agni

A two-way ANOVA and correlation analysis were conducted to examine the relationship between age and work status, with gender tested as a potential moderator. The ANOVA model included age group, gender, and their interaction term, while Pearson correlations were also computed overall and separately for males and females to further examine subgroup differences in the relationship.

Code:

In[1]:

import pandas as pd

df = pd.read_csv("ool_pds.csv.csv") print(df.columns)

Output:

Index(['CASEID', 'W1_CASEID', 'W2_CASEID2', 'W1_TM_START', 'W1_TM_FINISH', 'W1_WEIGHT1', 'W1_WEIGHT2', 'W1_WEIGHT3', 'W2_TM_START', 'W2_TM_FINISH', ... 'PPREG9', 'PPRENT', 'PPSTATEN', 'PPT01', 'PPT1317', 'PPT18OV', 'PPT25', 'PPT612', 'PPWORK', 'PPNET'], dtype='object', length=436)

In[2]: data = df[['PPAGE', 'PPWORK', 'PPGENDER']].copy()

In[3]:

data['PPAGE'] = pd.to_numeric(data['PPAGE'], errors='coerce') data['PPWORK'] = pd.to_numeric(data['PPWORK'], errors='coerce') data['PPGENDER'] = pd.to_numeric(data['PPGENDER'], errors='coerce')

data = data.dropna()

In[4]:

overall_r = data['PPAGE'].corr(data['PPWORK']) print("Overall correlation (Age vs Work):", overall_r)

Output:

Overall correlation (Age vs Work): 0.25863565449969084

In[5]:

male = data[data['PPGENDER'] == 1] female = data[data['PPGENDER'] == 2]

r_male = male['PPAGE'].corr(male['PPWORK']) r_female = female['PPAGE'].corr(female['PPWORK'])

print("Male correlation:", r_male) print("Female correlation:", r_female)

Output:

Male correlation: 0.341436825966627 Female correlation: 0.202204314205431

In[6]:

import pandas as pd import statsmodels.api as sm import statsmodels.formula.api as smf

In[7]:

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

data = df[['PPAGE', 'PPWORK', 'PPGENDER']].copy()

data['PPAGE'] = pd.to_numeric(data['PPAGE'], errors='coerce') data['PPWORK'] = pd.to_numeric(data['PPWORK'], errors='coerce') data['PPGENDER'] = pd.to_numeric(data['PPGENDER'], errors='coerce')

data = data.dropna()

In[8]: data['age_group'] = pd.qcut(data['PPAGE'], 3, labels=['young', 'middle', 'old'])

In[9]:

print(data.columns) print(data['age_group'].value_counts())

Output:

Index(['PPAGE', 'PPWORK', 'PPGENDER', 'age_group'], dtype='object') young 813 old 746 middle 735 Name: age_group, dtype: int64

In[10]:

import statsmodels.api as sm import statsmodels.formula.api as smf

model = smf.ols('PPWORK ~ C(age_group) * C(PPGENDER)', data=data).fit() anova_table = sm.stats.anova_lm(model, typ=2)

print(anova_table)

Output:

sum_sq df F PR(>F) C(age_group) 1110.717147 2.0 135.432220 2.579881e-56 C(PPGENDER) 91.689438 1.0 22.359796 2.398096e-06 C(age_group):C(PPGENDER) 46.200673 2.0 5.633351 3.626358e-03 Residual 9382.260831 2288.0 NaN NaN

Screenshot of the Code:

Interpretation:

The ANOVA results showed a significant main effect of age group on work status (F = 135.43, p < 0.001) and gender on work status (F = 22.36, p < 0.001). Importantly, the interaction between age group and gender was also statistically significant (F = 5.63, p = 0.0036), indicating that the relationship between age group and work status differs depending on gender. This confirms that gender acts as a moderator in the relationship between age and work status.

The correlation analysis supports this finding. The overall correlation between age and work status was moderate (r = 0.26). However, when separated by gender, the relationship was stronger for males (r = 0.34) compared to females (r = 0.20), demonstrating that the strength of the association varies across gender groups.

A Pearson correlation coefficient was computed to assess the linear relationship between age and school year among participants in the dataset. The analysis was conducted using cleaned numeric values, excluding missing data. A scatter plot was also generated to visually inspect the relationship between the two variables.

Code:

In[1]:

import pandas as pd

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

In[2]:

age = pd.to_numeric(df['age'], errors='coerce') sch_year = pd.to_numeric(df['SCH_YR'], errors='coerce')

In[3]:

clean_data = pd.DataFrame({ 'age': age, 'SCH_YR': sch_year }).dropna()

In[4]:

r = clean_data['age'].corr(clean_data['SCH_YR']) print("Correlation (r):", r)

Output: Correlation (r): -0.008887245841815121

In[5]:

r_squared = r**2 print("R-squared:", r_squared)

Output: R-squared: 7.898313865286016e-05

For Scatter Plot:

In[6]:

import pandas as pd import matplotlib.pyplot as plt

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

age = pd.to_numeric(df['age'], errors='coerce') sch_year = pd.to_numeric(df['SCH_YR'], errors='coerce')

clean_data = pd.DataFrame({ 'age': age, 'SCH_YR': sch_year }).dropna()

plt.figure(figsize=(8,5)) plt.scatter(clean_data['age'], clean_data['SCH_YR'], alpha=0.5)

plt.xlabel("Age") plt.ylabel("School Year") plt.title("Scatter Plot: Age vs School Year")

plt.grid(True) plt.show()

Output:

Sceenshot of Code:

Interpretation:

The Pearson correlation coefficient between age and school year was r = -0.009, indicating an extremely weak and negligible negative linear relationship. This value is effectively zero, showing no meaningful linear association between age and school year in the dataset.

