Dears
Kolmogorov-Smirnov and Shapiro-Wilk tests were conducted for normality of data. Sample size was80, and my question is that whether these tests are preferred for small sample size?
Then, this is the result of the normality of data distribution analysis:
given p = .042 for PBT version of TG one, p = .002 for CAT version of TG one, p = 000 for PBT version of TG two, and p = .000 for CAT version of TG two and using α = .001, it is concluded that the level of each observed variable as the independent variable of the study was not normally distributed. Then, for this piece of research work, it is confirmed that the assumption of normality as one of the most significant fundamental principal of statistical test is violated.
My question is what can be the reason(s) of the skewness in my research data (the scores of test takers' multiple choice achievement test) ? can the small sample size lead to violation of normal distribution of data? If yes, how the problem can be solved.
Dear Seyyed,
The best test of normality for a small sample size is Shapiro Wilk. Yes, you should use it. Skewness is only one possible form of non-normality. SPSS will measure skewness and its standard error. A significant skewness has an absolute value greater than roughly twice its standard error.
I cannot tell you why your data might be skewed or non-normal in another way. Non-normality can be a problem with parametric testing but in some circumstances you can still use the test (known as robust use). The robust exceptions depend upon the test being used. If they are violated then use the equivalent nonparametric test.
Please see my study guides for more information.
Thank you peter. But why does basically non- normality happen?
non-normality may be occur due to outliers, your sample size is reasonable but that there is chance your data set include outliers, check SD value of data plus draw scatter plot or QQ-Plot to visualise outlier behaviour...
Please cross check your data entries sometimes wrong entries also create skewness related data issues. Further high variance in responses can also create this problem. Detect the outliers through box plots and delete these then check the normality of the data. I hope it will be helpful.
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Sampling Design
- Sample Size