Trend Analysis Guide#

Overview#

Trend analysis determines whether a time series shows a statistically significant long-term increase or decrease. This guide covers both parametric (linear regression) and non-parametric (Sen's slope) methods.

Parametric Method: Linear Regression#

Linear regression fits a straight line to the data and tests if the slope is significantly different from zero.

python

from scipy import stats

slope, intercept, r_value, p_value, std_err = stats.linregress(years, values)

print(f"Slope: {slope:.2f} units/year")
print(f"p-value: {p_value:.2f}")

Assumptions#

• Linear relationship between time and variable
• Residuals are normally distributed
• Homoscedasticity (constant variance)

Non-Parametric Method: Sen's Slope with Mann-Kendall Test#

Sen's slope is robust to outliers and does not assume normality. Recommended for environmental data.

python

import pymannkendall as mk

result = mk.original_test(values)

print(result.slope)  # Sen's slope (rate of change per time unit)
print(result.p)      # p-value for significance
print(result.trend)  # 'increasing', 'decreasing', or 'no trend'

Comparison#

MethodProsConsLinear RegressionEasy to interpret, gives R²Sensitive to outliersSen's SlopeRobust to outliers, no normality assumptionSlightly less statistical power

Significance Levels#

p-valueInterpretationp < 0.01Highly significant trendp < 0.05Significant trendp < 0.10Marginally significantp >= 0.10No significant trend

Example: Annual Precipitation Trend#

python

import pandas as pd
import pymannkendall as mk

# Load annual precipitation data
df = pd.read_csv('precipitation.csv')
precip = df['Precipitation'].values

# Run Mann-Kendall test
result = mk.original_test(precip)
print(f"Sen's slope: {result.slope:.2f} mm/year")
print(f"p-value: {result.p:.2f}")
print(f"Trend: {result.trend}")

Common Issues#

IssueCauseSolutionp-value = NaNToo few data pointsNeed at least 8-10 yearsConflicting resultsMethods have different assumptionsTrust Sen's slope for environmental dataSlope near zero but significantLarge sample sizeCheck practical significance

Best Practices#

• Use at least 10 data points for reliable results
• Prefer Sen's slope for environmental time series
• Report both slope magnitude and p-value
• Round results to 2 decimal places