Basic Tools in Experimental Design

There are three basic tools in statistical experimental design (Paulsmi, 2003)  

Replication means that the basic experimental measurement is repeated. For example, if one is measuring the CO2 concentration of blood, those measurements would be repeated several times under controlled circumstances. Replication serves several important functions. First, it allows the investigator to estimate the variance of the experimental or random error through the sample standard deviation (s) or sample variance (i ). This estimate becomes a basic unit of measurement for determining whether observed differences in the data are statistically significant. Second, because the sample mean (x) is used to estimate the true population mean (/a), replication enables an investigator to obtain a more precise estimate of the treatment effect s value. If s is the sample variance of the data for n replicates, then the variance of the sample mean is = s /n. 

The practical aspect of this is that if few or no replicates are made, then the investigator may be imable to make a useful inference about the true population mean, /r. However, if the sample mean is derived from 

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