# Why is this normal probability plot graph skewed right?

First, I apologize for the bad image, but it's the best I can do with a mouse. Anyways, here it is: So the data is skewed right, but the normal probability plot bends up and over what would be the approximate linear equation. According to different websites1, 2, a normal probability plot with data skewed right goes under the approximate line of best fit, and my graph looks more like it's skewed left. What am I misunderstanding?

1: itl.nist.gov/div898/handbook/eda/section3/normprp4.htm
2: www.basic.northwestern.edu/statguidefiles/probplots.html#Data%20Skewed%20to%20Right

• The graph is impossible to understand without labels and scales for the axes. – whuber Oct 5 '11 at 3:13
• It's a normal probability plot from -3 to 3 on the y-axis and time on the x axis. – Anonymous Oct 5 '11 at 3:14
• Assuming time increases left to right and y increases bottom to top and that the normal plotting positions have been correctly computed, this is a plot of right-skewed times. Why does it look skewed left to you? – whuber Oct 5 '11 at 3:18
• The websites show that right skewed graphs don't look like that, while it looks like the examples for left skewed graphs. – Anonymous Oct 5 '11 at 3:21
• Is that a frequency histogram at the top? If you best want to understand your question, try making the normal probability plot yourself, without a computer. – Adam Oct 5 '11 at 3:55

## 2 Answers

This graph interchanges the axes compared to the cited websites, that's all.

In general, to read a probability plot, ask yourself "what changes in the data would be required to line the points up diagonally?" In this case, the data are shown on the x-axis, so changing the data would slide points horizontally along the x-axis while retaining their vertical positions. To get the points into a diagonal line we would have to slide the largest (rightmost) times to the left (that is, pull them in towards their middle) and we would have to slide the smallest (leftmost) times a little to the left as well (that is, push them away from the middle time value). That tells us the large times are too big compared to a normal distribution: they are skewed towards large values (considered the "right," no matter how the plot is drawn; better terminology is "positively skewed"). (For reading q-q plots in general, I have posted a more elaborate explanation with illustrations.)

When the axes are reversed, the times (or, generally, the data) are plotted vertically and the sliding has to happen in the vertical direction. There's no chance of confusion, though--provided the axes are clearly labeled!

That looks a lot like the efficient frontier from modern portfolio theory. The efficient frontier is a set of attainable portfolios, the x-axis being the scale of risk with higher risk to the right, and y-axis being the scale of return with higher return being higher. The frontier line is made up of theoretical portfolios of all risky assets.