The coefficient of determination (R² ≈ 0.00008) suggests that age explains virtually none of the variation in school year, meaning it has no predictive value for this variable in a linear sense.

The scatter plot confirms this result by showing a widely dispersed pattern with no observable linear trend.

Since this analysis involves a single pairwise relationship between two continuous variables, no post hoc analysis is required, as post hoc testing is only applicable in multi-group comparisons (e.g., ANOVA) where multiple pairwise differences are evaluated after a significant overall test.

Mars crater sizes vary across hemispheres, and a chi-square test with post hoc comparisons helps reveal where those differences actually show up between size groups.

Code:

In[1]:

import os print(os.listdir())

import pandas as pd

df = pd.read_csv("marscrater_pds.csv") df.head()

Output:

['_5e80885b18b2ac5410ea4eb493b68fb4_gapminder.csv', 'marscrater_pds.csv', 'Untitled3.ipynb', 'Untitled1.ipynb', '.ipynb_checkpoints', 'README.ipynb', 'Test01.ipynb', 'Untitled.ipynb', 'Getting Started with Your Lab.ipynb', 'Untitled2.ipynb', 'gapminder.csv.csv'] CRATER_IDCRATER_NAMELATITUDE_CIRCLE_IMAGELONGITUDE_CIRCLE_IMAGEDIAM_CIRCLE_IMAGEDEPTH_RIMFLOOR_TOPOGMORPHOLOGY_EJECTA_1MORPHOLOGY_EJECTA_2MORPHOLOGY_EJECTA_3NUMBER_LAYERS001-00000084.367108.74682.100.220101-000001Korolev72.760164.46482.021.97Rd/MLERSHuBL3201-00000269.244-27.24079.630.090301-00000370.107160.57574.810.130401-00000477.99695.61773.530.110

In[2]:

df['LATITUDE_CIRCLE_IMAGE'] = pd.to_numeric(df['LATITUDE_CIRCLE_IMAGE'], errors='coerce')

df['HEMISPHERE'] = df['LATITUDE_CIRCLE_IMAGE'].apply( lambda x: 'North' if x >= 0 else 'South' )

In[3]:

df['DIAM_CIRCLE_IMAGE'] = pd.to_numeric(df['DIAM_CIRCLE_IMAGE'], errors='coerce')

df['diam_group'] = pd.qcut(df['DIAM_CIRCLE_IMAGE'], 3, labels=['Small','Medium','Large'])

In[4]: df = df.dropna(subset=['HEMISPHERE', 'diam_group'])

In[5]:

import pandas as pd from scipy.stats import chi2_contingency

table = pd.crosstab(df['HEMISPHERE'], df['diam_group'])

print(table)

chi2, p, dof, expected = chi2_contingency(table)

print("\nChi-square:", chi2) print("p-value:", p)

Output:

diam_group Small Medium Large HEMISPHERE North 50305 52309 48280 South 79418 74922 79109 Chi-square: 294.7298418602536 p-value: 1.0005251593400214e-64

In[6]:

if p < 0.05: print("Significant relationship between hemisphere and crater size.") else: print("No significant relationship.")

Output: Significant relationship between hemisphere and crater size.

In[7]:

import itertools

categories = df['diam_group'].unique()

for pair in itertools.combinations(categories, 2): subset = df[df['diam_group'].isin(pair)] table = pd.crosstab(subset['HEMISPHERE'], subset['diam_group'])chi2, p, dof, exp = chi2_contingency(table) print(f"\nComparison: {pair}") print("p-value:", p)

Output:

Comparison: ('Large', 'Medium') p-value: 9.417245941573836e-62 Comparison: ('Large', 'Small') p-value: 4.655108487337578e-06 Comparison: ('Medium', 'Small') p-value: 1.3956409899865248e-33

For Histogram Analysis:

In[8]:

import seaborn as sns import matplotlib.pyplot as plt

size_col = [col for col in df.columns if 'diam' in col.lower()][0]

plt.figure(figsize=(10,6))

sns.distplot(df[size_col], bins=60, kde=True)

plt.title("Distribution of Mars Crater Sizes") plt.xlabel("Diameter") plt.ylabel("Frequency")

plt.show()

Output:

In[9]:

import matplotlib.pyplot as plt

table.plot(kind='bar', stacked=True, figsize=(10,6))

plt.title("Relationship between Crater Size Group and Density Group") plt.xlabel("Crater Size Group") plt.ylabel("Count")

plt.legend(title="Density Group") plt.tight_layout()

plt.show()

Output:

In[10]:

import seaborn as sns import matplotlib.pyplot as plt

plt.figure(figsize=(8,6))

sns.heatmap(table, annot=True, fmt="d", cmap="Blues")

plt.title("Chi-Square Contingency Table Heatmap") plt.xlabel("Density Group") plt.ylabel("Crater Size Group")

plt.show()

Output:

Screenshot of the Code:

Interpretation:

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: