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In experimental research, reproducibility is paramount. When a result is obtained, the critical question is whether it can be replicated under the same conditions. Repeatability measures the probability of a successful repeat, and it is most commonly quantified using the standard deviation (SD) or, more precisely, the standard deviation of the mean (SDM). By dividing the SD by the square root of the sample size, SDM provides a tighter estimate of the variability that would be observed if the experiment were repeated many times.
Reliable repeatability analysis requires that the same procedure be performed multiple times, ideally by the same researcher, with identical materials, instruments, and environmental settings. After collecting all observations, the following statistics are computed:
A smaller SD or SDM indicates higher repeatability and, consequently, greater confidence in the experimental findings.
A company developing a bowling‑ball launcher claims the device delivers the ball exactly to the distance set on its dial. Researchers set the dial to 250 ft and performed eight trials, retrieving and re‑launching the ball each time to control for weight differences and verifying wind speed before each launch. The recorded distances were: 250, 254, 249, 253, 245, 251, 250, and 248 ft.
1. Compute the mean: (250 + 254 + 249 + 253 + 245 + 251 + 250 + 248) ÷ 8 = 250 ft.
2. Calculate the sum of squared deviations: (0² + 4² + (–1)² + 3² + (–5)² + 1² + 0² + (–2)²) = 56.
3. Determine the standard deviation: √(56 ÷ (8 – 1)) = 2.83 ft.
4. Compute the standard deviation of the mean: 2.83 ÷ √8 ≈ 1.00 ft.
An SD or SDM of zero would indicate perfect consistency. In this case, the SDM of 1 ft reflects a small but non‑zero variability. Whether this level of repeatability meets the company's standards depends on its quality criteria.
