Examples of sample in the following topics:


 Other empirical approaches in the social sciences also think in terms of cases or subjects or sample elements and the like.
 The seven friends are in our sample because John is (and viceversa), so the "sample elements" are no longer "independent.
 The nodes or actors included in nonnetwork studies tend to be the result of independent probability sampling.
 Often network studies don't use "samples" at all, at least in the conventional sense.
 Of course, the populations included in a network study may be a sample of some larger set of populations.

 In the analysis of variables, this is testing a hypothesis about a singlesample mean or proportion.
 The parameter "Number of samples" is used for estimating the standard error for the test by the means of "bootstrapping" or computing estimated sampling variance of the mean by drawing 5000 random subsamples from our network, and constructing a sampling distribution of density measures.
 The sampling distribution of a statistic is the distribution of the values of that statistic on repeated sampling.
 The standard deviation of the sampling distribution of a statistic (how much variation we would expect to see from sample to sample just by random chance) is called the standard error.
 Using this alternative standard error based on random draws from the observed sample, our test statistic is 3.7943.


 The main question is: if I repeated the study on a different sample (drawn by the same method), how likely is it that I would get the same answer about what is going on in the whole population from which I drew both samples?
 The basic logic of hypothesis testing is to compare an observed result in a sample to some null hypothesis value, relative to the sampling variability of the result under the assumption that the null hypothesis is true.
 That is, estimating the expected amount that the value a a statistic would "jump around" from one sample to the next simply as a result of accidents of sampling.
 Instead, information from our sample is used to estimate the sampling variability.
 These approximations, however, hold when the observations are drawn by independent random sampling.

 But, sometimes different approaches are used (because they are less expensive, or because of a need to generalize) that sample ties.
 There is also a second kind of sampling of ties that always occurs in network data.
 When we collect network data, we are usually selecting, or sampling, from among a set of kinds of relations that we might have measured.

 Because network methods focus on relations among actors, actors cannot be sampled independently to be included as observations.
 As a result, network approaches tend to study whole populations by means of census, rather than by sample (we will discuss a number of exceptions to this shortly, under the topic of sampling ties).
 This type of design (which could use sampling methods to select populations) allows for replication and for testing of hypotheses by comparing populations.

 This sampling distribution can then be used to assess the frequency with which the observed result would occur by sampling from a population in which ties were randomly distributed.
 The last portion of the results gives the values of the premutionbased sampling distribution.
 Most important here is the standard deviation of the sampling distribution of the index, or its standard error (.078).
 Given this result, we can compare the observed value in our sample (.563) to the expected value (.467) relative to the standard error.
 The observed difference of about .10 could occur fairly frequently just by sampling variability (p = .203).

 Results for both the standard approach and the bootstrap approach (this time, we ran 10,000 subsamples) are reported in the output.
 The conventional approach greatly underestimates the true sampling variability, and gives a result that is too optimistic in rejecting the null hypothesis that the two densities are the same.
 That is, the observed difference would arise very rarely by chance in random samples drawn from these networks.
