Resolution of Students t-tests, ANOVA and analysis of variance components from intermediary data.

Kallner Anders

doi:10.11613/bm.2017.026

Abstract

Significance testing in comparisons is based on Student’s t-tests for pairs and analysis of variance (ANOVA) for simultaneous comparison of several procedures. Access to the average, standard deviation and number of observations is sufficient for calculating the significance of differences using the Student’s tests and the ANOVA. Once an ANOVA has been calculated, analysis of variance components from summary data becomes possible. Simple calculations based on summary data provide inference on significance testing. Examples are given from laboratory management and method comparisons. It is emphasized that the usual criteria of the underlying distribution of the raw data must be fulfilled.

Highlights

Comparison of results from different experimental designs, between instruments and between methods is an everyday task in analytical chemistry and its applied sciences, e.g. laboratory medicine
We describe how this can be accomplished if the datasets are independent and fulfil the requirements of Student’s ttest or analysis of variance (ANOVA)
The same limitations regarding normality and equal variances will apply as when using raw data but since the input data, the standard deviation, already require normality this is usually not a major issue

Summary

Introduction

Comparison of results from different experimental designs, between instruments and between methods is an everyday task in analytical chemistry and its applied sciences, e.g. laboratory medicine. The obvious procedure is to start with inspecting the raw data to determine the appropriate statistical methods to be used. Sometimes the raw data may not be available whereas the central tendency (e.g. the average), the dispersion (e.g. the standard deviation) and the number of observations may be. It may be desirable to evaluate the significance of a difference between datasets. Typical situations may be related to laboratory management and scientific evaluation of reports. We describe how this can be accomplished if the datasets are independent and fulfil the requirements of Student’s ttest or analysis of variance (ANOVA). Resolution of an ANOVA table to provide analysis of variance components is discussed

Methods

Findings

Discussion