Centering Headers in a Siunitx Column with Uncertainties

Question

I have been stuck on this problem for the last two hours, scouring this forum for any tips. Nothing has worked.
I want to present a table with uncertainties. I am describing the performance of models, so I need to display the standard deviation as a measure of the stability of the models. This is the code I have:
documentclass{article}

usepackage{graphicx,booktabs}
usepackage[separate-uncertainty=true, tight-spacing=true]{siunitx}

begin{document}
    begin{table}
        centering
        caption{Why won't the headers just align to the centre?}
        resizebox{textwidth}{!}{%
            begin{tabular}{%
                    l
                    *{3}{S}[table-format=1.5(5)]
                }
                toprule
                {Thing} & multicolumn{1}{c}{Statistic 1} & multicolumn{1}{c}{Statistic 2} & multicolumn{1}{c}{Statistic 3} 
                midrule
                One thing & 0.77442pm0.00123 & 0.98234pm0.00033 & 0.99971pm0.00011 
                Second thing & 0.46622pm0.04567 & 0.91248pm0.01203 & 0.99925pm0.00022 
                bottomrule
            end{tabular}
        }
    end{table}
end{document}

I had thought this would work, but irritatingly it produces headers that are offset. I added the multicolumn command to try to fix it, but it doesn't work. I had thought it was the uncertainties, so I played around with the table-format option, but nothing seems to do it. The spacing is all off anyway, so I suspect I am doing something stupid.
Does anyone have any ideas?

egreg · Accepted Answer

You want three columns with S[table-format=1.5(5)], but your input actually specifies
SSS[table-format=1.5(5)]

because you have a misplaced }. You want
*{3}{S[table-format=1.5(5)]}

Full code:
documentclass{article}

usepackage{booktabs}
usepackage[separate-uncertainty=true, tight-spacing=true]{siunitx}

begin{document}

begin{table}
centering

caption{The headers align to the centre}

begin{tabular}{%
  l
  *{3}{S[table-format=1.5(5)]} %%% <----- HERE
}
toprule
{Thing} & {Statistic 1} & {Statistic 2} & {Statistic 3} 
midrule
One thing    & 0.77442pm0.00123 & 0.98234pm0.00033 & 0.99971pm0.00011 
Second thing & 0.46622pm0.04567 & 0.91248pm0.01203 & 0.99925pm0.00022 
bottomrule
end{tabular}

end{table}

end{document}

Centering Headers in a Siunitx Column with Uncertainties

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