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The Completely Randomized Design (CRD). Lab # 1. Definition. Achieved when the samples of experimental units for each treatment are random and independent of each other Design is used to compare the treatment means:. The hypotheses are tested by comparing the differences
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Definition • Achieved when the samples of experimental units for each treatment are random and independent of each other • Design is used to compare the treatment means:
The hypotheses are tested by comparing the differences between the treatment means. • Test statistic is calculated using measures of variability within treatment groups and measures of variability between treatment groups
Steps for Conducting an Analysis of Variance (ANOVA) for a Completely Randomized Design: • 1- Assure randomness of design, and independence, randomness of samples • 2- Check normality, equal variance assumptions • 3- Create ANOVA summary table • 4- Conduct multiple comparisons for pairs of means as necessary/desired
assumptions 1- Normality: You can check on normality using 1- plot 2- Kolmogorve test 2- Constant variance: You can check on homogeneity of variances using 1- Plot 2- leven’s test.
multiple comparisons of means • A significant F-test in an ANOVA tells you that the treatment means as a group are statistically different. • Does not tell you which pairs of means differ statistically from each other • With k treatment means, there are c different pairs of means that can be compared, with c calculated as
Example 1 • A manufacturer of television sets is interested in the effect on tube conductivity of four different types of coating for color picture tubes. The • following conductivity data are obtained.
Solution • Enter data in spss as follows: