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| courses:ast201:3 [2023/10/22 05:30] – [5. Propagation] asad | courses:ast201:3 [2023/10/22 05:37] (current) – [2. Population and sample] asad | ||
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| ^ Astronomer ^ Precision ^ Accuracy ^ Decision ^ | ^ Astronomer ^ Precision ^ Accuracy ^ Decision ^ | ||
| - | | A | Precise | Accurate | Evacuate | | + | | A (cyan) |
| - | | B | Precise | Inaccurate | Stay | | + | | B (magenta) |
| - | | C | Imprecise | Accurate | Uncertain | | + | | C (yellow) |
| - | | D | Imprecise | Inaccurate | Uncertain | | + | | D (black) |
| Systematic errors are more important and dangerous for astronomy than stochastic errors. Astronomers A and B have the same precision, but after all the measurements B realizes that her values differ from the values of everyone else and, hence, unlikely to be true. Another reason for her inaccuracy is that her deviation from others is much greater than her precision. Astronomer C sees a systematic errors in his stochastic errors because his values decrease with time predictably. | Systematic errors are more important and dangerous for astronomy than stochastic errors. Astronomers A and B have the same precision, but after all the measurements B realizes that her values differ from the values of everyone else and, hence, unlikely to be true. Another reason for her inaccuracy is that her deviation from others is much greater than her precision. Astronomer C sees a systematic errors in his stochastic errors because his values decrease with time predictably. | ||
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| [[https:// | [[https:// | ||
| - | In this example, the velocities of 50 stars perpendicular to the Galactic plane are plotted as a bar-chart histogram. The stars are divided into two sets: 25 stars are iron-rich and the other 25 stars are iron-poor. The iron-poor stars have a greater dispersion of velocities as evident from the plot. The mean and the standard deviation are shown as vertical lines and shades, respectively. | + | In this example, the velocities of 50 stars perpendicular to the [[uv:mw|Galactic plane]] are plotted as a bar-chart histogram. The stars are divided into two sets: 25 stars are iron-rich and the other 25 stars are iron-poor. The iron-poor stars have a greater dispersion of velocities as evident from the plot. The mean and the standard deviation are shown as vertical lines and shades, respectively. |
| Standard deviation is sometimes better than variance in describing physical phenomena because $\sigma$ has the same unit as $\mu$, but the units are squared in $\sigma^2$ statistic. In this example, the variance among iron-rich stars is $57.25$ km$^2$ s$^{-2}$ whereas the standard deviation is $7.57$ km s$^{-1}$. | Standard deviation is sometimes better than variance in describing physical phenomena because $\sigma$ has the same unit as $\mu$, but the units are squared in $\sigma^2$ statistic. In this example, the variance among iron-rich stars is $57.25$ km$^2$ s$^{-2}$ whereas the standard deviation is $7.57$ km s$^{-1}$. | ||
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| $$ \sigma^2 = \sum_{i=1}^n \left(\frac{\partial G}{\partial x_i}\right)^2 \sigma_i^2 + \mathcal{C} $$ | $$ \sigma^2 = \sum_{i=1}^n \left(\frac{\partial G}{\partial x_i}\right)^2 \sigma_i^2 + \mathcal{C} $$ | ||
| - | where $\mathcal{C}$ is the [[uv: | + | where $\mathcal{C}$ is the [[uv: |
courses/ast201/3.1697974222.txt.gz · Last modified: 2023/10/22 05:30 by asad