1) Suppose we sit at a restaurant and watch what servers do and how much they get tipped. Suppose we find that servers get bigger tips when they touch their customers. Such a study
3) If we do an experiment on the effects of touching on tipping, our first step would be to assign participants to different levels of touch. Touch would be our (manipulated) variable; tipping would be our (measured) variable.
If our results were not statistically significant, the results may be due to chance. If the results were statistically significant, the results are probably due to manipulating the variable.
Put another way, thanks to assignment, there are only two differences between our control group and our group. First, because of assignment, the groups may differ due to . Second, because participants are randomly to different levels of the experimental manipulation, the groups may differ due to the variable. Fortunately, we can use to estimate the degree to which our groups might reasonably differ by chance alone. If the groups differ by more than what would reasonably be expected by chance alone, we say the difference is significant. If the groups differ by less than that amount, we realize that the results may be due to chance alone. In that case, we say the results are statistically significant.