Consider the following scenario: each of six randomly selected workers completed a task using two different methods (Method 1 and Method 2). The completion times for each worker are shown in the graph below. Each dot in the graph represents the completion time (in minutes) for the two methods performed by each worker. Method 1 is on the y-axis and Method 2 is on the x-axis. For points above the diagonal line, the Method 1 time was longer; for points on the line, the times were equal for the two methods; and for points below the line, the time using Method 2 was longer.

The overall mean difference d, the standard deviation s(d) of the differences, the t-statistic, and its p-value are reported at the top of the graph. Each data point can be dragged. As a point is dragged, its difference d is displayed next to the point and the summary statistics are also updated. Drag the various points to see how changing their location changes the reported statistics. Can you drag the points so that there is a statistically significant difference with p = 0.05? Double-click on the graph to restore the original values.