I found that researchers had sent a questionnaire to a population of 200 people, of which 156 replied (Rate Of Return =78%). They also used PCA, t-test and other statistical techniques. I am not sure that if their reported significance level is meaningless! What do you think? Isn't there any difference between statistical analysis on sample and population? Any ideas?
I agree that you indeed have a sample. I would return to the objective and scientific question that was set out to be answered by this survey. If the intent was to assess some differences, remember that your groups for a t-test are not randomized, so PCA or regression might be a better approach than a t-test. It really depends on your research question. I would encourage descriptive stats with confidence intervals. Ideally you should have a plan set out a priori otherwise your analyses are data driven and subject to the inherent bias of humans looking for (and finding!) patterns. If its too late for that, at least try to write out what your hypotheses are and formulate how to best answer those questions without looking into the data. Searching the data for a difference is highly subject to type I errors, so be wise!
The point of inferential statistics is to make inferences about a population using a sample. If you indeed have a population, there's no point of inferential statistics. ie a p-value would be meaningless. If we had the population we'd only have to consider what is meaningful and the question of statistical significance becomes irrelevant.
What's also interesting about this problem is you cannot know the difference (if any) between those who responded and those who chose not to respond. PCA might try, but you don't know what you didn't collect and you don't know the unmeasurable characteristics of either group.
By using mainly descriptive statistics. Not inferential Statistics.
Hi Ali -
I'm curious. Do you have regressor data? You mentioned PCA. Principal components? If you have regressor data, you could perhaps 'predict' for the missing data in your finite population. If you can stratify along with that, so much the better.
- Jim
I agree that you indeed have a sample. I would return to the objective and scientific question that was set out to be answered by this survey. If the intent was to assess some differences, remember that your groups for a t-test are not randomized, so PCA or regression might be a better approach than a t-test. It really depends on your research question. I would encourage descriptive stats with confidence intervals. Ideally you should have a plan set out a priori otherwise your analyses are data driven and subject to the inherent bias of humans looking for (and finding!) patterns. If its too late for that, at least try to write out what your hypotheses are and formulate how to best answer those questions without looking into the data. Searching the data for a difference is highly subject to type I errors, so be wise!
The point of inferential statistics is to make inferences about a population using a sample. If you indeed have a population, there's no point of inferential statistics. ie a p-value would be meaningless. If we had the population we'd only have to consider what is meaningful and the question of statistical significance becomes irrelevant.
What's also interesting about this problem is you cannot know the difference (if any) between those who responded and those who chose not to respond. PCA might try, but you don't know what you didn't collect and you don't know the unmeasurable characteristics of either group.
Thank you very much, indeed, for your kind contribution to this post.
1- I agree with Subrata and doing any statistical inference is cautious.
2- I am concerned about the approach, not on a particular stat. technique. So, James comments on regression or stratifying assumes that we have sample NOT total population.
3- I don't agree with Paulo! Of course there is a difference between a Sample and Census. Missing data can not chance the nature of "total population" to "sample."
4- I totally agree with Melanie. As you sure that we can do a regression or PCA in this case? What about stat. error? Can we report any sampling error?
Again my special thanks go to your kind reply and comments.
I think when you have a data for all the population you can use only the discribtive statistics. But in your case you have a sample of percentages 78% from the population.
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