## 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
**

- 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.- We also performed pairwise comparisons using the Bonferroni method, which confirmed the significant difference between treatment levels 2 and 5.
- Multiple comparisons without adjustment and using Fisherโs LSD and Tukey's HSD methods were conducted. They yielded consistent results indicating a significant difference between treatment level 2 and 5.
- We considered combinations of treatments (๐ +๐1+๐4/2 , ๐ +๐2+๐5/2, ๐ +๐3+๐6/2) to evaluate their effects on weight loss.
- 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.
- We considered multiple comparisons with Scheffรฉโs method for the preplanned contrasts. The results confirmed the significant difference between treatment levels 2 and 3.
- 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.
- We conducted an ANOVA, which indicated a significant difference between treatment levels in reaction time.
- 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.
- 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.
- Outlier detection showed that treatment levels 3 and 5 contained outliers.
- 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].
- 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].

**Problem 3.1:** Comparing Treatment Effects

**Question 4: **Weight Loss Combinations

**Question 5:** Pairwise Comparisons of Combinations

**Question 6: **Other Methods of Multiple Comparisons

**Reaction Time Experiment
**

**Problem 3.2:** Auditory vs. Visual Cues

**Problem 3.3:** Assumption Checks

**Problem 3.4: **Metal Content Experiment

## 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.