Calculating sample size for logistic regression taking statistical power into account These approximations depend on the normal distribution. The percentage of observations with X1 1.Odds ratio: The ratio between the probability that Y=1, when X1 =1 and the probability that Y=1 when X1 =0.P1 (alternative probability): The probability that Y=1 when X1 =1. ![]() P0 (baseline probability): The probability that Y=1 when X1=0.If X1 is binary and follow a binomial distribution. The R² obtained with a regression between X1 and all the other explanatory variables included in the model.Odds ratio: The ratio between the probability that Y=1, when X1 is equal to one standard deviation above its mean and the probability that Y=1 when X1 is at its mean value.P1 (alternative probability): The probability that X1 be equal to one standard error above its mean value, all other explanatory variables being at their mean value.P0 (baseline probability): The probability that Y=1 when all explanatory variables are set to their mean value.If X1 is quantitative and has a normal distribution, the parameters of the approximation are: Power is computed using an approximation which depends on the type of variable. That means that the X1 explanatory variable has no effect on the model.Ĭalculation of the statistical power for logistic regression P is equal to: P = exp(β0 + β1X1 + … + βkXk) / We have: log(P/(1-P)) = β0 + β1X1 + … + βkXk The test used in XLSTAT-Power is based on the null hypothesis that the β1 coefficient is equal to 0. In the general framework of logistic regression model, the goal is to explain and predict the probability P that an event appends (usually Y=1). The main application of power calculations is to estimate the number of observations necessary to properly conduct an experiment. The statistical power calculations are usually done before the experiment is conducted. For a given power, it also allows to calculate the sample size that is necessary to reach that power. The XLSTAT-Power module calculates the power (and beta) when other parameters are known. We therefore wish to maximize the power of the test. The power of a test is calculated as 1-beta and represents the probability that we reject the null hypothesis when it is false. We cannot fix it up front, but based on other parameters of the model we can try to minimize it. In fact, it represents the probability that one does not reject the null hypothesis when it is false. The type II error or beta is less studied but is of great importance. It is set a priori for each test and is 5%. It occurs when one rejects the null hypothesis when it is true. The null hypothesis H0 and the alternative hypothesis Ha.When testing a hypothesis using a statistical test, there are several decisions to take: XLSTAT-Power estimates the power or calculates the necessary number of observations associated with this model. XLSTAT-Base offers a tool to apply logistic regression. ![]() E.g., " Accounting for a potential attrition rate of 20% based on previous research (see reference ), an additional # participants will be recruited"].Statistical Power for Logistic regression Try to include a reference to justify this increased sample size. In your research proposal / ethics application you may want to increase your proposed sample size to account for potential attrition. I recommend reporting the results of each power analysis and then selecting the larger sample size needed from among them as a basis of recruitment.įor analysis that compares groups, be sure to include the number of participants required per group (e.g., "G*Power suggests we would need # participants per group ( N = #) in an independent samples t-test"). If you have multiple hypotheses that each require different data analysis strategies (e.g., Hypothesis 1 is to be tested using correlation Hypothesis 2 is to be tested using a multiple regression), you may need to perform a separate power analysis for each hypothesis.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |