Descriptive statistics describes data (for example: how many people have partners and how many do not? How many people have children and how many do not?) and inferential statistics allows you to make predictions (“inferences”) from that data (for example: if a person gets a partner, what are the chances that that person will get a child?). With inferential statistics, you take data from samples and make generalizations about a population.
There is a way to discover whether the difference in group means is caused by error variance or by systematic variance. Inferential statistics are used for this purpose. Inferential statistics refers to drawing conclusions. This method assumes that the independent variable has had an effect, when the difference between the means of the conditions is larger than is expected based on chance alone. Therefore, we compare the group means that we found with the group means that we expect to find if there is only error variance. Unfortunately, this method does not provide certainty. We are only able to determine the chance that the differences in group means are caused by error variance.
Scientists try to test their hypotheses by analyzing different group means. First, they formulate a null hypothesis. This hypothesis states that the independent variable did not have an effect on the dependent variable. On the contrary, there is an experimental hypothesis which states that the independent variable did have an effect on the dependent variable. The experimental hypothesis may (directional) or may not (non-directional) indicate a direction of the effect. A directional experimental hypothesis is called one-sided. With a one-sided hypothesis, the researcher indicates whether he expects the independent variable to cause a decrease or increase of the dependent variable. When the researcher does not have an indication of the direction of the expected effect, a two-sided hypothesis can be used. With a two-sided hypothesis, the direction of the effect is not indicated. Based on statistical analyses, the null hypothesis can be rejected or preserved (failing to reject the null hypothesis).
Rejecting the null hypothesis implies that the independent variable did have an effect on the dependent variable. By rejecting the null hypothesis, you indicate that there is a difference between the means. The independent variable thus had an effect, and there is some systematic variance. Rejecting the null hypothesis implies that the difference in group means is larger than expected on error variance only. When the null hypothesis is preserved, it does not mean per se that the independent variable did not have an effect on the dependent variable. Instead, it means that the effect that is found is not large enough to reject the null hypothesis. Whether a null hypothesis is rejected, is dependent upon the confidence interval, which is controlled by the researcher (the researcher determines the significance level). It is important to understand that not rejecting the null hypothesis does not mean that there is no effect.
