# Unveiling Insights: The Statistical Tapestry in Experimental Research

Embarking on a statistical analysis assignment through diverse experiments, we delve into the intricate realm of data analysis. From deciphering the impact of chemotherapy on spatial memory to uncovering the nuances of nausea medication effectiveness, each study unfolds with statistical prowess. Join us as we explore the pivotal role of statistics in understanding seizures, unravelling the age-severity dynamics of chicken pox, and scrutinizing the effects of breakfast cereals on blood sugar levels. Through this unique lens, discover how statistical methodologies illuminate patterns, differences, and relationships, elevating experimental research to new dimensions of insight.

## Problem Set 1: Spatial Memory and Chemotherapy

### Problem Description:

A researcher investigates the impact of chemotherapy on spatial memory in rats. The experiment involves training 25 rats in a maze for 30 days, and data on completion times during the last 5 days are collected.

Graphical Representation:

Graph 1: estimated marginal means vs. factor for chemotherapy on rats

Statistical Hypothesis:

• Null Hypothesis: The mean completion times for rats are the same over the last five days of training.
• Alternative Hypothesis: The mean completion times for rats differ for at least two of the last five days.
• Statistical Test: Repeated measures ANOVA (no follow-up comparison needed).

Descriptive Statistics:

• Estimates for the Last 5 Days:

Statistical Hypothesis Test Result:

• Tests of Within-Subjects Effects

Verbal Description of Scientific Result:

• Since p-value (0.621) > 0.05, we fail to reject the null hypothesis. No significant difference, so the second phase of the experiment is not warranted.

## Problem Set 2:

Nausea Medications

Problem Description: The study compares the effectiveness of three nausea medications.

Graphical Representation:

Graph 2: estimated marginal means vs. drug for nausea medication

Statistical Hypothesis:

• Null Hypothesis: The three nausea medications have the same mean severity of symptoms.
• Alternative Hypothesis: At least two of the three nausea medications have different mean severity of symptoms.
• Statistical Test: ANOVA with post hoc LSD tests.

Statistical Test Result:

• ANOVA
• Multiple Comparisons (LSD)

Result Description:

• Since p-value (0.000) < 0.05, reject the null hypothesis. All three drugs have significantly different means of symptom severity.

## Problem Set 3: Seizure Reduction Drug

### Problem Description:

Researchers test a new drug's effectiveness in reducing seizures.

Expected Effect Size (Cohen's d):

• Cohen's d: 0.9607689 (95% CI: -0.5572812 to 2.411237)

Sample Size Calculation:

• Control group: 23, Treated group: 23 (to detect a significant effect).

Pre/Post Design Sample Size:

• Total sample size: 12 (assuming effect size remains the same).

New Drug Evaluation:

• Use power analysis to determine the trade-offs between increased effectiveness (20%) and higher cost (50%).

## Problem Set 4: Chicken Pox Severity

### Problem Description:

The study explores how the age of onset impacts the severity of chickenpox in children.

Graphical Representation:

Graph 3: estimating symptom severity depending on the participant’s age

Statistical Hypothesis:

• Null Hypothesis: Age of onset has no impact on chicken pox severity.
• Alternative Hypothesis: Age of onset impacts chicken pox severity.

Statistical Test Result:

Regression Coefficients:

• Intercept: 6.8667 (p < 0.01)
• ParticipantAge: -0.2751 (p < 0.01)

Predicted Severity at Age 5:

• Predicted: 5.491 (95% CI: 5.277 to 5.706)
• Prediction is considered good.

Prediction for 20s:

• No, as the model predicts negative severity, which is out of the range (0 - 10).

Problem Set 5: Blood Sugar Levels and Cereals

### Problem Description:

The study examines how different cereals affect short-term blood sugar levels.

Graphical Representation:

Graph 4: the effects of cereals on blood sugar levels

Censoring in Data:

• Right and Type I censoring.

Statistical Test and Null Hypothesis:

• Statistical Test: Log-rank test.
• Null Hypothesis: No difference in the probability of blood sugar dropping below 100 at any time point.

Descriptive Statistics:

Result Description:

• Chi-Square (Log Rank): 7.030 (df = 1, p = 0.008).
• Reject the null hypothesis, indicating a significant difference between populations in the probability of blood sugar dropping below 100.