MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Randomized Block Design Analysis Consider the experimental results for the following randomized block design. The objective is to make the calculations necessary to set up the analysis of variance table. #### Experimental Data The experimental results are outlined in the table below: | Treatment | A | B | C | |-----------|------|------|-----| | Block 1 | 10 | 10 | 8 | | Block 2 | 12 | 6 | 5 | | Block 3 | 19 | 16 | 15 | | Block 4 | 20 | 18 | 19 | | Block 5 | 9 | 8 | 8 | **Note:** Use \( \alpha = 0.05 \) to test for any significant differences. Show entries to 2 decimal places but p-value to 4 decimal places, if necessary. Round all intermediate values to two decimal places in your calculations. If your answer is zero, enter "0". #### Analysis of Variance (ANOVA) Table Fill in the analysis of variance table based on the provided data. | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value | |---------------------|----------------|--------------------|-------------|------|---------| | Treatments | | 2 | | | | | Blocks | | 4 | | | | | Error | | 8 | | | | | Total | | 14 | | | | The \( p \)-value is **between 0.025 and 0.05**. **Conclusion:** Based on the \( p \)-value: - Select the conclusion: **Conclude not all treatment means are equal** **Result:** Partially Correct **Hints and Feedback:** Users are encouraged to review their calculations and the assignment of values in the ANOVA table to ensure compliance with the provided instructions. Remember to consider the implications of the \( p \)-value when drawing conclusions.
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Transcribed Image Text:### Randomized Block Design Analysis Consider the experimental results for the following randomized block design. The objective is to make the calculations necessary to set up the analysis of variance table. #### Experimental Data The experimental results are outlined in the table below: | Treatment | A | B | C | |-----------|------|------|-----| | Block 1 | 10 | 10 | 8 | | Block 2 | 12 | 6 | 5 | | Block 3 | 19 | 16 | 15 | | Block 4 | 20 | 18 | 19 | | Block 5 | 9 | 8 | 8 | **Note:** Use \( \alpha = 0.05 \) to test for any significant differences. Show entries to 2 decimal places but p-value to 4 decimal places, if necessary. Round all intermediate values to two decimal places in your calculations. If your answer is zero, enter "0". #### Analysis of Variance (ANOVA) Table Fill in the analysis of variance table based on the provided data. | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value | |---------------------|----------------|--------------------|-------------|------|---------| | Treatments | | 2 | | | | | Blocks | | 4 | | | | | Error | | 8 | | | | | Total | | 14 | | | | The \( p \)-value is **between 0.025 and 0.05**. **Conclusion:** Based on the \( p \)-value: - Select the conclusion: **Conclude not all treatment means are equal** **Result:** Partially Correct **Hints and Feedback:** Users are encouraged to review their calculations and the assignment of values in the ANOVA table to ensure compliance with the provided instructions. Remember to consider the implications of the \( p \)-value when drawing conclusions.
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