4/4/2023 0 Comments No regressWithout those plots or the actual values in your question it's very hard for anyone to give you solid advice on what your data need in terms of analysis or transformation. In summary, it's generally recommended to not rely on normality tests but rather diagnostic plots of the residuals. It's extraordinarily difficult to tell normality, or much of anything, from the last plot and therefore not terribly diagnostic of normality. par(mfrow = c(1, 3)) # making 3 graphs in a row now Try the following simulation comparing histograms, quantile-quantile normal plots, and residual plots. But normality is difficult to derive from it. You can see outliers, the range, goodness of fit, and perhaps even leverage. The standard residual plot in SPSS is not terribly useful for assessing normality. And conversely, with a low N distributions that pass the test can look very far from normal. The distributions will all look normal but still fail the test at about the same rate as lower N values. If you want to see an extreme value of that try n <- 1000. Hopefully, after going through the simulations you can see that a normality test can easily reject pretty normal looking data and that data from a normal distribution can look quite far from normal. # set the plot area to show two plots side by side (make the window wide) If you run the following simulation in R a number of times and look at the plots then you'll see that the normality test is saying "not normal" on a good number of normal distributions. Your N is in that range where sensitivity starts getting high. Tests also get very sensitive at large N's or more seriously, vary in sensitivity with N. But given that the data are a sample you can be quite certain they're not actually normal without a test. Normality tests do not tell you that your data is normal, only that it's not. Rather than relying on a test for normality of the residuals, try assessing the normality with rational judgment.
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