successive-independent-samples design

Examples of successive-independent-samples design in the following topics:

• Surveys

  • A successive-independent-samples design draws multiple random samples from a population at one or more times.
  • For successive independent samples designs to be effective, the samples must be drawn from the same population, and must be equally representative of it.
  • A study following a longitudinal design takes measure of the same random sample at multiple time points.
  • Unlike with a successive independent samples design, this design measures the differences in individual participants’ responses over time.
  • This attrition of participants is not random, so samples can become less representative with successive assessments.

• Identifying when the sample proportion is nearly normal

  • If we represent each "success" as a 1 and each "failure" as a 0, then the sample proportion is the mean of these numerical outcomes:
  • we expected to see at least 10 successes and 10 failures in our sample, i.e. np ≥ 10 and n(1 − p) ≥ 10.
  • This is called the success-failure condition.
  • If data come from a simple random sample and consist of less than 10% of the population, then the independence assumption is reasonable.
  • Alternatively, if the data come from a random process, we must evaluate the independence condition more carefully.

• Sampling

  • Sampling involves providing a sample of a consumer product to consumers so that they may try said product before committing to a purchase.
  • The success of a sampling program for a new product introduction is dependent on sound planning of overall project objectives and selection of the best distribution technique, sample design, and packager.
  • Marketers who are considering sampling their next product introduction should define the objectives of the sampling program.
  • There are a number of popular sampling techniques:
  • The distribution technique will not be totally effective unless it is accompanied by a proper sample design, which should have maximum visual impact and identification with the full-size package.

• Sampling Techniques

  • Where the population embraces many distinct categories, the frame can be organized by these categories into separate "strata. " Each stratum is then sampled as an independent sub-population, out of which individual elements can be randomly selected.
  • Additionally, since each stratum is treated as an independent population, different sampling approaches can be applied to different strata, potentially enabling researchers to use the approach best suited for each identified subgroup.
  • Stratified sampling can increase the cost and complicate the research design.
  • In quota sampling the selection of the sample is non-random.
  • Accidental sampling (or grab, convenience, or opportunity sampling) is a type of non-probability sampling which involves the sample being drawn from that part of the population which is close to hand.

• Assumptions

  • Assumptions of a $t$-test depend on the population being studied and on how the data are sampled.
  • Typically, $Z$ is designed to be sensitive to the alternative hypothesis (i.e., its magnitude tends to be larger when the alternative hypothesis is true), whereas $s$ is a scaling parameter that allows the distribution of $t$ to be determined.
  • where $\bar { X }$ is the sample mean of the data, $n$ is the sample size, and $\hat { \sigma }$ is the population standard deviation of the data; $s$ in the one-sample $t$-test is $\hat { \sigma } /\sqrt { n }$, where $\hat { \sigma }$ is the sample standard deviation.
  • For example, in the $t$-test comparing the means of two independent samples, the following assumptions should be met:
  • The data used to carry out the test should be sampled independently from the two populations being compared.

• Random Samples

  • Each observation measures one or more properties (such as weight, location, color) of observable bodies distinguished as independent objects or individuals.
  • In survey sampling, weights can be applied to the data to adjust for the sample design, particularly stratified sampling (blocking).
  • Simple random sampling is a basic type of sampling, since it can be a component of other more complex sampling methods.
  • Sampling done without replacement is no longer independent, but still satisfies exchangeability.
  • Conceptually, simple random sampling is the simplest of the probability sampling techniques.

• Introduction to nodes

  • This means that the actors are usually not sampled independently, as in many other kinds of studies (most typically, surveys).
  • John has been selected to be in our sample.
  • The seven friends are in our sample because John is (and vice-versa), so the "sample elements" are no longer "independent.
  • The nodes or actors included in non-network studies tend to be the result of independent probability sampling.
  • Network data sets also frequently involve several levels of analysis, with actors embedded at the lowest level (i.e. network designs can be described using the language of "nested" designs).

• When to retreat

  • The individual observations must be independent.
  • A random sample from less than 10% of the population ensures the observations are independent.
  • If independence fails, then advanced techniques must be used, and in some such cases, inference may not be possible.
  • Other conditions focus on sample size and skew.
  • For this reason, there are books, courses, and researchers devoted to the techniques of sampling and experimental design.

• Comparing Two Independent Population Proportions

  • The two independent samples are simple random samples that are independent.
  • The number of successes is at least five and the number of failures is at least five for each of the samples.
  • Twenty out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication.
  • Twelve out of another random sample of 200 adults given medication B still had hives 30 minutes after taking the medication.

• Assumption

  • Your data should be a simple random sample that comes from a population that is approximately normally distributed.
  • You use the sample standard deviation to approximate the population standard deviation.
  • The population you are testing is normally distributed or your sample size is sufficiently large.
  • When you perform a hypothesis test of a single population proportion p, you take a simple random sample from the population.
  • You must meet the conditions for a binomial distribution which are there are a certain number n of independent trials, the outcomes of any trial are success or failure, and each trial has the same probability of a success p.