Fundamentals of Statistical Experimental Design and Analysis

3Fundamentals of Statistical Data Analysis

Introduction

Once an experiment has been conducted and the data collected, the next task is to extract and communicate the information contained in the data (as depicted in the cloud cartoon; Fig. 1.1). The structure of an experiment dictates, to a large extent, the nature of the statistical data analysis to be carried out. (Indeed, careful planning of an experiment includes the anticipated analyses and even anticipated results.) In the remaining chapters in this book, detailed statistical data analyses will be discussed and illustrated in conjunction with the different experimental designs addressed. Some general principles and basic analyses, though, are set forth in this chapter and illustrated with simple two-treatment experiments. Two types of intertwined analysis are discussed—graphical and quantitative. My general approach is as follows:

Analysis 1. Plot the data! An analysis will often cycle between plots and calculations related to the plots as the message in the data is extracted and communicated.

Analysis 2. Do appropriate number crunching to characterize patterns seen in data plots, to separate and measure what is real from what could just be random variation, and to point the way to further data displays and analyses.

The two experiments addressed in some detail in this chapter are from the classic experimental design ...