Hello everyone,
I am checking my assumptions before running an ANCOVA, one of which is that the DV is normally distributed across all levels of the IV. MY IV is 3 groups (Ns of 32, 31, and 32) and my DV is a continuous variable from 1 - 5. Before splitting into groups, it looks normal and the skew statistic is -.25. However, when I split into groups and run the Shapiro Wilk test, all three groups come back significant - indicating non-normality. Shapiro Wilk is recommended for samples < 50, which I have when looking at separate groups.
Here is where it gets weird. Visually, the data look normal using Q-Q plots and histograms (perhaps a bit pointy, which may be the issue). In addition, when I use the skew statistics to calculate this on my own (Z Skewness= Skewness-0 / SE Skewness and Z Kurtosis= Kurtosis-0 / SE Kurtosis), both values come back UNDER 1.96.
An example:
Group 1
skew = -.502, SE skew = .421;
-.502 / .421 = -1.19
kurtosis = .131, SE kurtosis = .821.
; .131 / .821 = .159.
However, Shapiro Wilk = .899, p < .05
The same is true in all 3 groups.
Needless to say, I would prefer not to transform if I don't have to, but I am unable to find any resources or citations stating why this would occur and whether it's ok to go with my hand calculations over the Shapiro-Wilk test.
Any insight is very much appreciated!
Thank you all!
I am checking my assumptions before running an ANCOVA, one of which is that the DV is normally distributed across all levels of the IV. MY IV is 3 groups (Ns of 32, 31, and 32) and my DV is a continuous variable from 1 - 5. Before splitting into groups, it looks normal and the skew statistic is -.25. However, when I split into groups and run the Shapiro Wilk test, all three groups come back significant - indicating non-normality. Shapiro Wilk is recommended for samples < 50, which I have when looking at separate groups.
Here is where it gets weird. Visually, the data look normal using Q-Q plots and histograms (perhaps a bit pointy, which may be the issue). In addition, when I use the skew statistics to calculate this on my own (Z Skewness= Skewness-0 / SE Skewness and Z Kurtosis= Kurtosis-0 / SE Kurtosis), both values come back UNDER 1.96.
An example:
Group 1
skew = -.502, SE skew = .421;
-.502 / .421 = -1.19
kurtosis = .131, SE kurtosis = .821.
; .131 / .821 = .159.
However, Shapiro Wilk = .899, p < .05
The same is true in all 3 groups.
Needless to say, I would prefer not to transform if I don't have to, but I am unable to find any resources or citations stating why this would occur and whether it's ok to go with my hand calculations over the Shapiro-Wilk test.
Any insight is very much appreciated!
Thank you all!