class: center, middle, inverse, title-slide .title[ # To p or not to p? ] .author[ ### Claus Thorn Ekstrøm<br>UCPH Biostatistics ] .date[ ### May 12th, 2022<br>.small[<a href="mailto:ekstrom@sund.ku.dk" class="email">ekstrom@sund.ku.dk</a> ]<br><svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:steelblue;overflow:visible;position:relative;"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg> <span class="citation">@ClausEkstrom</span> <br> .small[Slides: <a href="https://www.biostatistics.dk/talks/">biostatistics.dk/talks/</a>] ] --- class: animated, fadeIn layout: true ??? This slide defines a default animated fade-in slide transition --- background-image: url("pics/process.png") background-size: 45% background-position: 50% 63% ??? Epistemologi. Videnskab = skab af viden --- class: middle, center, inverse # Quiz --- You want to see if the means of two groups are different. You compare the means statistically and get a ** `\(p\)` value of 0.05** when testing at a **significance level of 0.07**. What is the conclusion? 1. You reject the null hypothesis.<br>Thus you cannot reject that the two population means are the same. 2. You fail to reject the null hypothesis.<br>Thus you cannot reject that the two population means are the same. 3. You reject the null hypothesis.<br>Thus you reject that the two population means are the same. 4. You fail to reject the null hypothesis.<br>Thus you reject that the two population means are the same. 5. Help!! --- --- # Hvad er det nu, at en `\(p\)`-værdi er? > *The `\(p\)` value is the probability of having obtained a result **at least as extreme** as the one found with our sample if the null hypothesis were true.* --- Kirkwood & Sterne -- HVIS nulhypotsen er sand<br> .yellow[OG ALLE ANDRE antagelser *også* er sande]<br> SÅ udtrykker `\(p\)`-værdien sandsynligheden for at observere en teststørrelse, der er mindst lige så ekstrem, som den i din stikprøve. -- `\(p\)`-værdien måler, hvor *overrasket* man er. --- # Hvad er problemet med `\(p\)`-værdier? Forskeren vil typisk gerne have svare på `$$P(H | D)$$` men `\(p\)`-værdien udregner `$$P(D | H)$$` ??? They try to answer the *"wrong"* question They give a very precise answer to the wrong question instead of an approxiomate answer to the right question. --- # `\(p\)`-værdien bruges forkert Som beslutningsregel: `$$p \text{-værdi} \left\{\begin{array}{ll}<0.05 & \text{forkast} - \text{"signifikant"} \\ \geq 0.05 & \text{ikke forkast} - \text{"ikke signifikant"/"ingen association"} \end{array} \right.$$` * Arbitrær tærskel * Signifikant betyder ikke relevant * Ikke-signifikant betyder ikke at `\(H_0\)` er sand eller accepteres. Vi har ikke nok evidens til at forkaste den (*"fraværet af evidens er ikke evidens for fravær"*). ??? "No association" is wrong to say binary thinking makes everything worse in that people inappropriately combine probabilistic statements with Boolean rules. --- background-image: url(pics/tea.png) background-size: 105% --- background-image: url(pics/pvalues.jpg) background-size: 100% --- # `\(p\)`-værdien indeholder to typer information .pull-left[ `\(p\)`-værdien kombinerer *effektstørrelsen* med *stikprøvestørrelsen*. Når `\(N\rightarrow\infty\)` bliver *alt* signifikant. ] .pull-right[ <img src="pics/donkey.jpg" width="100%" /> ] --- # Veterinærstudier og statistik Fra konsultationen: * Lille stikprøve * Gentagne målinger * Studerende som "klemmelus" -- Hvad er forskningsspørgsmålet? --- # Alternativer * Deskriptiv statistik * Eksplorativ statistik * Drop fokus på signifikanstest * Holder antagelserne? * Hvad er effektstørrelsen? * Pilotstudier