1-A randomized block design ANOVA has five treatments and four blocks. The computed test statistic (value of F) is 4.35. With a 0.05 significance level, the appropriate table value and conclusion will be?
2-A randomized block experiment having five treatments and six blocks produced the following values: SSTR = 287, SST = 1,446, SSE = 180. The value of SSB must be? Thank you
1. Use an ANOVA table to determine your table value using 0.05 level of significance. If the test statistic exceeds the critical value from the table, you reject the null. If the test statistic does not exceed the critical value from the table, you do not reject the null.
2. If SST represents the total SS, then you should be able to determine SSB from the values given.
1. To determine the appropriate table value for the randomized block design ANOVA, you need to refer to the F-distribution table. Since the number of treatments is 5, the degrees of freedom for the numerator (df1) would be (number of treatments - 1) = 4. Similarly, the degrees of freedom for the denominator (df2) would be (number of blocks - 1) = 3.
Now, you need to find the critical F value in the table for the given significance level of 0.05 with the degrees of freedom df1 = 4 and df2 = 3. Looking up the table, you will find the critical F value to be 3.238.
The computed test statistic (value of F) for the experiment is 4.35. Comparing the computed F-value with the table F-value, we can make the following conclusion:
If the computed F-value is greater than the critical F-value (4.35 > 3.238), then we reject the null hypothesis. This means there is a significant difference between the treatments in the randomized block design ANOVA.
2. In a randomized block experiment, the total sum of squares (SST) can be decomposed into three components: sum of squares due to treatments (SSTR), sum of squares due to blocks (SSB), and sum of squares of errors (SSE).
Given that SSTR = 287, SSE = 180, and SST = 1,446, we can calculate SSB as follows:
SSB = SST - SSTR - SSE
= 1,446 - 287 - 180
= 979.
Therefore, the value of SSB in the randomized block experiment is 979.