The concept underlying measurement invariance is often introduced using a metaphoric example via physical measurements such as length or weight (Millsap, 2011). Suppose I developed an instrument to estimate the perimeter of any object. My instrument is invariant if it produces the same estimate of the object’s perimeter, regardless of the object’s shape. For example, if my instrument provides the same estimate of the perimeter for a circle and a rectangle that have the same true perimeter, then it is invariant. However, if for a circle and a rectangle of the same true perimeter my measure systematically overestimates the perimeters of rectangles, then my measure is not invariant across objects. The object’s shape should be an irrelevant factor in that my instrument is expected to provide an accurate estimate of the perimeter, regardless of the object’s shape. However, when we have a lack of measurement invariance, the estimated perimeter provided by my instrument is influenced not only by the true perimeter but also by the object’s shape. When we lack measurement invariance, irrelevant factors systematically influence the estimates our instruments are designed to produce.