Formulas used
a = ȳ − b x̄
R² = 1 − SSE / Σ((y − ȳ)²)
Percent change = (y_last − y_first) / y_first × 100
CAGR% = ((y_last / y_first)^(1/(k−1)) − 1) × 100
z = b / SE(b)
p = 2(1 − Φ(|z|))
p = Σaᵢ / Σnᵢ
Z = Σ(sᵢ(aᵢ − nᵢp)) / √(p(1−p)(Σ(nᵢsᵢ²) − (Σ(nᵢsᵢ))²/Σnᵢ))
How to use this calculator
- Select Metric type that matches your survey output.
- Enter at least three waves with labels, values, and sample sizes.
- Set a moving average window to reduce wave-to-wave noise.
- Press Submit to display results above the form.
- Use Download CSV or Download PDF in the results panel.
- Review design factors like weighting, mode changes, and sampling.
Why trend analysis matters in tracking programs
Survey programs often move in small steps, so single-wave comparisons can mislead. This calculator summarizes direction using a fitted line across waves, helping teams separate real movement from routine sampling noise. When waves are quarterly, a slope of 0.08 points per wave implies about 0.32 points per year on a 1–5 index. Combining slope, residuals, and moving averages gives a clearer story for stakeholders.
Interpreting slope, R², and practical change
The slope estimates average change per wave, while R² indicates how consistently the line explains variation. An R² near 0.70 suggests the trend explains most movement, whereas 0.10 signals volatility or mixed drivers. The dashboard also reports first-to-last absolute and percent change. For example, moving from 58% to 64% favorable is a 6-point lift and about 10.34% relative growth.
Using sample size to judge stability
Each wave’s n affects how reliable changes appear. With n around 400, the standard error for a 60% proportion is roughly √(p(1−p)/n) ≈ 2.45 percentage points, so small swings may be expected. If n varies widely, interpret waves with lower n cautiously and rely more on the overall line and moving average to reduce overreaction.
When to use proportion trend testing
For percentage metrics, the calculator approximates successes and applies a monotonic trend test across ordered waves. This is useful for customer satisfaction, awareness, or compliance rates where outcomes are binomial. It also compares the first and last wave with a pooled-variance z test. A p-value below 0.05 can indicate statistical evidence of change, but practical impact and design effects still matter.
Operational tips for cleaner reporting
Keep wave spacing consistent, document questionnaire changes, and apply the same weighting rules each cycle. Use a moving average window of 3 for quarterly tracking and 4 for monthly pulses to smooth short-term shocks. Export the results table to share regression outputs, predicted values, and residuals in review decks. Finally, pair the trend numbers with subgroup cuts to ensure overall improvements are not hiding declines in key segments. If a wave is an outlier, investigate fieldwork timing, channel mix, and incentive changes before treating it as a permanent shift for action.
FAQs
1) What does the slope represent?
The slope is the average change per wave based on the fitted line. A positive slope indicates improvement over time, while a negative slope indicates decline.
2) How should I use R²?
R² shows how well the trend line explains variation across waves. Higher values indicate a steadier trend, while low values suggest volatility or mixed drivers.
3) Why does the calculator ask for sample size?
Sample size helps you judge stability and interpret swings. Larger n generally reduces sampling noise, making small changes more trustworthy.
4) When should I choose the proportion option?
Use it for percentage outcomes such as favorable, aware, or compliant. The tool estimates successes and provides a monotonic trend test plus an endpoint comparison.
5) What moving average window is recommended?
For quarterly tracking, a window of 3 is common. For monthly pulses, 4 can smooth short-term shocks while preserving real directional change.
6) Can I compare waves with different questionnaires?
You can, but interpret cautiously. Questionnaire, mode, or weighting changes can create artificial breaks. Document changes and consider analyzing pre-change and post-change periods separately.