ANOVA (Hypothesis Testing)

Its blow my mind often whenever Ideal with data , that it shows and display so much story about the user.

And often we deal with the dataset to know the values which allow us to move further with data story.

One of the things usually comes up when we have to choose among two dataset, here we play with A/B testing and in it contains ANOVA somewhat anokha(lol)

Lets delve deeper to the chapter of ANOVA -

Imagine you’re a teacher and you want to know if there’s a difference in the test scores of students who study with three different study methods: reading, watching videos, and attending group discussions. You collect test scores from a group of students who used each method.

Here’s how ANOVA could be applied:

1. Null Hypothesis (H0): There’s no significant difference in the average test scores between the three study methods.
2. Alternative Hypothesis (Ha): There is a significant difference in the average test scores between at least one pair of study methods.

You would then gather test scores from each group and calculate the means (averages) for the scores of students who used each study method. ANOVA helps you analyze whether the differences in the means are large enough to suggest that they’re not just due to random chance.

If ANOVA finds that the differences in test scores are significant enough, it means that at least one of the study methods is likely having a real impact on the students’ performance. However, ANOVA doesn’t tell you which specific groups are different from each other. For that, you might need to perform further statistical tests or comparisons.

In summary, ANOVA helps you determine if there’s a meaningful difference between the groups you’re comparing, and it’s commonly used when you’re dealing with multiple groups and want to see if the differences are more than what you’d expect by random chance.

Certainly! There are several types of ANOVA, each designed to handle different experimental setups and research questions. Here are some of the most common types of ANOVA:

One-Way ANOVA: This is used when you’re comparing the means of three or more independent groups or conditions. For example, comparing the performance of students in different study methods (Group A: traditional teaching, Group B: online tutorials, Group C: interactive workshops).

import numpy as np
from scipy.stats import f_oneway

# Simulated test scores for three schools
school_a_scores = np.array([80, 85, 78, 92, 88])
school_b_scores = np.array([75, 82, 70, 91, 85])
school_c_scores = np.array([90, 92, 88, 95, 87])

# Performing ANOVA
f_statistic, p_value = f_oneway(school_a_scores, school_b_scores, school_c_scores)

# Checking the results
alpha = 0.05  # significance level
if p_value < alpha:
    print("There is a significant difference in the average scores of the schools.")
else:
    print("There is no significant difference in the average scores of the schools.")

Output

Two-Way ANOVA: This extends the one-way ANOVA to include two independent variables (factors). It helps you explore how two factors might interact to influence the dependent variable. For instance, studying how both gender and study method impact students’ test scores.

import numpy as np
import pandas as pd
from scipy.stats import f_oneway
import statsmodels.api as sm
from statsmodels.formula.api import ols

# Simulated data
np.random.seed(42)
diet = np.repeat(['A', 'B', 'C'], 9)
exercise = np.tile(['Low', 'Medium', 'High'], 9)
weight_loss = np.random.normal(5, 1, 27)

# Create a DataFrame
data = pd.DataFrame({'Diet': diet, 'Exercise': exercise, 'WeightLoss': weight_loss})

# Perform two-way ANOVA
model = ols('WeightLoss ~ Diet + Exercise + Diet * Exercise', data=data).fit()
anova_table = sm.stats.anova_lm(model, typ=2)

print(anova_table)

Output

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