Hi everybody. This lecture is about alignment of power and data analysis. In life, we all appreciate proper alignment, whether it's poster, car tires, or anything like that. In power analysis, it is no different. So, we're going to talk about alignment in this particular context. We'll learn about what actually needs to be aligned, and we're going to understand why it's important to align our power and our data analysis. Alignment here means our power analysis methods must be similar as our data analysis methods. Usually, researchers will already know what their data analysis plan is going to be. So, you want to consider to make sure power analysis is as similar as possible. This means considering things like the same data collection, scientific goals, hypothesis, analysis, models, tests, and Type I error rates. For example, talking about Type I error rate, if we're going to do a test, all of our hypotheses at 0.05, we've got to calculate the power at 0.05 as well. If you check your power and analysis in your data analysis describe the same experiment, you're in good shape and you've achieved alignment. So, we're going to discuss how to conduct an aligned power analysis through a particular example. The study we'll be using is an example of the same study we've used a couple of times already, the dental example where researchers are testing the effectiveness of a treatment on observed pain over time following a procedure, a longitudinal study of pain recall. As a reminder, here's this scenario. Researchers did a study to test if patients who are instructed to use some kind of sensory focus process had a different pattern of long-term memory of pain than those that did not have the sensory focus. Participants were randomly assigned to either the intervention group or the control group. You may remember that the intervention group consisted of participants listening to specific instructions to pay close attention only to the physical sensations in their mouth during the procedure, while the control group listened to a neutral topic of their procedure unrelated to the physical sensations of their mouth. The null hypothesis is there will be no difference in the pattern of pain over time between groups, that the sensory focus and the control will result in the same pattern of pain over time for participants. Remember, we're not looking at one point in time, but the pattern over time of their long-term memory of pain. So, participants were measured initially following the intervention, three and six months after. This is a longitudinal feature of the study. The goal was to compare the pattern of pain over time for those who received the sensory focus treatment with those who did not. We already discussed the null, and planned analysis was repeated measures ANOVA. I know we don't discuss analysis too often in this course, but this just means that the analysis will account for longitudinal aspects of the multiple measurements over time, and it will compare the treatment group to the control group. So, general linear multivariate model fits this study very well. Repeated measurements of memory of pain was the outcome variable, and the predictors were the groups, treatment and control. This implies using a binary dummy variable that represents one group versus group two. The statistical test was the Hotelling-Lawley test, to test the interaction between the variables, group and time. Researchers use one percent Type I error rate. So, an Alpha was set to 0.01. Here's the flow chart representing how this study was run. There's a randomization of dental patients to start into the sensory focus group or the standard of care group. Then measurements are taken at baseline, six months and twelve months concluding the study. So, what kind of alignment would this study look for? It simply means that pretty much all of the components of the study we just described need to match both the power analysis and the data analysis. As you can see in this table, it means we need the same Type I error rate, hypothesis, analysis plan, statistical model, and more. It is obvious here that the power analysis and the data analysis approach described the same experiment. Now we will talk about some of the ways in which misalignment can occur, resulting in incorrect in power and sample size calculations. First off, you can have the wrong power and sample size for some various reasons. You might be using the wrong criterion. As an example of this, we'll be using a p-value or a Type I error. You might be using a confidence interval which are different approaches to answering the question. One is dependent on power calculation, while the other might be dependent on confidence interval width. You may specify the wrong correlation structure. This could be a result of having imperfect knowledge about how some variables might be correlated or how much decay there is in correlation over time. Another issue could be if you have a mismatch between the hypothesis that's being tested in your analysis and the hypothesis that your power analysis is testing. Here is a table that shows power values multiplied by 100, because we know power is a value between zero and one, based on different hypotheses being tested and different cell sizes used. The take-home message of this table is that, depending on various options you have, as a researcher, the power values can come out very different, showing the importance of misalignment in alignment. If your power analysis is misaligned with your data analysis, your power or sample size values come out very different than it should be. You could see that this table, the power ranges anywhere from 14 percent to 83 percent power depending on how these data are analyzed. It's for various reasons the designs and options that power values fluctuate like this. So, the take-home message is, be careful and make sure you align your power and your data analysis carefully. Let's do a review of alignment. In order to make sure you conduct an accurate power and sample size analysis, you must align your power and data analysis, and make sure they described the same study. Specifically, you need to make sure that your data collection, scientific goals, hypothesis, analysis, statistical model and test, and Type I error rates are the same between power analysis and data analysis. This wraps up this lecture. Thank you for your time.