ANOVA

ANOVA stands for Analysis of Variance. ANOVA is commonly used in research studies where there are multiple groups of data to compare, such as in medicine, psychology, and social sciences. It is used to analyze the differences between groups and to determine if those differences are statistically significant. ANOVA is based on the assumptions that the samples are independent, normally distributed, and have equal variances. If these assumptions are met, ANOVA can be a powerful tool for analyzing data and drawing conclusions.

Python

import statsmodels.api as sm
from statsmodels.formula.api import ols
import pandas as pd

# Create a pandas dataframe with the data
data = pd.DataFrame({'Group': ['A', 'A', 'A', 'B', 'B', 'B', 'C', 'C', 'C'],
                     'Values': [1, 2, 3, 2, 3, 4, 3, 4, 5]})

# Fit the ANOVA model
model = ols('Values ~ Group', data=data).fit()

# Print the ANOVA table
anova_table = sm.stats.anova_lm(model, typ=2)
print(anova_table)

In this example, we have a dataset with one independent variable Group and one dependent variable Values. We use the ols function to fit an ANOVA model to the data, and then use the anova_lm function to print the ANOVA table. The typ=2 argument specifies that we want to perform a type 2 ANOVA, which is the default in most cases.

# Load necessary library
library(car)

# Create a data frame with the data
data <- data.frame(Group = c('A', 'A', 'A', 'B', 'B', 'B', 'C', 'C', 'C'),
                   Values = c(1, 2, 3, 2, 3, 4, 3, 4, 5))

# Fit the ANOVA model
model <- lm(Values ~ Group, data=data)

# Print the ANOVA table
anova_table <- Anova(model, type=2)
print(anova_table)

The lm function is used to fit the ANOVA model.

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