#anova

In [1]: import osprint(os.listdir())

Output: ['_5e80885b18b2ac5410ea4eb493b68fb4_gapminder.csv', 'Outlook on Life Surveys_READ ME.pdf', 'OutlookOnLife Codebook.pdf', 'Mars Crater Codebook.pdf', 'Untitled1.ipynb', '.ipynb_checkpoints', 'UPLOADING YOUR OWN DATA SET TO SAS STUDIO.pdf', 'README.ipynb', 'Untitled.ipynb', 'Getting Started with Your Lab.ipynb', 'NESARC Wave 1 Code Book w toc.pdf', 'gapminder.csv.csv']

In[2]:

import pandas as pd

df = pd.read_csv("gapminder.csv.csv")

In[3]: df['alcconsumption'] = pd.to_numeric(df['alcconsumption'], errors='coerce')

In[4]: df = df.dropna(subset=['alcconsumption'])

In[5]: df['alc_group'] = pd.qcut(df['alcconsumption'], 3, labels=['Low','Medium','High'])

In[6]: df['incomeperperson'] = pd.to_numeric(df['incomeperperson'], errors='coerce')

In[7]: df = df.dropna(subset=['incomeperperson', 'alc_group'])

In[8]:

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

model = ols('incomeperperson ~ C(alc_group)', data=df).fit() anova_table = sm.stats.anova_lm(model, typ=2)

print(anova_table)

Output:

sum_sq df F PR(>F) C(alc_group) 2.382063e+09 2.0 13.223572 0.000004 Residual 1.585211e+10 176.0 NaN NaN

In[9]:

from statsmodels.stats.multicomp import pairwise_tukeyhsd

tukey = pairwise_tukeyhsd( endog=df['incomeperperson'], groups=df['alc_group'], alpha=0.05 )

print(tukey)

Output:

Multiple Comparison of Means - Tukey HSD, FWER=0.05 ============================================================= group1 group2 meandiff p-adj lower upper reject ------------------------------------------------------------- High Low -8252.7305 0.001 -12350.9346 -4154.5263 True High Medium -6925.4869 0.001 -11005.7075 -2845.2663 True Low Medium 1327.2435 0.7119 -2821.0142 5475.5013 False

Screenshot of the code:

Not sure when to use one-way vs. two-way ANOVA?

The ANOVA model you choose can make or break your insights. One factor or two, with or without interaction—the right choice leads to clearer results and stronger decisions.

For Categorical Variable consisting of 2 values and a response variable

Interpretation of the ANOVA Results

An analysis of variance (ANOVA) was conducted to examine whether depression scores differed across age groups (12–17 and 18–21). The response variable in the model was the depression score (DEP1), while the explanatory variable was age group.

The results of the model indicated a statistically significant association between age group and depression scores (F = 32.21, p < .001). This suggests that depression levels differ significantly between the two age groups.

The coefficient for the older age group (18–21) was 1.1196, indicating that individuals in the older age group reported, on average, higher depression scores compared to those in the younger age group (12–17). The intercept value of 8.0841 represents the estimated average depression score for the reference group (ages 12–17).

Although the association is statistically significant, the R-squared value of 0.007 indicates that age group explains only about 0.7% of the variation in depression scores. This suggests that while age group has a measurable effect on depression levels, many other factors likely influence depression among adolescents.

Overall, the findings indicate that older adolescents tend to report slightly higher depression scores than younger adolescents, but the effect size is relatively small.

2. ANOVA test for feature variable with more than 2 values and a response variable ( Multiple C -> Q ):

Understanding ANOVA and Its Importance in Data Analysis

Accurate research relies on selecting the right statistical test. ANOVA (Analysis of Variance) is a powerful tool used to compare the means of three or more groups and determine whether observed differences are statistically significant. Researchers, academic institutions, and businesses rely on ANOVA statistical analysis services for precise insights.

One-Way ANOVA: Comparing Single Variable Groups

One-Way ANOVA is ideal when a single independent variable is involved, such as comparing student performance across different teaching methods using data analysis services.

Two-Way ANOVA: Analyzing Interaction Effects

Two-Way ANOVA evaluates two independent variables and their interactions, like analyzing employee productivity based on work environment and experience.

N-Way ANOVA: Complex Data Analysis for Multiple Variables

For datasets with three or more variables, N-Way ANOVA offers deeper insights—for example, evaluating patient recovery rates considering treatment type, age, and diet using qualitative data analysis services.

Ensuring Accurate Results: Assumptions and Post-Hoc Tests

Before applying ANOVA, it’s essential to check key assumptions, including normality, homogeneity of variance, and independence of observations. Post-hoc tests are often performed to identify where significant differences exist.

Statswork ANOVA Statistical Analysis Services

At Statswork, we provide end-to-end ANOVA statistical analysis services, helping researchers and businesses interpret data accurately, select the right tests, and achieve reliable results. Our expertise ensures that your research insights are actionable, error-free, and aligned with your goals.