# I QQplot, question about my textbook's interpretation

#### Frank Einstein

Summary
Reading a qqplot in an example, I find that the graph in question doesn't match with the conclussions. Can anyoe please confirm this?
Hello everyone. I am currently reading a book on quality control. In the part of experimental design, here, the effect vector, beta, takes the following form: beta=(81.75, 9, 0.75, -4, -0.5, 0.25, 3, -0.25), which corresponds to the effects of lenght, width, type of steel and their interactions, LW, LT, WT and LWT. The book then present the qqplot to determine the significance of each one of the effects. All the terms of beta but the first are present, that one is the mean effect (see attached image).

Then, the analysis of the graph goes as follows: L and LWT are significant, LT is on the fence and the rest are not.

My question goes as follows: The elements of the vector beta don't appear in order on the qqplot, however, the book treats them as if the first element of the vector is the first element of the qqplot (L) and so on. Is my book right or does the graph shows the elements of the qqplot on a different order that they were at beta?

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#### scottdave

Homework Helper
Gold Member
Are these numbers different variables taken from the same sample, or are they the same variable from different samples?
I have seen QQ plots used to show if a set of samples follow a normal distribution. The values are sorted in ascending order, then plotted against normally distributed coordinates.

#### WWGD

Gold Member
My understanding is that a QQ normal plot uses a Chi-squared goodness of fit by calculating sample mean , S.E an then seeing the fit between the sample values and the 1-2-3 rule using the sample values. EDIT: So we expect 34.3% of values to be within $\pm 1 \text SE$ , etc.

Homework Helper
I'm not sure what is meant by "L and LWT are significant, LT is on the fence and the rest are not.".

QQplots, as almost always presented, are graphical tools to give a quick idea about whether it's reasonable to assume that some values are from a specified distribution (usually the normal distribution, with the values being residuals from some fit, but that doesn't have to be the case).
The "QQ" portion of the name comes (as I'm sure you know) from the fact that the plot shows the quantiles of your values plotted against the quantiles of the distribution in question: better the fit between distribution and data the closer the points follow the "reference line". The original data are plotted in order of increasing magnitude to represent the sample quantiles. (And, just for fun: different software calculate them in different ways).

Is there some other characteristic for this graph that you haven't thought to include?

"QQplot, question about my textbook's interpretation"

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