Experimental Designs; CRD; Completely Randomized Design; One-Way ANOVA

The first paragraph introduces the concept of the Completely Randomized Design (CRD), which is a fundamental type of experimental design used in field research. It explains that treatments, representing categories of the independent variable, are assigned randomly to experimental units to observe the response of the dependent variable. The purpose of the experiment is to identify differences in responses to various treatments, with any variation among units receiving the same treatment attributed to experimental error. CRD is suitable for homogeneous experimental units where environmental conditions are easily controlled, such as in laboratory settings. The paragraph also emphasizes the importance of replication and randomization in CRD to reduce error and ensure the validity of experimental results.

This paragraph delves into the process of randomization in CRD, illustrating how treatments are applied without any specific pattern to experimental units kept under similar conditions to minimize experimental error. It identifies the two main sources of variation in CRD: treatments, which are the intended source of variation, and experimental error, which arises from uncontrollable extraneous factors. The paragraph explains the goal of experimental design to reduce experimental error and highlights the simplicity of CRD, making it suitable for environments with controlled conditions. An example is provided to demonstrate the application of CRD in an experiment studying the effects of fertilizer doses on plant growth.

The third paragraph discusses the statistical analysis of data obtained from a CRD experiment, specifically using one-way ANOVA. The process begins with organizing data according to treatments and calculating descriptive statistics, including mean values and variances. The homogeneity of variances is tested using the F max test, ensuring that variances among treatments are not significantly different. The paragraph outlines the steps for calculating the correction term, total sum of squares, treatment sum of squares, and sum of squares for experimental error, which are essential for conducting the ANOVA.

This paragraph continues the explanation of the ANOVA process by detailing the calculation of the correction term, total sum of squares, treatment sum of squares, and sum of squares for experimental error. It describes how to verify these calculations and move on to determining degrees of freedom for total, treatment, and error. The paragraph also explains the calculation of mean squares (MS) for treatments and experimental error, which are crucial for the F test to compare variances.

The final paragraph concludes the ANOVA process by comparing the variances through the F test. It calculates the F value and compares it with the critical F value to determine the significance of the results. In this case, the result is non-significant, indicating that the different fertilizer doses did not affect the fresh weight of plants. The paragraph summarizes the findings in an ANOVA summary table and states the conclusion that there is no effect of fertilizer dose on plant growth under the CRD setup. It reinforces the understanding of CRD and its application in controlled experimental conditions.