class: center, middle, inverse, title-slide .title[ # Common Statistical Errors ] .author[ ### Yue Jiang ] .date[ ### STA 583 / Workshop 1 / Spring 2025 ] --- ### GitHub Entry Code <br><br><br><br> .center[ **4JBD87** ] --- ### Warm-up activity <img src="img/persimmon.png" width="80%" style="display: block; margin: auto;" /> --- ### Project option 1 <img src="img/lofex.png" width="80%" style="display: block; margin: auto;" /> --- ### Project option 2 <img src="img/nba.png" width="80%" style="display: block; margin: auto;" /> --- ### Project option 3 <img src="img/durham.jpg" width="80%" style="display: block; margin: auto;" /> --- ### Project option 4 <img src="img/names.png" width="80%" style="display: block; margin: auto;" /> --- ### Heavy metal exposure and reaction time <img src="img/int8.png" width="100%" style="display: block; margin: auto;" /> --- ### Heavy metal exposure and reaction time <img src="img/int9.png" width="100%" style="display: block; margin: auto;" /> .question[ Critique the following conclusion: ] > *There is a 58% chance that the results we observe for the model involving lead arose due to chance alone. Since this is so high, we conclude that this is an insignificant result: there is no association between cadmium exposure and reaction time (adjusting for age and sex), with there being a 95% chance that the slope is between -11.47 and 20.30.* --- ### Interpreting p-values .vocab[p-values do **not** allow you to make affirmative statements about the null hypothesis] Absence of evidence is not evidence of absence; moreover, you don't even have the ability to measure evidence "in favor" of the null at all! .vocab[p-values **cannot** be interpreted as the probability that "the results arose from random chance alone"] p-values do not give any information by the mechanism by which observed results arose; they are simply conditional probabilities of *observing* such results under a specific assumption about the parameters. .vocab[p-values should **not** be used to gauge real-world, scientific, or clinical significance] (see board for a few demonstrations of this fact) --- ### What is a confidence interval anyway? <img src="img/confidence.png" width="80%" style="display: block; margin: auto;" /> .center[(check out the interactive demonstration [here](https://digitalfirst.bfwpub.com/stats_applet/stats_applet_4_ci.html))] --- ### Be careful with study design! Researchers are interested in the special population of HIV+ women on antiretroviral therapy in sub-Saharan Africa. They would like to know whether in this population, a new pregnancy is related to the probability of having an AIDS-defining event (that is, their HIV being classified as AIDS). To test for an association, they recruit women from a large network of health care clinics and find the following: | | AIDS progression | No AIDS progression| | ------------- | :-----: | :-----:| | Pregnant | 31 | 44 | | Not Pregnant | 124 | 99 | .question[ Conduct an appropriate hypothesis test and calculate an odds ratio (and 95% CI). What is your conclusion? ] --- ### Pregnancy, HIV, and AIDS Consider the following data, which is for all HIV+ women in the area, not just those who visited a clinic: | | AIDS progression | No AIDS progression| | ------------- | :-----: | :-----:| | Pregnant | 44 | 175 | | Not Pregnant | 248 | 990 | .question[ Calculate the same odds ratio as before and associated 95% CI using these data. What might you conclude? How might you explain this? ] --- ### Pregnancy, HIV, and AIDS The original sample was collected due to easier data collection (the women are already in the clinic). However, this is problematic since not all HIV+ women are equally likely to visit a health clinic: | | Visited clinic | Did not visit clinic | | ------------- | :-----: | :-----:| | Pregnant + AIDS | 31 | 13 | | Pregnant only | 44 | 131 | | AIDS only | 124 | 124 | | Neither | 99 | 891 | This is an example of a .vocab[selection bias]; our original sample was not representative of the intended target population of interest.