Why we need statistical measures of spread
When we have quantitative data, one thing we often want to know is where the center is, and, for that, we can look at the mean, median, mode, trimmed mean, and other measures. But we also want to know how spread out the numbers are. Are they all clustered near the median? Or are they all over the place? This can be very important. For example, if you were a 9th grade math teacher, then you would have very different classes if one had scores on a previous test like this:
9.1 9.0 8.9 8.9 9.1 9.0 9.1 8.9 9.0 8.9 9.2 8.8 8.8 9.1
And another had
10.0 8.0 9.0 10.2 7.8 9.0 9.0 7.2 10.8 10.0 8.0 7.5 10.5
Even though both have means right around 9.0.
Abstract definition of independent variable and dependent variable
Most generally, a dependent variable (DV) is something which we think depends on one or more independent variables (IV). That is, we think that, if the IVs change, the DV will change. There is a causal element here – but statistics cannot test the causation, it can only see if there is a relationship.
The proper interpretation of IVs and DVs depends on whether we are doing an experiment, or conducting an observational study. In an experiment, the IV is under the control of the experimenter. In an observational study, it is not. Thus, the common notion that an independent variable is something which the researcher varies is not completely correct. Continue reading 'Peter Flom’s Statistics 101: What are dependent and independent variables?'»