1. T HE C OMPLETELY R ANDOMIZED D ESIGN (CRD) L AB # 1

2. D EFINITION 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:

3. 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

4. S TEPS FOR C ONDUCTING AN A NALYSIS OF V ARIANCE (ANOVA) FOR A C OMPLETELY R ANDOMIZED D ESIGN : 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

5. 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.

6. ONE WAY ANOVA

7. 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

8. MULTIPLE COMPARISONS OF MEAN S

9. E XAMPLE 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. Conductivity Coating 1431411501461 1521491371432 1341361321273 1291271321294

10. S OLUTION Enter data in spss as follows:

11. A NALYSIS Test of Homogeneity of Variances conductiivity Levene Statisticdf1df2Sig. 2.370312.122 Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk StatisticdfSig.StatisticdfSig. conductiivity.13316.200 *.92816.230 a. Lilliefors Significance Correction *. This is a lower bound of the true significance.

13. O NE WAY A NOVA ANOVA conductiivity Sum of SquaresdfMean SquareFSig. Between Groups 844.6883281.56214.302.000 Within Groups 236.2501219.688 Total 1080.93815

14. Multiple Comparisons Dependent Variable:conductiivity (I) coating(J) coating Mean Difference (I- J)Std. ErrorSig. 95% Confidence Interval Lower BoundUpper Bound Tukey HSD12 -.250-3.1371.000-9.56-9.06 3 12.750 * 3.137.0073.4422.06 4 15.750 * 3.137.0016.4425.06 21.2503.1371.000-9.06-9.56 3 13.000 * 3.137.0063.6922.31 4 16.000 * 3.137.0016.6925.31 31 -12.750 * 3.137.007-22.06--3.44- 2 -13.000 * 3.137.006-22.31--3.69- 4 3.0003.137.776-6.31-12.31 41 -15.750 * 3.137.001-25.06--6.44- 2 -16.000 * 3.137.001-25.31--6.69- 3 -3.000-3.137.776-12.31-6.31

15. LSD12 -.250-3.137.938-7.09-6.59 3 12.750 * 3.137.0025.9119.59 4 15.750 * 3.137.0008.9122.59 21.2503.137.938-6.59-7.09 3 13.000 * 3.137.0016.1619.84 4 16.000 * 3.137.0009.1622.84 31 -12.750 * 3.137.002-19.59--5.91- 2 -13.000 * 3.137.001-19.84--6.16- 4 3.0003.137.358-3.84-9.84 41 -15.750 * 3.137.000-22.59--8.91- 2 -16.000 * 3.137.000-22.84--9.16- 3 -3.000-3.137.358-9.84-3.84

16. Thanks for all