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a c
Sample means
Experimental design Differences in means
b
POINTS OF VIEW
Treatment A
Treatment B
9
Two-sample t-tests
C
A B
0.18
P = 0.27
Avg. response
1.5
11.0
Designing comparative experiments
dA
dB
10.5
11.5
9.5
Avg. response ~
17
17
Control
17
A/C
B/C
1.0
0.5
0.5
B/A
10.0
0
0.009
n = 17
A/C B/C B/A0.180.47
0.009P 0.95
d
0.150.50
8 10 11 12 13
Good experimental designs limit the impact of variability and reduce sample-size requirements.
npg 201 4 Nature America, Inc. All rights reserved.
In a typical experiment, the effect of different conditions on a biological system is compared. Experimental design is used to identify data-collection schemes that achieve sensitivity and specificity requirements despite biological and technical variability, while keeping time and resource costs low. In the next series of columns we will use statistical concepts introduced so far and discuss design, analysis and reporting in common experimental scenarios.
In experimental design, the researcher-controlled independent variables whose effects are being studied (e.g., growth medium, drug and exposure to light) are called factors. A level is a subdivision of the factor and measures the type (if categorical) or amount (if continuous) of the factor. The goal of the design is to determine the effect and interplay of the factors on the response variable (e.g., cell size). An experiment that considers all combinations of N factors, each with ni levels, is a factorial design of type n1n2nN.
For example, a 3 4 design has two factors with three and four levels each and examines all 12 combinations of factor levels. We will review statistical methods in the context of a simple experiment to introduce concepts that apply to more complex designs.
Suppose that we wish to measure the cellular response to two different treatments, A and B, measured by fluorescence of an aliquot of cells. This is a single factor (treatment) design with three levels (untreated, A and B). We will assume that the fluorescence (in arbitrary units) of an aliquot of untreated cells has a normal distribution with =10 and that real effect sizes of treatments A and B are dA=0.6 and dB=1 (A increases response by 6% to 10.6 and B by 10% to 11). To...