![]() As request, I will provide all three code chunks: sample.R, server.R and ui.R here. I realized that I don't have enough free space to provide this app online. Conversely, you can use it in a way that given the pattern of QQ plot, then check how the skewness etc should be.įor further details, see the documentation therein. In this app, you can adjust the skewness, tailedness (kurtosis) and modality of data and you can see how the histogram and QQ plot change. I made a shiny app to help interpret normal QQ plot. You may also find the suggestion here useful when trying to decide how much you should worry about a particular amount of curvature or wiggliness.Ī more suitable guide for interpretation in general would also include displays at smaller and larger sample sizes. As sample sizes become larger, generally speaking the plots 'stabilize' and the features become more clearly interpretable rather than representing noise. It's possible to discern more features than those (such as discreteness, for one example), but with $n=21$, even such basic features may be hard to spot we shouldn't try to 'over-interpret' every little wiggle. Sometimes straight relationships look curved, curved relationships look straight, heavy-tails just look skew, and so on - with such small samples, often the situation may be much less clear: Note that at $n=21$ the results may be much more variable than shown there - I generated several such sets of six plots and chose a 'nice' set where you could kind of see the shape in all six plots at the same time. Here's what QQ-plots look like (for particular choices of distribution) on average:īut randomness tends to obscure things, especially with small samples: ![]() This allows us to spot a heavy tail or a light tail and hence, skewness greater or smaller than the theoretical distribution, and so on. Local behaviour: When looking at sorted sample values on the y-axis and (approximate) expected quantiles on the x-axis, we can identify from how the values in some section of the plot differ locally from an overall linear trend by seeing whether the values are more or less concentrated than the theoretical distribution would suppose in that section of a plot:Īs we see, less concentrated points increase more and more concentrated points increase less rapidly than an overall linear relation would suggest, and in the extreme cases correspond to a gap in the density of the sample (shows as a near-vertical jump) or a spike of constant values (values aligned horizontally). If the values lie along a line the distribution has the same shape (up to location and scale) as the theoretical distribution we have supposed.
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