Group1-BAN100ZAA_ANOVA Assignment

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BAN 100 Statistics for Analytics Group 1 - Assignment 2 - ANOVA Page 1 of 17 1. Performing One-Way ANOVA (10 points) Montana Gourmet Garlic is a company that grows garlic using organic methods. It specializes in hardneck varieties. Knowing a little about experimental methods, the owners design an experiment to test whether growth of the garlic is affected by the type of fertilizer used. They limit the experimentation to a Rocambole variety named Spanish Roja, and test three organic fertilizers and one chemical fertilizer (as a control). They blind themselves to the fertilizer by using containers with numbers 1 through 4. (In other words, they design the experiment in such a way that they do not know which fertilizer is in which container.) One acre of farmland is set aside for the experiment. It is divided into 32 beds. They randomly assign fertilizers to beds. At harvest, they calculate the average weight of garlic bulbs in each of the beds. The data are in the DATALIB.Garlic data set. These are the variables in the data set: Fertilizer The type of fertilizer used (1 through 4) BulbWt The average garlic bulb weight (in pounds) in the bed BedID A bed identification number Analysis of Variance with Garlic Data Consider an experiment to study four types of fertilizer, labeled 1, 2, 3, and 4. One fertilizer is chemical and the rest are organic. You want to see whether the average of weights of garlic bulbs are significantly different for plants in beds using different fertilizers. Solution: a. Test the hypothesis that the means are equal.  Using a statistical test called Analysis of Variance (ANOVA), we aim to determine if there is a notable distinction in the average weights of garlic bulbs treated with four distinct types of fertilizer.  We establish a hypothesis (H0) that there is no difference in the mean weights, and an alternative hypothesis (Ha) that there is indeed a difference in mean. Code: libname mylib '/home/u63735261/my_shared_file_links/u63661134/DATALIB'; proc means data=mylib.Garlic printalltypes maxdec=3; var BulbWt; class Fertilizer; title 'Descriptive Statistics of Garlic Weight'; run;

BAN 100 Statistics for Analytics Group 1 - Assignment 2 - ANOVA Page 2 of 17 b. Be sure to check that the assumptions of the analysis method that you choose are met. Before relying on the results of the ANOVA test, it's crucial to verify that the assumptions underlying the analysis are met. These assumptions include:  Normality: To ensure reliable analysis, data within each group should conform to a bell-curve pattern (normal distribution). This assumption can be verified visually using graphs called Q-Q plots or through statistical tests such as the Shapiro-Wilk test.  Homogeneity of variance: To ensure reliable results, the variability of the dependent variable (response) should be consistent among all groups in the analysis. This assumption can be verified visually by plotting the residuals (differences between observed and predicted values) against the fitted values. Alternatively, Levene's test can be used to formally assess the equality of variances across groups.  Independence: To ensure reliable results, the observations collected within each group of a study should not influence each other. This is often achieved by using a randomized experimental design, where participants are randomly assigned to different groups, reducing the likelihood of bias and external factors affecting the results. c. What conclusions can you reach at this point in your analysis?  After performing the one-way ANOVA analysis, we check the p-value linked to the F-statistic.  If this p-value falls below the selected significance level (usually 0.05), we reject the null hypothesis and determine that at least one pair of means significantly differs.  Conversely, if the p-value exceeds 0.05, we fail to reject the null hypothesis, suggesting that there are no significant differences in the means.

BAN 100 Statistics for Analytics Group 1 - Assignment 2 - ANOVA Page 3 of 17 d. Perform a post hoc test to look at the individual differences among means. Conduct pairwise comparisons with an experiment-wise error rate of a=0.05. (Use the Tukey adjustment.) Which types of fertilizer are significantly different? Post hoc Tukey adjustment  Since ANOVA indicates significant differences among groups, we can conduct pairwise comparisons using Tukey's HSD (Honestly Significant Difference) test to identify which groups are significantly different from each other.  The output in this test provides confidence intervals for the differences between means and indicates which pairs are significantly different. Significant differences are determined based on whether the confidence interval includes zero or not.  By examining the results of the Tukey test, we can identify which types of fertilizer lead to significantly different garlic bulb weights. Code: /* Tukey adjustmemt */ ods graphics; proc glm data=mylib.garlic; class Fertilizer; model BulbWt = Fertilizer; means Fertilizer / hovtest=levene welch plots=none; lsmeans Fertilizer /adjust=Tukey alpha=.05; title "One-Way ANOVA with Fertilizer as Predictor"; run; quit;

BAN 100 Statistics for Analytics Group 1 - Assignment 2 - ANOVA Page 4 of 17 e. Please provide the syntax and output – please interpret the output Interpretation  The degrees of freedom, p-value, and F-statistic are all provided in the ANOVA summary output. ANOVA p-values less than 0.05 indicate the presence of significant differences between the groups.  Confidence intervals and p-values for each pairwise comparison between the groups will be provided by the Tukey's HSD test output.  The experiment-wise error rate (0.05) can be used to compare the p-values and identify significant changes across groups. The groups differ from one another considerably if the p-value is less than 0.05.

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