EXPERIMENTAL DESIGN 217 



The number of degrees of freedom is w — 1 = 6, and in the t table 

 we find that the chances of a t value this large are less than one in a 

 thousand. Therefore, this particular difference between means does not 

 belong with the distribution where the mean difference is zero. We must 

 reject the hypothesis that the two means are equal, or in other words, 

 we conclude that the differences observed are statistically significant and 

 that maleic hydrazide does have an effect on the respiration of yeast 

 cells. Incidentally, if the pairing design is not used, the difference be- 

 tween the two means is not significant. 



More complex designs 



The simple experimental designs are adequate when only one pair of 

 conditions is to be tested. If a larger number of comparisons is to be 

 made, however, performing one set of measurements at a time may 

 become unduly laborious. With the application of a little ingenuity it 

 becomes possible to make several comparisons in a single experiment and 

 still have legitimate statistical tests available. In most of these instances, 

 analysis of variance is used. In the following discussion, three general 

 types of experimental designs with examples are described, and then a 

 typical analysis of variance is performed on one of these. 



Completely Randomized Design: In this design, as the name suggests, 

 the choice of samples and treatments is left entirely to chance. The 

 following example will not only illustrate this design but can be modified 

 later for some other designs. We are interested in studies using chloro- 

 plasts isolated from leaves. We have decided to use sugar beet plants 

 and to raise the plants in a special constant-temperature chamber under 

 artificial light. The hope is to provide uniformly active plants. We have 

 our choice of soil, vermiculite (heat-expanded mica), or an aerated solu- 

 tion as a medium in which to raise the plants. We perform the following 

 preliminary experiment to determine which medium provides the great- 

 est weight of leaves. 



Four plants (or groups of plants) are to receive each treatment. Since 

 the space in the plant growth room is essentially uniform, the groups of 

 plants are placed at random within the space available. They might be 

 arranged on the bench in a pattern consisting of 4 rows of 3. Randomiza- 

 tion could be achieved with one of a pair of dice in the following manner. 

 Assign the numbers 1 to 4 to the plants in each of the three groups. 

 Now, number the possible locations on the bench from 1 to 12. Start- 

 ing with position 1, throw the die; use this throw to decide which of 



