基于R语言：23个品种高低密度种植发芽试验差异分析咨询

Hey there! Let's walk through how to analyze and visualize the germination rate differences between high-density (32 seeds/plot) and low-density (12 seeds/plot) planting for your 23 varieties, focusing on comparisons by plant.id (your unique variety identifier). Here's a structured approach with actionable steps and code examples:

1. Statistical Analysis Methods #

First, we need to quantify both overall and variety-specific differences between the two densities:

1.1 Descriptive Statistics #

Start by summarizing key metrics for each variety and density combination to spot initial trends. This includes mean germination rate, standard deviation, and sample size.

# Python example with pandas
import pandas as pd

# Load your dataset
df = pd.read_csv("germination_data.csv")

# Calculate descriptive stats grouped by plant.id and density
summary_stats = df.groupby(["plant.id", "density"])["发芽率"].agg(
    mean_germ="mean",
    std_germ="std",
    sample_size="count"
).reset_index()

print(summary_stats)

1.2 Paired Statistical Tests #

Since you're measuring the same variety under two densities, paired t-tests (for normally distributed data) or Wilcoxon signed-rank tests (for non-normal data) are ideal to test if density has a significant effect on germination rate.

from scipy.stats import ttest_rel, wilcoxon

# Reshape data to wide format (one row per variety, two columns for densities)
wide_df = df.pivot(index="plant.id", columns="density", values="发芽率").dropna()

# Paired t-test
t_stat, p_val = ttest_rel(wide_df["高密度"], wide_df["低密度"])
print(f"Paired t-test results: t = {t_stat:.3f}, p-value = {p_val:.4f}")

# If data is non-normal, use Wilcoxon test
w_stat, w_pval = wilcoxon(wide_df["高密度"], wide_df["低密度"])
print(f"Wilcoxon signed-rank test results: W = {w_stat:.3f}, p-value = {w_pval:.4f}")

1.3 Mixed-Effects Model (For Replicated Plots) #

If you have multiple plots per variety-density combination, use a mixed-effects model to account for variability between plots while testing the effect of density, variety, and their interaction:

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

# Model formula: germination rate ~ density + variety + density:variety + (1|plot_id)
model = mixedlm(
    "发芽率 ~ density + variety + density:variety",
    data=df,
    groups=df["plot_id"]  # Replace with your plot identifier column
)
result = model.fit()
print(result.summary())

2. Visualization Approaches #

Visuals will help you communicate differences clearly, both across all varieties and for individual ones:

2.1 Grouped Bar Plot (Variety-by-Density Comparison) #

This plot shows mean germination rate for each variety, with side-by-side bars for high/low density, plus error bars to show variability:

import seaborn as sns
import matplotlib.pyplot as plt

plt.figure(figsize=(14, 8))
sns.barplot(
    data=df,
    x="plant.id",
    y="发芽率",
    hue="density",
    errorbar="sd",  # Shows standard deviation
    palette="Set2"
)
plt.xticks(rotation=45, ha="right")
plt.title("Germination Rate by Variety and Planting Density", fontsize=14)
plt.xlabel("Plant ID (Variety)", fontsize=12)
plt.ylabel("Germination Rate (%)", fontsize=12)
plt.tight_layout()
plt.show()

2.2 High vs Low Density Scatter Plot #

This plot compares each variety's germination rate under both densities. Points above the red dashed line mean higher germination in high density; points below mean better performance in low density:

plt.figure(figsize=(8, 8))
sns.scatterplot(
    data=wide_df,
    x="低密度",
    y="高密度",
    s=100,
    color="teal"
)
# Add reference line (no difference between densities)
plt.plot(
    [wide_df.min().min(), wide_df.max().max()],
    [wide_df.min().min(), wide_df.max().max()],
    "r--",
    label="No Density Difference"
)
plt.title("High Density vs Low Density Germination Rate per Variety", fontsize=14)
plt.xlabel("Low Density Germination Rate (%)", fontsize=12)
plt.ylabel("High Density Germination Rate (%)", fontsize=12)
plt.legend()
plt.grid(alpha=0.3)
plt.tight_layout()
plt.show()

2.3 Box Plot (Overall Density Distribution) #

If you want to see the overall distribution of germination rates across all varieties for each density:

plt.figure(figsize=(8, 6))
sns.boxplot(
    data=df,
    x="density",
    y="发芽率",
    palette="Set1"
)
plt.title("Overall Germination Rate Distribution by Planting Density", fontsize=14)
plt.xlabel("Planting Density", fontsize=12)
plt.ylabel("Germination Rate (%)", fontsize=12)
plt.tight_layout()
plt.show()

Key Notes #

• Check Normality: Before using a paired t-test, verify if your germination rate data is normally distributed (use a Q-Q plot or Shapiro-Wilk test). If not, stick to the Wilcoxon test.
• Sort Visuals: For the grouped bar plot, sort varieties by the difference in germination rates to make patterns easier to spot.
• Highlight Significant Differences: In your visuals, you can add asterisks or annotations to mark varieties where density had a statistically significant effect.

内容的提问来源于stack exchange，提问作者Utsav Kumar