Normality test may be easier to establish in ideal conditions but in real life working conditions, say in industrial-type organizations, such a test does face some challenges. Data collection for my study is based on stratified sampling i.e closeness of fit to the population. If the respondents do not have much time, nor do they have every opportunity to be to be sampled, it could be more practical to pre-select the respondents due to their availablility. Under such conditions, the results of a normality test could be less than 0.05 and the data may not be normal. Could this be accepted or should countermeasures be carried out? Are there exceptions for not carrying out normality tests or how could this problem be addressed to meet the 0.05 requirement? E.g. transform the data, parametric test? What are your views?
1) Normality tests are often too sensitive. How do you define a sensible/reasonable sensitivity (power)?
2) Deviations from normality ofen compromise the power, but not the type-I error rate. What is more important for you?
3) What is your explanation for the fact that your "availbility sampling" seems to change resonable assumptions about the errors (that is, seem to give "non-normal" data whereas the other selection method gives "normal" data)?
4) Transformations are a good option, especially when they can be interpreted in a sensible natural, logical way. If you transform, then you need to transform all similar data, not just those for which a transformation seems to improve "normality".
5) Non-parametric tests (i.e. rank-based tests) are possible, but here you need to specifiy what you actually are testing. To test a location shift, the frequency distributions for the groups must be identical (except for the location). Otherwise, such tests will just indicate differences in the compound of symmetry&location of the distributions.
1) Normality tests are often too sensitive. How do you define a sensible/reasonable sensitivity (power)?
2) Deviations from normality ofen compromise the power, but not the type-I error rate. What is more important for you?
3) What is your explanation for the fact that your "availbility sampling" seems to change resonable assumptions about the errors (that is, seem to give "non-normal" data whereas the other selection method gives "normal" data)?
4) Transformations are a good option, especially when they can be interpreted in a sensible natural, logical way. If you transform, then you need to transform all similar data, not just those for which a transformation seems to improve "normality".
5) Non-parametric tests (i.e. rank-based tests) are possible, but here you need to specifiy what you actually are testing. To test a location shift, the frequency distributions for the groups must be identical (except for the location). Otherwise, such tests will just indicate differences in the compound of symmetry&location of the distributions.
Remember that when performing a distribution based parametric hypothesis test or a parametric regression model it is the test residuals that need to be normally distributed (or other distribution in line with the model assumptions) not necessarily the data itself. Either way you may wish to investigate Box-Cox transformations or Box-Cox regression.
In the "real world" example you describe it may be OK to preform ad-hoc sampling however, it is vitally important that you also record any potential confounding factors. For example if it is more likely that older people make time (or are available) to respond then this could potentially introduce a confounding factor that will influence your inference of the population when tested. Inclusion of this confounding variable (age) in your analysis - regression / logistic regression (or simply ANACOVA) may help normalize your residuals which will then make the assumptions of the modelling technique valid.
Without further details about your study it is difficult to say more.
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