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

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:

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

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

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.

ONE WAY ANOVA

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

MULTIPLE COMPARISONS OF MEAN S

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

S OLUTION Enter data in spss as follows:

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

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

Multiple Comparisons Dependent Variable:conductiivity (I) coating(J) coating Mean Difference (I- J)Std. ErrorSig. 95% Confidence Interval Lower BoundUpper Bound Tukey HSD * * * * * * * *

LSD * * * * * * * *

Thanks for all