Abstract
In this chapter, we will study the introductory model of experimental design, which is the independent single-factor plan. Experiments are a powerful research method commonly used across many fields of study to verify whether theories or hypotheses are correct or not.
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For example, if there are three levels of the factor “industry” such as “primary”, “secondary”, and “tertiary”, and the population ratios in that region are 0.4, 0.3, 0.3, then \(\mu =0.4 \times \mu _{\text {primary}}+0.3 \times \mu _{\text {secondary}}+0.3 \times \mu _{\text {tertiary}}\). In this case, even if the number of data points per level does not proportionally reflect the population ratios, it is acceptable to use weights that reflect the population ratios.
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Fonken, L.K., Workman, J.L., Walton, J.C., Weil, Z.M., Morris, J.S., Haim, A., & Nelson, R.J (2010) Light at night increases body mass by shifting the time of food intake. Proceedings of the National Academy of Sciences of the United States of America, 107, 18664–18669.
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Toyoda, H. (2024). Analysis of Single-Factor Experiments. In: Statistics with Posterior Probability and a PHC Curve. Springer, Singapore. https://doi.org/10.1007/978-981-97-3094-0_10
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DOI: https://doi.org/10.1007/978-981-97-3094-0_10
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