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<title>Maik Thalmann&#39;s blog</title>
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<description>A blog on experimental linguistics with a focus on statistical methods</description>
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  <title>The likelihood principle, stopping rules, and \(p\)-values</title>
  <dc:creator>Maik Thalmann</dc:creator>
  <link>https://maikthalmann.com/posts/2026-03-29_likelihood-principle/</link>
  <description><![CDATA[ In this post, I will merely be rehashing, to the best of my ability, the well-known issue of the likelihood principle and the question of what <img src="https://latex.codecogs.com/png.latex?p">-values have to do with it. ]]></description>
  <guid>https://maikthalmann.com/posts/2026-03-29_likelihood-principle/</guid>
  <pubDate>Sat, 28 Mar 2026 23:00:00 GMT</pubDate>
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  <title>The case for precise hypotheses</title>
  <dc:creator>Maik Thalmann</dc:creator>
  <link>https://maikthalmann.com/posts/2026-02-24_hypothesis-plots/hypothesis-plots.html</link>
  <description><![CDATA[ We know in advance that the null hypothesis of zero effect and zero systematic error is false. This is often brought up as one of the first criticisms of the null hypothesis significance testing approach, but there is an additional error with the logic of null hypothesis significance testing. Typically, the process of hypothesis testing in this framework depends only on a precise null hypothesis, i.e., <img src="https://latex.codecogs.com/png.latex?%5Ctheta%20=%200"> for some mean difference, and not on any specific alternative hypothesis, even though we generally could not care less about the null hypothesis (because we know it to be false). We accept an alternative hypothesis simply when <img src="https://latex.codecogs.com/png.latex?%5Ctheta%20%5Cneq%200">. But since in practice we know that the null hypothesis is false from the get go, rejecting that competitor is trivial and uninformative: every effect is different from zero, at least to some minuscule degree. Thus, rejecting the null is simply a question of sample size: at some point, your p-value will clear your <img src="https://latex.codecogs.com/png.latex?%5Calpha"> threshold. Accepting a non-null hypothesis is thus just a matter of time and money under this approach. ]]></description>
  <guid>https://maikthalmann.com/posts/2026-02-24_hypothesis-plots/hypothesis-plots.html</guid>
  <pubDate>Mon, 23 Feb 2026 23:00:00 GMT</pubDate>
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  <title>Biased estimators II: Too many participants</title>
  <dc:creator>Maik Thalmann</dc:creator>
  <link>https://maikthalmann.com/posts/2026-01-31_biased-estimators-2-too-many-participants/</link>
  <description><![CDATA[ In continuation of the post on biased estimators, today we ask: what’s the harm in running what some people call one-shot experiments where you have very few items but many participants? In this blogpost I want to attempt to hint at an answer to this question by simulating loads of data and seeing how well the experimental data recover the features of the distributions we sampled from, i.e., their true values. We will talk about all of this against the backdrop of the previous post on biased estimators where we discussed what happens to our standard deviation estimates in the face of low sample sizes. ]]></description>
  <guid>https://maikthalmann.com/posts/2026-01-31_biased-estimators-2-too-many-participants/</guid>
  <pubDate>Fri, 30 Jan 2026 23:00:00 GMT</pubDate>
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  <title>Biased estimators</title>
  <dc:creator>Maik Thalmann</dc:creator>
  <link>https://maikthalmann.com/posts/2025-12-20_biased-estimators/</link>
  <description><![CDATA[ The plan for today is to talk about an oft-neglected difference between means and standard deviations in statistics. As we will see, while means are relatively immune to over- or undershooting the true value when the sample size is low, standard deviations are a lot less robust in low-n scenarios. In this post, we will focus on seeing this property in simuated data and understanding what this could potentially mean. I will argue that, given the integral role that standard deviations play in inferential statistics,<sup>1</sup> we should be very aware of the detrimental effects of low-n studies. ]]></description>
  <guid>https://maikthalmann.com/posts/2025-12-20_biased-estimators/</guid>
  <pubDate>Fri, 19 Dec 2025 23:00:00 GMT</pubDate>
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