I have a population of 552, the sample size is 227. the sample size is large compared to the population, with the non-response expected, is it better to conduct a census?
What is the best technique to prove the validity of my sample, while am using a SEM-PLS to prove my conceptual model?
I would first use a histogram. I would also run one of the normality tests (many available) BUT exert caution, keeping in mind that the large sample size will produce a very small p-value so be careful not to jump to conclude non normality based on a small p-value, with your large sample. However, a large p-value in this case would be a valid proof of normality.
Box-plot is the best way to understand normality as it gives five number summary. Also there is one test Shapiro Test which can be used to test normality of data. If you are covering more that 50% of the population in sample, it is large enough to estimate population parameters though if costs allow you to do census, would be better.
Please do not abuse statistics. A failure to reject the null-hypothesis is NOT proof that the null hypothesis is true. In general, statistics cannot be used to prove anything. It is a tool that helps us make a more educated guess based on the probability of an event occurring or not-occurring. However with so many experiments some scientist are bound to encounter that 1-in-a-million event and draw the wrong conclusions.
If you can, go with the census. Start with the first round of sampling. Return to the non-responders and try to get some of them to respond. Check for differences between these two sets of responses. If there are no differences then assume that the remaining non-respondents are similar to what you already have. If there are differences, then you have sampled a distinct sub-population.
I recommend kolmogrov-smirinov test in statistical softwares and if the p-value is more than 0.05 ,the the variable is normal. This test is for scale variables.
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