![]() ![]() This contribution aims to remind readers what power analysis is, emphasize why it matters, and articulate when and how it should be used. It takes more than a single number, and it’s not “the effect of X on Y,” but sometimes it’s a better way to communicate what is really going on, especially to non-research audiences.Power analysis is an important tool to use when planning studies. You can’t use a single number on the probability scale to convey the relationship between the predictor and the probability of a response. So if you do decide to report the increase in probability at different values of X, you’ll have to do it at low, medium, and high values of X. Likewise, the difference in the probability (or the odds) depends on the value of X. An odds ratio of 1.08 will give you an 8% increase in the odds at any value of X. The rate stays constant, but the actual amount earned differs based on the amount invested. So at the end of the year, you’ll earn $8 if you invested $100, or $40 if you invested $500. I can tell you that an annual interest rate is 8%. It works exactly the same way as interest rates. Second, when X, the predictor is continuous, the odds ratio is constant across values of X. ![]() These differences in probabilities don’t line up with the p-values in logistic regression models, though. They do this because they’ve been trained to do this in linear models. If you present a table of probabilities at different values of X, most research audiences will, at least in their minds, make those difference comparisons between the probabilities. The probability a person has a relapse in an intervention condition compared to the control condition makes a lot of sense.īut the p-value for that effect is not the p-value for the differences in probabilities. Presenting probabilities without the corresponding odds ratios can be problematic, though.įirst, when X, the predictor, is categorical, the effect of X can be effectively communicated through a difference or ratio of probabilities. The odds ratio is a single summary score of the effect, and the probabilities are more intuitive. This is a great approach to use together with odds ratios. What you can do, and many people do, is to use the logistic regression model to calculate predicted probabilities at specific values of a key predictor, usually when holding all other predictors constant. So if you need to communicate that effect to a research audience, you’re going to have to wrap your head around odds ratios. So while we would love to use probabilities because they’re intuitive, you’re just not going to be able to describe that effect in a single number. The effect of X on the probability of Y has different values depending on the value of X. What that means is there is no way to express in one number how X affects Y in terms of probability. If we try to express the effect of X on the likelihood of a categorical Y having a specific value through probability, the effect is not constant. In regression models, we often want a measure of the unique effect of each X on Y. ![]() For example, in logistic regression the odds ratio represents the constant effect of a predictor X, on the likelihood that one outcome will occur. The problem is that probability and odds have different properties that give odds some advantages in statistics. In either case, without a lot of practice, most people won’t have an immediate understanding of how likely something is if it’s communicated through odds. ![]() I’m not sure if it’s just a more intuitive concepts, or if it’s something were just taught so much earlier so that it’s more ingrained. Although probability and odds both measure how likely it is that something will occur, probability is just so much easier to understand for most of us. Odds ratios are one of those concepts in statistics that are just really hard to wrap your head around. ![]()
0 Comments
Leave a Reply. |