What does this report measure?

It measures the crown ratio C = (H−h)/H in 5 mango trees to test if the mean is statistically equivalent to the mathematical value √2−1 within a margin Δ=±0.03.

Statistical Analysis Report — Testing Crown Ratio Equivalence with Reference Value √2−1

Researcher: Abdulla Mohammed Nasser Al-Jabri

Location: Sho'ub, Sana'a, Yemen

Measurement Date: 2026-10-14

1. Data Source and Measurement Protocol

Tool: Metal measuring tape (direct vertical measurement from ground level to the top of the tree).
H (Total Height): Vertical distance from the ground to the highest point in the crown.
h (First Main Branch Height): Height of the first clear split of the trunk into two main branches, each at least 30% of the original trunk diameter.
Sample Size: n = 5 separate mango trees at the same site.
Original Readings: Preserved exactly as recorded from the field, without modification.

2. Raw Data

Tree	H (m)	h (m)	C = (H−h)/H
1	7.80	4.50	0.42308
2	8.50	5.00	0.41176
3	7.20	4.20	0.41667
4	9.00	5.40	0.40000
5	7.50	4.40	0.41333

3. Descriptive Statistics

Measure	Value
Mean	0.41297
Standard Deviation (SD)	0.00845
Standard Error (SE)	0.00378
90% Confidence Interval	[0.40491, 0.42102]

4. Statistical Equivalence Test (TOST)

The Two One-Sided Tests (TOST) equivalence test was used to compare the mean crown ratio against the reference value √2 − 1 ≈ 0.414214.

Practical Equivalence Margin: Δ = 0.03.
Significance Level: α = 0.05.
Equivalence Interval: [0.384214, 0.444214].
Equivalence Test Value: p_TOST ≈ 0.000801.

Statistical Decision: We reject the null hypothesis, and the results support the statistical equivalence of the mean crown ratio with the reference value within the specified equivalence margin.

5. Conclusion and Limitations

This conclusion is conditional on the suitability of the statistical assumptions. Given the small sample size and single location, the results are insufficient to establish a general geometric law. Replication with a larger sample is recommended.

Note on Pre-registration: There is no dated record proving that the hypothesis was registered prior to data collection. Therefore, the results are presented as an exploratory analysis, and are not claimed to be a pre-registered confirmatory test.