Jim -

I'm not clear on what you are doing.  There are various kinds of weights, such as regression weights and survey weights.  Sometimes weights are modified to account for nonresponse, as opposed to doing imputation.

First you should look at the software documentation. You should be able to find out what it does for a given routine (say "REG" for SAS, don't know about SPSS). 

You should probably avoid "significance."  That is generally misused and almost always misunderstood, and not very useful.  See

 https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS

I'll guess that you are talking about probability of selection based sampling from a finite population, the most commonly used form of "survey" sampling - which may not be what you'd think of as a survey, and perhaps not for a finite population, though 'weights' indicate that, and nevertheless a randomized sample where each member of a population has a known probability of selection which determines its survey weight.  Here is an explanation of this in its simplest form: https://www.researchgate.net/publication/262971887_SURVEY_WEIGHTS

If you are looking at a stratified random sample, then there is a (sub)population standard deviation for each stratum, and along with each there is the sample size for that stratum resulting in a standard error for say the mean, or total in that stratum. You then add variances across independent strata to obtain a variance for, say, overall mean, perhaps. 

Your use of SPSS sounds like you are probably looking at a simple random sample, or one using probability proportionate to size (PPS), as you said nothing about strata or clusters or multi-stage sampling.  I don't know what you are doing with inverse variances.  That sounds related to regression weights, but not in the context you gave. 

My guess is that you are looking at weights related to probabilities of selection in randomized sampling, and need to look at a sampling book such as one of the following:

Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 

Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.

Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.

But first, perhaps you should look at the SPSS routines you are using and find documentation on what they are doing.  If you look at it closely, you may find it is not what you wanted to do.  It is always important not to use software as a "black box." 

Weights are important in your estimations. 

I think you may be confusing sample size n, with population size N. 

Cheers - Jim

Article Practical Interpretation of Hypothesis Tests - letter to the...

Article SURVEY WEIGHTS

Jim -

I'm not clear on what you are doing.  There are various kinds of weights, such as regression weights and survey weights.  Sometimes weights are modified to account for nonresponse, as opposed to doing imputation.

First you should look at the software documentation. You should be able to find out what it does for a given routine (say "REG" for SAS, don't know about SPSS). 

You should probably avoid "significance."  That is generally misused and almost always misunderstood, and not very useful.  See

 https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS

I'll guess that you are talking about probability of selection based sampling from a finite population, the most commonly used form of "survey" sampling - which may not be what you'd think of as a survey, and perhaps not for a finite population, though 'weights' indicate that, and nevertheless a randomized sample where each member of a population has a known probability of selection which determines its survey weight.  Here is an explanation of this in its simplest form: https://www.researchgate.net/publication/262971887_SURVEY_WEIGHTS

If you are looking at a stratified random sample, then there is a (sub)population standard deviation for each stratum, and along with each there is the sample size for that stratum resulting in a standard error for say the mean, or total in that stratum. You then add variances across independent strata to obtain a variance for, say, overall mean, perhaps. 

Your use of SPSS sounds like you are probably looking at a simple random sample, or one using probability proportionate to size (PPS), as you said nothing about strata or clusters or multi-stage sampling.  I don't know what you are doing with inverse variances.  That sounds related to regression weights, but not in the context you gave. 

My guess is that you are looking at weights related to probabilities of selection in randomized sampling, and need to look at a sampling book such as one of the following:

Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 

Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.

Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.

But first, perhaps you should look at the SPSS routines you are using and find documentation on what they are doing.  If you look at it closely, you may find it is not what you wanted to do.  It is always important not to use software as a "black box." 

Weights are important in your estimations. 

I think you may be confusing sample size n, with population size N. 

Cheers - Jim

Article Practical Interpretation of Hypothesis Tests - letter to the...

Article SURVEY WEIGHTS

Thanks very much Jim. Let me try to clarify my situation. I am extracting data from a dissertation for inclusion in a meta-analysis. The dissertation was based on a data set (National Longitudinal Study of Adolescent Health) which includes sample weights to provide nationally representative estimates. The author of the dissertation conducted a logistic regression using SPSS, weighting cases by their sample weights. The author reported an odds ratio (which we have coded as our effect size), but no standard error or sampling variance for the odds ratio. The author also reported that the original N was 2,263, but the weighted N is slightly over 21 million.

We are meta-analyzing log odds ratios (transformation of the odds ratio), and weighting studies in the meta-analysis by the inverse of the log odds' sampling variances. Because the author of the dissertation did not provide sampling variance we need to calculate it. Our question is, which N should be use in calculating the sampling variance - the weighted N of 21 million or unweighted N of 2,263?

Dear Jim

The weighted N may have been computed to expand to the Size of all the original population, which would be good for presenting tables and graphs, but misleading for your purpose. Using the unweighted N is not good because it is the same thing that giving equal sample weight to each observation and that would be against the original design. You may use the original weight but multiplied by 2263/21 millon.