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(This article was first published on <strong><a href="https://xianblog.wordpress.com/2018/03/28/a-null-hypothesis-with-a-99-probability-to-be-true/"> R – Xi'an's Og</a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<p><strong><a rel="nofollow" href="https://xianblog.files.wordpress.com/2018/03/xvaledst3.jpg" target="_blank"><img data-orig-file="https://xianblog.files.wordpress.com/2018/03/xvaledst3.jpg" data-orig-size="480,480" data-medium-file="https://xianblog.files.wordpress.com/2018/03/xvaledst3.jpg?w=300" data-attachment-id="35722" data-image-meta="{" data-image-description="" src="https://xianblog.files.wordpress.com/2018/03/xvaledst3.jpg?w=450&h=450&fit=450%2C450&resize=450%2C450" data-permalink="https://xianblog.wordpress.com/2018/03/28/a-null-hypothesis-with-a-99-probability-to-be-true/xvaledst3/" data-large-file="https://xianblog.files.wordpress.com/2018/03/xvaledst3.jpg?w=450&amp;h=450&amp;fit=450%2C450&amp;resize=450%2C450" alt="" data-image-title="xvaledSt3" sizes="(max-width: 450px) 100vw, 450px" width="450" data-comments-opened="1" class="wp-image-35722" data-recalc-dims="1" height="450"></a>W</strong>hen checking the <a rel="nofollow" href="https://stats.stackexchange.com/q/336050/7224" target="_blank">Python t distribution random generator</a>, np.random.standard_t(), I came upon <a rel="nofollow" href="https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.random.standard_t.html#numpy.random.standard_t" target="_blank">this manual page</a>, which actually does not explain how the random generator works but spends instead the whole page to recall Gosset’t test, illustrating its use on an energy intake of 11 women, but ending up misleading the readers by interpreting a .009 one-sided p-value as <a rel="nofollow" href="https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.random.standard_t.html#numpy.random.standard_t" target="_blank">meaning</a> “the null hypothesis [of the hypothesised mean] has a probability of about 99% of being true”! Actually, <a rel="nofollow" href="https://stackoverflow.com/q/24067996/1154578" target="_blank">Python’s standard deviation estimator x.std()</a> also also returns by default a non-standard standard deviation, dividing by n rather than n-1…</p>
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