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QQ Plots and PP Plots (Değişik sitelerden copy-past yapılarak toplanmıştır)

Hem kompozit değişkenler için, hem bireysel değişkenler için (PPT Sunusu İnternetten alınmıştır) Bir makale

Normallik testine ilişkin Bir başka örnek Normality Test

For SPSS through the GUI interface if you go to Analyze -> Descriptive Statistics -> QQ-plots one can get a QQ plot of the observed against various theoretical distributions. Check out the EXAMINE command in help for tests of normality like Shapiro-Wilks and KS. normality test attempts to compare the shape of your sample distribution to the shape of normal curve. shapiro-wilks test is much more common due to sample size. for tests including small and medium samples up to 2000 we use s-w test and if the sample size exceeds over 2000 we take the kolmogorov-samirnov. it is worth mentioning that W is the test statistic. for interpreting the results after choosing the appropriate kind of test mentioned before due to your sample size, look at the word "sig" which is stand for significance of the test or in the other words p-value, if sig>0.05 accept the hypothesis H0 (normality) which means the test is insignificant. or simply your sample distribution follows normal curve

The QQ plot says that the data indeed has normal distribution but when we go for Shapiro Wilks or Konglomerov test..the P value is >.05. If KS < .05 it means the hypothesis of normality is rejected. Over .05 means the hypothesis is not rejected

Another, more visual way would be using p-p plots (Analyze --> "Descriptive statistics" --> "P-P Plots"). You provide your variable, check if "Normal" is chosen at "Test Distribution" and press OK. The plots can be interpreted as follows: A variable is considered to follow a Gaussian distribution, if in the "Normal P-P Plot of [variable name]" the dots align (relatively) linear in a 45° angle (along the continuous line drawn from 0/0 to 1/1). In contrast, in the "Detrended Normal P-P Plot of [variable]", no systematic alignment (for example U-shape, etc.) must be detected. However, the is no test statistics for this approach

KS (Kolmogorov-Smirnov) Test of Normality. Essentially doing the same as the Shapiro-Wilk test previously mentioned. If you need the pros and cons of both tests, wikipedia might give a good answer. A very conservative approach would be to apply the Kolmogorov-Smirnov test. For this, you open "Analyze" --> "Nonparametric Tests" --> "Legacy Dialogs" --> One-Sample Kolmogorov-Smirnov Test ("1-Sample K-S") and provide the variables, of which you want to assess whether they follow a Gaussian (normal) distribution. As test distribution, you tick "Normal" and press "OK". If with the Test statistics (Output file --> "NPar Tests" the Asymp. Sig. is statistically significant (0.05), the probability, that your data follows a Gaussian distribution, is very low. So you need at least a non-significant result (p>0.05) for a normally distributed variable. This is the most simple way to check for normal distribution, although it is very conservative, that means that the deviation from Gaussian distribution can be quite high and though the test would suggest a normal distribution. So if you check your variable by drawing a histogramm ("Graphs"-->"Legacy Dialogs"-->"Histogramm"), you might see that sometimes, your variable is quite deviated (to the left or to the right), although your K-S test is insignificant, which indicates a normal distribution. However, most of the statistical tests that require a normal distribution (parametric tests) are very resistent against violations of this assumption.

In many cases Likert scales are skewed, since people tend to do yea-saying if the data is from the US. So you will probably standardize each Likert variable by subtracting mean and dividing by standard deviation. You can then conduct the KS test on the transformed variables.

Skewness you can already detect by looking at the descriptives.

Çoklu normallik için Lisrel veya amos. Using AMOS©, multivariate normality is determined by using the
“$normalitycheck” command. This command produces statistics on skewness and
kurtosis.

If you have ordinal data why would you be concerned about a normal distribution? The only reason I can think of is if you are thinking of a latent trait that is manifested categorically; in that case, one can make the assumption that the latent trait is normally distributed. If you consider it a latent trait, and are truly concerned about the normality of that latent trait, you may be able to use an ordinal probit regression (which assumes a latent normal variable) and assess the fit

https://statistics.laerd.com/features-data-setup.php