The Beast of Bias Discovering Statistics（偏见的野兽发现统计数据）.pdf

Exploring Data: The Beast of Bias Sources of Bias A bit of revision. We鈥檝e seen that having collected data we usually fit a model that represents the hypothesis that we want to test. This model is usually a linear model, which takes the form of: outcome = 饊亸饊亸 饊亱饊亱 +饊亸饊亸 饊亱饊亱 鈰€亸饊亸 饊亱饊亱 +error Eq. 1 ! $ $! ! ) )! ! Therefore, we predict an outcome variable, from one or more predictor variables (the Xs) and parameters (the bs in the equation) that tell us something about the relationship between the predictor and the outcome variable. Finally, the model will not predict the outcome perfectly so for each observation there will be some error. When we fit a model, we often estimate the parameters (b) usin the method of least squares (known as ordinary least squares or OLS). We鈥檙e not interested in our sample so much as a general population, so we use the sample data to estimate the value of the parameters in the population (that鈥檚 why we call them estimates rather than values). When we estimate a parameter we also compute an estimate of how well it represents the population such as a standard error or confidence interval. We can test hypotheses about these parameters by computing test statistics and their associated probabilities (p-values). Therefore, when we think about bias, we need to think about it within three contexts: 1. Things that bias the parameter estimates. 2. Things that bias standard errors and confidence intervals. 3. Things that bias test statistics and p-values. T