Inferential statistics are used to make inferences about an unknown variable based on known descriptions. Making sure you have a solid understanding of descriptive statistics plays an important role in taking this data to the next step. In this chapter we discussed basic inferential procedures and the different scenarios in which they are used. A t-test is a simple procedure used to compare the means of two groups. An ANOVA allows us to compare multiple groups on multiple independent variables and therefore can look at both main and interaction effects within the data set. The factor analysis is used to find subgroups or factors within a large distribution of scores. A regression analysis uses the correlation in order to make predictions about future or unknown scores. And finally, the meta analysis is used to combine multiple studies into one larger study.
We also discussed alternative and null hypothesis and the determination of type I and type II errors. These last two identify the significance of any results section. Remember, if the probability of error in your study is greater than your accepted error, no matter what the numbers look like, you must accept the null hypothesis. In this case, the difference that may appear in the raw data is not significant enough to infer a difference in the overall population.
Conversely, if the accepted error is less than the probability of error, you must reject the null hypothesis. There is no gray area in this aspect as there are only two outcomes of any inferential procedure: reject or accept the null.