Hi there - I'm working on a regression analysis to investegate the influence of dark personality traits' collected through HDS on overall leadership quality examined through a manager quality survey. The sample is composed of 999 participants. I ran test for normality and the data was not normally distributed with both Kolmogorove-Smirnove and Shapiro-Wilk coming out significant.
I transformed the data in SPSS using the 2 step approach (Fractional Rank using Rank Case, then Computing Variable using Inverse DF function group) (Templeton, 2011), however when I retested the the normality, again both tests came as significant, despite the graphs looked normally distributed. So shall I disregard the Kolmogorove-Smirnove and Shapiro-Wilk results of the normalized data, or I'm missing something here.
Thanks in advance,
Ehab
References:
Templeton, G.F. 2011. "A Two-Step Approach for Transforming Continuous Variables to Normal: Implications and Recommendations for IS Research," Communications of the AIS, Vol. 28, Article 4.
If you are talking about standard (OLS) regression, the assumption about normality is about the regression residuals, not about the distribution of your outcome (e.g. see: https://www.theanalysisfactor.com/assumptions-about-residuals/). Checking the distribution of the residuals is much more informative than checking normality of your data.
With respect to Kolmogorov-Smirnove and Shapiro-Wilk: these being ordinary significance tests, their "significance" is depends on, among other things the size of the deviation from normality and the size of your data. Chances are that at a large sample it can signal deviation from normality even when so small it would never pose a problem. The reverse is true for small data.
Hello. As far as i know, normality isn't an issue for regression analysis. You may look at http://www.statisticssolutions.com/normality/
And the following paper will help you
Article Linear regression and the normality assumption
If you are talking about standard (OLS) regression, the assumption about normality is about the regression residuals, not about the distribution of your outcome (e.g. see: https://www.theanalysisfactor.com/assumptions-about-residuals/). Checking the distribution of the residuals is much more informative than checking normality of your data.
With respect to Kolmogorov-Smirnove and Shapiro-Wilk: these being ordinary significance tests, their "significance" is depends on, among other things the size of the deviation from normality and the size of your data. Chances are that at a large sample it can signal deviation from normality even when so small it would never pose a problem. The reverse is true for small data.
The assumption of normality is about the residuals not the variables as Maarten already stated.
Graphical approaches to testing for normality in the residuals are more effective, and might assist you in making a good transformation. A q-q plot (normality) and a plot of the residuals against the predicted (heteroscedasticity) will be helpful.
A plot of observed data, regression line and 95% confidence interval might help. With that figure do you believe the outcome?
The test for normality will get you into trouble. It is an important issue and you should look at how well the model fits the data. Yet if the test for normality is significant then you either need to transform the data or use a non-parametric model. If the test for normality is not significant then you are going to behave as if such a test proves that the data are normally distributed. Sadly, failing to reject the null hypothesis is not proof that the null hypothesis is true. It is also generally possible to make tests like the test for normality produce a significant outcome by increasing sample size. So the end result is an unsatisfying mess.
The problem with the graphical approach is that it requires some experience to look at the graphs and decide if corrective measures are needed. The only way to gain experience is to look at a great deal of data.
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