A pharmaceutical company will use ANOVA to compare blood pressure reductions across three drug formulations (30 patients per group). Which assumption is MOST critical to check? Variance in blood pressure reduction should be similar across groups (homogeneity of variance) The correlation between drugs must be positive Each drug must produce normally distributed outcomes All patients must have identical baseline blood pressure
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Step 1: Recall the key assumptions of one-way ANOVA: independence of observations, normality of the residuals within groups, and homogeneity of variances (equal variances across groups). Show more…
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A pharmaceutical manufacturer wants to investigate the bioactivity of a new drug. A completely randomized single-factor experiment was conducted with three dosage levels, and the following results were obtained: Dosage Observations 20g 24(5) 28(6) 37(10) 30(4) 30g 37(12) 44(1) 31(9) 35(3) 40g 42(7) 47(11) 52(2) 38(8) 1. Is there evidence to indicate that dosage level affects bioactivity? Use α = 0.05. 2. Analyze the residuals from this experiment and comment on model adequacy. 3. Use the data in the above table to estimate the overall mean and the treatment effects. 4. Find the 95 percent confidence interval on the mean of treatment 3 (40g dosage). 5. Test the hypothesis of equal variances in all treatments using the modified Levene test. (This test evaluates whether or not the mean of these deviations are equal. If the mean deviations are equal, the variances of the observations in all treatments will be the same.) Use data transformation if this test prove that the variance is not constant. 6. Write down the Regression model for the pharmaceutical manufacturer experiment. 7. Construct a set of orthogonal contrasts, assuming that at the outset of the experiment you suspected the bioactivity response of dosage level 30g to be different from the other two. (Because the null hypotheses was rejected, we know that some dosage produce different bioactivity than others, but which ones actually causes this difference?) 8. Use the Kruskal–Wallis test for the experiment in pharmaceutical manufacturer experiment. Compare the conclusions obtained with those from the usual analysis of variance.
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A pharmaceutical manufacturer wants to investigate the bioactivity of a new drug. A completely randomized single-factor experiment was conducted with three dosage levels, and the following results were obtained: Table P-02 Dosage Observations 20 g 24 28 37 30 30 g 37 44 31 35 40 g 42 47 52 38 a. Determine the suitable statistical method to make comparison between the pairs of means and why it is chosen? b. Use manual calculation of Ftesting to calculate the Fvalue for equal variance assumption and compare the calculated Fvalue to the reference Ftable from the F distribution table, and what is the conclusion of this experiment? Use α = 0.05. c. Use Graphical summary in Minitab software to test the normality assumption and 95% CI of mean and median, give your short explanation of each graphs! d. Using Minitab or other statistical software make any analysis for the data and test these hypotheses using α = 0.05. Show your statistical analysis and compare the result with part (b) and what is your conclusion? e. Use Fisher method to show further grouping information and pairwise comparison among groups, and give your short explanation! f. Determine the fitting empirical model using regression analysis and explain the impact factor of dosage level to the bioactivity of the new drug!
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