### Abstract

The data from several types of bioassays is usually presented as a quotient as an intuitive parameter and a means of comparing results between experiments. For the example we considered here, we look at experiments with an experiment-wide negative control used to generate percent activity quotients from each experimental group. We asked if there was a valid means to statistically evaluate the transformed rather than the raw data. The experimental system chosen was a dose response of the agonist compound 48/80, which causes release of histamine from mast cells, thus providing test data from replicates of n=24. Descriptive statistics, the Ryan-Joiner test for normality of distribution of data, and normal probability plots confirm the normality of the distribution of data at each dose level. In parametric analysis, when the control group was treated as an errorless constant, there was a distinct consistent bias in the standard error of the data of 10% or less, which was not present if the control group's mean was treated as a variable with experimental error. This would be of minor interest in qualitative studies and might be safely ignored, but might be of considerable importance in quantitative assessments of activity using confidence intervals. When using Bootstrap estimates of standard error and probability plots of the bootstrap samples, the transformed data does not deviate significantly from normality. The standard, bias-corrected percentile limits (BCa), and empirical percentile methods gave very similar results when using resampling statistics to generate the transformed data from groups of n=6. Sample size can be as low as n=4 and still provide useful results. Thus, we have shown that resampling (i.e., bootstrap, Monte Carlo method, computer-intensive methods) can produce the data transform as well as provide confidence intervals using this type of raw data in small groups (n=4 to 6), giving improved statistical analysis of the transformed data (ratio estimates) without accepting a bias from methodology ignoring variation in the control group.

Original language | English |
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Pages (from-to) | 103-114 |

Number of pages | 12 |

Journal | Journal of Immunological Methods |

Volume | 296 |

Issue number | 1-2 |

DOIs | |

State | Published - 1 Jan 2005 |

### Keywords

- Bootstrap
- Computer-intensive
- Histamine release
- Monte Carlo
- Nonparametric

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## Cite this

*Journal of Immunological Methods*,

*296*(1-2), 103-114. https://doi.org/10.1016/j.jim.2004.11.013