200m MLR Estimate

16 April 2019 Formula (19/718 sampled)

\begin{align*}\rm{200m} &\approx \rm{100m} \left[ 1.997383 + \left( \dfrac{7.633557}{\rm{60m}} \right) \right] - 11.1841 \pm 0.3 \\& \approx
\rm{100m} \left[ 2 + \left( \dfrac{7.65}{\rm{60m}} \right) \right] - 11.2 \pm 0.3 \\& \\&
\rm{Conditions:} \\& \\&
(1) \Longrightarrow 1.5 \leq \dfrac{\rm{100m}}{\rm{60m}} \leq 1.56 \\&
(2) \Longrightarrow 0.64 (\rm{100m}) \leq \rm{60m} \leq 0.67 (\rm{100m}) \\& \\& \rm{Using \: (2):} \\& \\& \therefore
2(\rm{100m}) - 0.22 \leq \rm{200m} \leq 2(\rm{100m}) + 0.92 \end{align*}

17 April 2019 Formula (47/718 Sampled)

\begin{align*}
\rm{200m} &\approx \rm{100m} \left[ 2.320164 + \left( \dfrac{7.29805}{\rm{60m}} \right) \right] - 13.85742 \pm 0.3875 \\& \approx
\rm{100m} \left[ 2.32 + \left( \dfrac{7.3}{\rm{60m}} \right) \right] - 13.86 \pm 0.39 \\& \\&
\rm{Conditions:} \\& \\&
(1) \Longrightarrow 1.5 \leq \dfrac{\rm{100m}}{\rm{60m}} \leq 1.56 \\&
(2) \Longrightarrow 0.64 (\rm{100m}) \leq \rm{60m} \leq 0.67 (\rm{100m}) \\& \\& \rm{Using \: (2):} \\& \\& \therefore
2.32(\rm{100m}) - 3.36 \leq \rm{200m} \leq 2.32(\rm{100m}) - 2.06
\end{align*}

19 April 2019 Formula (81/718 Sampled)

\begin{align*}
\rm{200m} &\approx \rm{100m} \left[ 1.88428 - \left( \dfrac{5.65085}{\rm{60m}} \right) \right] + 10.37741 \pm 0.443 \\& \approx
\rm{100m} \left[ 1.89 - \left( \dfrac{5.65}{\rm{60m}} \right) \right] + 10.38 \pm 0.45 \\& \\&
\rm{Conditions:} \\& \\&
(1) \Longrightarrow 1.5 \leq \dfrac{\rm{100m}}{\rm{60m}} \leq 1.56 \\&
(2) \Longrightarrow 0.64 (\rm{100m}) \leq \rm{60m} \leq 0.67 (\rm{100m}) \\& \\& \rm{Using \: (2):} \\& \\& \therefore
1.89(\rm{100m}) - 1.11 \leq \rm{200m} \leq 1.89(\rm{100m}) + 2.4
\end{align*}

Sample Size Timeline

• 16 April 2019
• 19 = 2.65% of TP
• 5% MOE = 34.14% CL
• 1% MOE = 7.22% CL
• R - Squared = 0.467
• Standard Error = 0.3
• 17 April 2019
• 27 = 3.76% of TP
• 5% MOE = 40.36% CL
• 1% MOE = 8.43% CL
• R - Squared = 0.482
• Standard Error = 0.292
• 17 April 2019
• 47 = 6.55% of TP
• 5% MOE = 52.17% CL
• 1% MOE = 11.27% CL
• R - Squared = 0.474
• Standard Error = 0.388
• 19 April 2019
• 81 = 11.28% of TP
• 5% MOE = 66.05% CL
• 1% MOE = 15.15% CL
• R - Squared = 0.182
• Standard Error = 0.443
• ?
• 150 = 20.89% of TP
• 5% MOE = 83.14% CL
• 1% MOE = 21.69% CL
• ?
• 264 = 36.77% of TP
• 5% MOE = 95.9% CL
• 1% MOE = 31.71% CL

REFERENCES

https://www.iaaf.org/records/all-time-toplists/sprints/60-metres/indoor/men/senior?regionType=world&timing=electronic&page=1&bestResultsOnly=true&firstDay=1899-12-30&lastDay=2019-04-14

https://www.omnicalculator.com/statistics/sample-size

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