x̄ - > Data analysis example of a Lesion sizes measured weekly, parasite loads determined from spleen smears, and statistical analysis using ANOVA and chi-square.

Sure! Let's walk through an example data analysis involving lesion sizes measured weekly, parasite loads determined from spleen smears, and statistical analysis using ANOVA and chi-square tests.

Scenario

Imagine a study investigating the effect of a new treatment on lesion sizes and parasite loads in mice infected with a certain parasite. The study involves three groups of mice:

1. Control group (no treatment)
2. Treatment A group
3. Treatment B group

Lesion sizes are measured weekly for four weeks, and parasite loads are determined from spleen smears at the end of the fourth week.

Data Collection

Lesion Sizes (in mm)

• Weekly measurements for 4 weeks.
• Collected for each mouse in each group.

Parasite Loads (parasites per 100 spleen cells)

• Determined at the end of the 4th week.
• Collected for each mouse in each group.

Example Data

Lesion Sizes

Mouse ID	Group	Week 1	Week 2	Week 3	Week 4
M1	Control	5.2	5.8	6.1	6.4
M2	Control	5.1	5.7	6.0	6.3
M3	Treatment A	4.5	4.8	4.9	5.0
M4	Treatment A	4.6	4.9	5.0	5.1
M5	Treatment B	3.8	4.0	4.1	4.2
M6	Treatment B	3.9	4.1	4.2	4.3

Parasite Loads

Mouse ID	Group	Parasite Load
M1	Control	80
M2	Control	85
M3	Treatment A	30
M4	Treatment A	35
M5	Treatment B	20
M6	Treatment B	25

Statistical Analysis

1. ANOVA for Lesion Sizes

To determine if there are significant differences in lesion sizes between the three groups over the four weeks, we can perform a repeated measures ANOVA.

2. Chi-Square Test for Parasite Loads

To determine if there is a significant association between the treatment groups and parasite loads, we can categorize the parasite loads into bins (e.g., low, medium, high) and perform a chi-square test.

Python Code Implementation

Let's implement this in Python using relevant libraries.

import pandas as pd
import numpy as np
from scipy.stats import f_oneway, chi2_contingency

# Example data
lesion_data = {
    'Mouse ID': ['M1', 'M2', 'M3', 'M4', 'M5', 'M6'],
    'Group': ['Control', 'Control', 'Treatment A', 'Treatment A', 'Treatment B', 'Treatment B'],
    'Week 1': [5.2, 5.1, 4.5, 4.6, 3.8, 3.9],
    'Week 2': [5.8, 5.7, 4.8, 4.9, 4.0, 4.1],
    'Week 3': [6.1, 6.0, 4.9, 5.0, 4.1, 4.2],
    'Week 4': [6.4, 6.3, 5.0, 5.1, 4.2, 4.3]
}

parasite_data = {
    'Mouse ID': ['M1', 'M2', 'M3', 'M4', 'M5', 'M6'],
    'Group': ['Control', 'Control', 'Treatment A', 'Treatment A', 'Treatment B', 'Treatment B'],
    'Parasite Load': [80, 85, 30, 35, 20, 25]
}

df_lesions = pd.DataFrame(lesion_data)
df_parasites = pd.DataFrame(parasite_data)

# ANOVA for lesion sizes
week_data = [df_lesions[df_lesions['Group'] == group].iloc[:, 2:].values.flatten() for group in df_lesions['Group'].unique()]
anova_result = f_oneway(*week_data)
print(f"ANOVA result for lesion sizes: F={anova_result.statistic}, p={anova_result.pvalue}")

# Chi-square test for parasite loads
# Binning the parasite loads into categories
bins = [0, 30, 60, 90]
labels = ['Low', 'Medium', 'High']
df_parasites['Parasite Category'] = pd.cut(df_parasites['Parasite Load'], bins=bins, labels=labels)

# Contingency table
contingency_table = pd.crosstab(df_parasites['Group'], df_parasites['Parasite Category'])
chi2_result = chi2_contingency(contingency_table)
print(f"Chi-square result for parasite loads: chi2={chi2_result[0]}, p={chi2_result[1]}")
    

Explanation

1. Data Preparation: The lesion sizes and parasite loads are stored in separate dataframes.
2. ANOVA: A repeated measures ANOVA is performed on the lesion sizes to see if there are significant differences between the groups.
3. Chi-Square Test: Parasite loads are categorized into bins, and a chi-square test is performed to determine the association between treatment groups and parasite load categories.

This is a simplified example, but it demonstrates the process of analyzing experimental data using ANOVA and chi-square tests in Python.