Three diets for hamsters (labeled \"I\",\"II\",\"III\") were tested for differen

Question

Three diets for hamsters (labeled "I","II","III") were tested for differences in weight gain (measured as grams of increase) after a specified period of time. Six inbred laboratory lines (labeled "A","B","C", "D", "E", "F") were used to represent the responses of different genotypes to the various diets. The lines were treated as blocks and all three diets were assigned randomly within each block. The data consisted of a total of 18 observations. Both one-way ANOVA and two-way ANOVA models were fit to the data. Below are two different models of the data.

What are your conclusions and the reasons for those conclusions about the different diets, based on:

i. Model 1?

ii. Model 2?

b. Which model and conclusion is a better one? Justify your answer by discussing the effects of blocking for these data. Refer in particular to the residual sums of squares and residual mean squares, and their effects on the p-values in the two models.

Model 1: gain = Intercept + CI*line + Cd"diet Df Sum Sq Mean Sq F value Pr (>F) line diet Residuals 1e19. 5 71.17 14.23 7.491 .365 36.33 18.17 9.561 .477 1.90 Model 2: gain = Intercept + Cd"diet Df Sum Sq Mean Sq F value 236.33 18.167 3.022 Pr(OF) .0789 diet Residuals 15 90.17 6.011

Explanation / Answer

a) For Model 1, The p-value for diet = 0.0047 which is less than alpha 0.05, thus, we reject H0.

That means, the 3 types of diets are different

    For Model 2, the p-value for diet = 0.0789 which is greater than alpha 0.05, thus, we accept H0.

That mean, the 3 types of diets are same

b)

Generally, if the model which has residual mean square is low, then the model is good fit to the given data.

Here, Model 1 is better one. Since the residual mean square 1.90 of model 1 is low compare that of model 2 (residual error 6.011) .

Therefore, we suggested that the p-value for diet = 0.0047 which is less than alpha 0.05, thus, we reject H0.

That means, the 3 types of diets are different. This conclusion is valid.

In the total variation of model 1, block effects play an important role in this model. sum of square value of lines is 71.17 is major part in the entire variation (total variation = 126.5). The p-value of line is 0.00365 which is less than alpha 0.05, we reject H0(blocks). That means, the 6 laboratory lines are different.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.