SPSSS Andy Field Chapter 5 - 9 Summary

SPSSS Andy Field Ch. 5 - 9 SPSSS Andy Field Ch. 5 - 9 SPSSS Andy Field – summary Chapter 5 Bias = Things that lead us to a wrong conclusion. When we estimate a parameter we compute an estimate of how well it represents the population, such as a standard error or confidence intervals, or test statistics and their associated probabilities. Assumption = a condition that ensures that what you’re attempting to do works. When the assumption is not met, it is called a violation. The main assumptions we look at are (1) additivity and linearity, (2) normality, (3) homoscedasticity, and (4) independence. Outlier = a score very different from the rest of the data. An outlier can bias a parameter estimate, such as decreasing or increasing the mean. Outliers also affect the sum of squared error dramatically, because we use squared errors, so any bias created by the outlier is magnified by the fact that deviations are squared. If the sum of squared errors is biased, so are the standard error and the confidence intervals. The assumption of additivity and linearity means that the outcome variable is, in reality, linearly related to any predictors (i.e. a straight line). If this assumption is not true, even if all other assumptions are not met, your model is invalid. The normal distribution is valid to: 1. Parameter estimates: parameters (such as a mean) are affected by nonnormal distributions (such as outliers). It depends on the parameter how much they are biased, a median is less biased by a skewed distribution than the mean. 2. Confidence intervals: the standard normal distribution is used to compute the confidence intervals around a parameter estimate. 3. Null hypothesis significance testing: to test a hypothesis we use the normal distribution, because we assume the parameter has a normal distribution. 4. Errors: any model we fit include some error. These residuals need to be normally distributed The assumption of normality: The estimate of the confidence interval needs to come from a normal distribution, and the sampling distribution must be normal, and the estimates of the parameters must be normal. (This is not the same as that the data needs to be normally distributed). The central limit theorem revisited: As our sample sizes get bigger the sampling distributions become more normal, up to point at which the sample is big enough that the sampling distribution is normal. This is the central limit theorem: regardless of the shape of the population, parameter estimates of that population will have a normal distribution provided the samples are big enough. The central limit theorem means that there are a variety of situations in which we can assume normality regardless of the shape of our sample data. If our sample is large enough we do not need to worry about the assumption of normality. If you want to estimate parameters of your model then normality doesn’t really matter. Homoscedasticity: assume that each of the samples come from populations with the same variance. We have to assume homoscedasticity in order to make sure our estimates of the parameters that define our model and our significance test are accurate. Example: 10 people are on tour with the loudest band and are measured for how many hours after the concert these people had ringing in their ears. The scores are presented by dots in a graph and the means are presented by blocks. In case there is homoscedasticity the circles will lay around the dots every time the score is measured. In case there is no homoscedasticity (thus, heteroscedascitiy) the dots do not lay equally around the blocks, but differ along the y-axis (see page 175 for the example graphs). If variances for the outcome variable differ along the predictor variable then the estimates of the parameters within the model will not be optimal. Heteroscedascitity creates a bias and inconsistency in the estimate of the standard error. Independence: this assumption means that the errors in your model are not related to each other. Example: Paul and Julie need to answer whether they have seen certain photos before. In case they are not able to confer, the scores will be independent. A histogram or a boxplot is an easy way to spot outliers.