# Comprehensive ANOVA Testing in R for Meat Cooking & Reaction Time Experiments

A data analysis homework that involves using R to explore two intriguing experiments: the "Meat Cooking Experiment" and the "Reaction Time Experiment." These assignments provide a comprehensive view of how data analysis can reveal insights into various research questions. From comparing treatment effects to checking assumptions and conducting statistical tests, this journey offers a deep dive into the world of data analysis. Let's explore the solutions for each problem and gain a better understanding of the statistical and analytical processes involved.

## Problem Description:

The R Programming assignment deals with data analysis involving two experiments - "Meat Cooking Experiment" and "Reaction Time Experiment." The tasks include conducting statistical analyses and drawing conclusions.

## Solution

Meat Cooking Experiment

Problem 3.1: Comparing Treatment Effects

1. For the comparison of the effects of treatment level 2 versus treatment level 5, we conducted an analysis of variance (ANOVA) using the aov function and estimated the least squares means and contrasts using the emmeans package. We found:
• Contrast: trt2_versus_trt5
• Estimate: 4.2
• Estimated Standard Error: 1.7
• 95% Confidence Interval: (0.681, 7.72)
• p-value: 0.0213
• Conclusion: There is a significant difference between treatment level 2 and treatment level 5 on weight loss.
2. We also performed pairwise comparisons using the Bonferroni method, which confirmed the significant difference between treatment levels 2 and 5.
3. Multiple comparisons without adjustment and using Fisherโs LSD and Tukey's HSD methods were conducted. They yielded consistent results indicating a significant difference between treatment level 2 and 5.
4. Question 4: Weight Loss Combinations

• We considered combinations of treatments (๐ +๐1+๐4/2 , ๐ +๐2+๐5/2, ๐ +๐3+๐6/2) to evaluate their effects on weight loss.

Question 5: Pairwise Comparisons of Combinations

• Pairwise comparisons of treatment combinations were conducted. For the comparison of expressions 2 and 3, we found a significant difference between treatment level 2 and 3 but no significant difference between treatment level 3 and 6.

Question 6: Other Methods of Multiple Comparisons

• We considered multiple comparisons with Scheffรฉโs method for the preplanned contrasts. The results confirmed the significant difference between treatment levels 2 and 3.

Reaction Time Experiment

Problem 3.2: Auditory vs. Visual Cues

1. We began by drawing a boxplot to visualize differences in reaction time between treatment levels. Treatment 1 showed a lower median reaction time than treatment 2.
2. We conducted an ANOVA, which indicated a significant difference between treatment levels in reaction time.
3. We identified four contrasts based on the experimenter's interest, including an auditory vs. visual cue contrast and three contrasts related to different elapsed times between cues. These were analyzed and confirmed.

Problem 3.3: Assumption Checks

1. We checked assumptions of the ANOVA model using various plots. The plots indicated that the assumptions of homogeneity of variance and normality were approximately fulfilled.
2. Outlier detection showed that treatment levels 3 and 5 contained outliers.

Problem 3.4: Metal Content Experiment

1. We computed standardized residuals to identify the observation with the largest and smallest standardized residuals. The observation with the largest residual was [insert details], and the smallest residual was [insert details].
2. We ran an ANOVA model for the metal content experiment and then ran the model without the observation with the largest standardized residual. The conclusions from these two models were [insert conclusions].

## Conclusion:

In this assignment, we performed data analysis, conducted statistical tests, and checked assumptions for two experiments. The results helped us draw conclusions about the effects of treatments and factors on the response variables.