A statistical test which can be used to ascertain if the difference in outcome scores between values of an explanatory variable are statistically significant. There are several types of t-test, for example an independent t-test coud be used to assess whether males and females differ in their mathematics test score, while a paired t-test might be used to determine whether a group of individuals improved their scores over time. In multiple regression the t-statistic it is used to test whether the regression coefficient for an explanatory variable is significantly different from zero - essentially whether the explanatory variable has any predictive merit or not.
Tolerance is a measure of multicollinearity within explanatory variables in a regression model. It is derived from the Variable Inflation Factor (VIF) and is very similar but interpreted in a slightly different way (in fact tolerance is 1/VIF). If the value is 0.2 or below you may have a problem with multicollinearity in your model. SPSS will calculate both the VIF and the tolerance statistics for you.
Type I and Type II Error
When drawing conclusions about your hypothesis from your analysis the following two types of error can be made:
- Type I error: When we conclude that there is a relationship or effect but in fact there is not one (false positive).
- Type II error: When we conclude that there is no relationship or effect when in fact there is one (false negative).