Analysing differences in mutual fund returns across fund types adjusted for market volatility Using One-Way ANOVA

Project info

• Field of studyEconomics and Finance
• LevelUndergraduate thesis (S1)
• Method typeInferential Statistics
• Estimated build time± 3 working days
• Toolsscipy.stats f_oneway, levene, tukey_hsd
• PriceUS$16 - US$106

Research goal

Apply One-Way ANOVA to synthetic data to test differences in mutual fund returns across fund types adjusted for market volatility and conclude on statistical significance.

Variables

Example result

• 6.096F statistic
• 0.001ANOVA p-value
• 0.095Eta squared
• 0.079Omega squared
• 0.416Levene p-value
• 0.847Shapiro p-value

One-way ANOVA on Mutual fund return across 4 groups is significant (F = 6.096, p < 0.001); the eta-squared effect size is 0.095.

Computed from illustrative synthetic data, not from a real study.

About One-Way ANOVA

One-way ANOVA tests whether the means of three or more groups differ significantly. It is used to compare several treatments, followed by post-hoc tests to find which pairs differ.

Steps

1. 1State hypotheses and collect data per group
2. 2Test residual normality and variance homogeneity (Levene)
3. 3Run one-way ANOVA
4. 4If significant, run Tukey HSD post-hoc
5. 5Compute effect size (eta squared)
6. 6Plot boxplots per group

Assumptions to check

• Residuals are normally distributed
• Group variances are homogeneous
• Observations are independent

Reading and reporting the results

Report F, degrees of freedom, p-value, and eta squared, then the group pairs that differ per Tukey. If variances are not homogeneous, use Welch ANOVA or a nonparametric test.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as st

rng = np.random.default_rng(26)
fund_type = rng.normal(50, 6, 30)   # treatment A
market_volatility = rng.normal(55, 6, 30)   # treatment B
x3 = rng.normal(60, 6, 30)       # treatment C
mutual_fund_return = np.concatenate([fund_type, market_volatility, x3])
groups = [fund_type, market_volatility, x3]

print("Levene p:", round(st.levene(*groups).pvalue, 3))
res = st.f_oneway(*groups)
print("F =", round(res.statistic, 3), "p =", round(res.pvalue, 5))

grand = mutual_fund_return.mean()
ssb = sum(len(g) * (g.mean() - grand) ** 2 for g in groups)
sst = ((mutual_fund_return - grand) ** 2).sum()
print("Eta squared:", round(ssb / sst, 3))

if res.pvalue < 0.05:
    tk = st.tukey_hsd(*groups)
    print(tk)

plt.boxplot(groups)
plt.xticks([1, 2, 3], ["A", "B", "C"])
plt.ylabel("Response")
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions