Randomized completely Block design(RCBD)

In this design we are interested in comparing t treatment by using b blocks.

To analyze the above model we must to do the following steps: 1) Enter data 2) Describe the data 3) Check on the assumptions: Normality ( plot, kolomogorav sermanove) Constant variance (plot, leven’s test) Note: if the above assumptions are satisfied then we will go to the following steps: 4) Construct the ANOVA table by Analyze > General Linear Model > Univariate >

5- Decide if the hypothesis reject or accept based on: F-test (if, then we reject) F-test (if then we reject)

OR Based on P-value if P-value < 0.05, reject null hypothesis. Comment: we conclude that the treatments means are differs, or the treatments affect On the dependent variable at significance level =0.05. Note: We can covert RCBD to RCD where (SSE+SSB) in RCBD=SSE in RCD

Consider the following the data? An industrial engineer is conducting an experiment on eye focus time. He is interested in the effect of t he distance of the object from the eye on the focus time. Four different distances are of interest. He has five subjects available for the experiment. Because there may be differences between individuals, he decides to conduct the experiment in a randomized block design. The data obtained are shown below?

Subject Distances (Treatments) )Are there differences in the age focus time for four distances, use State the hypothesis Comment? 2) Does RCBD appear to be appropriate? Why?

Response Treatment Block

Levene's Test of Equality of Error Variances a Dependent Variable:focus Fdf1df2Sig Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept + Distances + Subject Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk StatisticdfSig.StatisticdfSig. focus a. Lilliefors Significance Correction

Between-Subjects Factors N Distances Subject Tests of Between-Subjects Effects Dependent Variable:focus Source Type III Sum of SquaresdfMean SquareFSig. Corrected Model a Intercept Distances Subject Error Total Corrected Total a. R Squared =.819 (Adjusted R Squared =.713)