Correspondence to Qimin Liu or Lijuan Wang.

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Lijuan Wang is grateful for the support from NIH 1R01HD091235, NIH 1R01HD087319, and NIH 1R01HD088482.

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Liu, Q., Wang, L. t-Test and ANOVA for data with ceiling and/or floor effects. Behav Res 53, 264–277 (2021). https://doi.org/10.3758/s13428-020-01407-2

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Keywords

  • Ceiling effect
  • Floor effect
  • t-Test
  • ANOVA