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  Encyclopedia of Keywords > Information > Science > Mathematics > Statistics > Sampling Distribution   Michael Charnine

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  1. A sampling distribution is the distribution of a statistic over repeated samples.
  2. A sampling distribution is the probability distribution, under repeated sampling of the population, of a given statistic.
  3. The sampling distribution is the probability distribution or probability density function of the statistic.
  4. Sampling distribution: the probability distribution of a statistic viewed as a random variable.
  5. A sampling distribution is a type of frequency distribution in which each element is a statistic based on a sample.

Difference Between

  1. The standard error of the difference between means is the standard deviation of a sampling distribution of differences between sample means.
  2. The sampling distribution should be approximately normally distributed.
  3. So, in other words, SD(population) = SD(sampling distribution) x sq.root(N in the sampling distribution).
  4. Elsewhere on this site, we show how to compute the margin of error when the sampling distribution is approximately normal.
  5. Second, the mean difference in raw-score units of the sampling distribution of difference reflects the theoretical difference between two population means.


  1. Under certain conditions, in large samples, the sampling distribution of the sample mean can be approximated by a normal distribution.
  2. The mean of the sampling distribution for a population is the same as the mean for the population, μ.
  3. The sampling distribution represented in a normal curve can be used to test hypotheses about means.
  4. Next assume you have a sample of sufficient size that the central limit theorem comes into action to give you a normal sampling distribution for your slope.
  5. In general, the sampling distribution of means is less spread out than the parent population.

Normal Distribution

  1. This is so because the sampling distribution is closer to a normal distribution than is the original exponential distribution.
  2. Also, the sampling distribution is even closer to a normal distribution, as can be seen from the histogram and the skewness.
  3. The sampling distribution of [ - m] ´ n - ¸ s, is the standard normal distribution.

Null Hypothesis

  1. Using the assumptions of step 1, find the theoretical sampling distribution of the statistic under the null hypothesis of step 2.
  2. This section describes how to find the critical value, when the sampling distribution of the statistic is normal or nearly normal.
  3. Second, the null hypothesis is used to stipulate the lone sampling distribution to be used in making the statistical decision about chance influences.


  1. The graph on the left shows the density function of the sampling distribution in blue and the sample values in red.
  2. Since the sample size is large, the sampling distribution will be roughly normal in shape.
  3. The greater the sample size, the closer the sampling distribution is to being normally distributed.

Random Sample

  1. It arises in connection with the sampling distribution of the sample variance for random samples from normal populations.
  2. In statistics bootstrapping is a method for estimating the sampling distribution of an estimator by resampling with replacement from the original sample.
  3. SAMPLING DISTRIBUTION. A distribution of statistics (not raw scores) computed from random samples of a given size taken repeatedly from a population.

Expected Value

  1. The expected value (analogous to the mean) of a sampling distribution will be represented here by the symbol m .
  2. An estimate of a parameter is unbiased if the expected value of sampling distribution is equal to that population.
  3. Unbiased Estimator An estimator whose expected value (namely the mean of the sampling distribution) equals the parameter it is supposed to estimate.

Sample Proportion

  1. Theoretically, the standard deviation of the sampling distribution is , whereas the standard deviation of this sample from the sampling distribution is .30.
  2. A t-distribution is like an approximation of a sampling distribution, but with only one sample.
  3. If the sample is a random sample then we know the sampling distribution of p ^ the sample proportion.
  4. For categorical data, the CLT holds for the sampling distribution of the sample proportion.
  5. We can then determine the probability of obtaining a particular sample value by seeing where such a value falls on the sampling distribution.

Frequency Distribution

  1. The infinite number of medians would be called the sampling distribution of the median.
  2. We can now compute the same parameters for the sampling distribution that we compute for populations and samples.
  3. This means that you can conceive of a sampling distribution as being a frequency distribution based on a very large number of samples.
  4. To be strictly correct, the sampling distribution only equals the frequency distribution exactly when there is an infinite number of samples.
  5. This is why the shape of the Chi Square sampling distribution changes for different df values.


  1. Let f be the sampling distribution of x, so that f( x | --) is the probability of x when the underlying population parameter is --.
  2. A sampling distribution may also be described with a parameter corresponding to a variance, symbolized by .
  3. Derivation of the sampling distribution is the first step in calculating a confidence interval or carrying out a hypothesis test for a parameter.


  1. The standard deviation of the sampling distribution is smaller than in the previous example because the size of each sample is larger.
  2. The m symbol is often written with a subscript to indicate which sampling distribution is being discussed.
  3. Notice that the skewness in sampling distribution of the mean rapidly disappears as n gets larger.

Sampling Distributions

  1. The purpose of the microcomputer simulation exercise (named SIM-SAM) is to demonstrate how a sampling distribution is created.
  2. There is an alternative way of conceptualizing a sampling distribution that will be useful for more complex distributions.
  3. To correctly interpret traditional inferential procedures, students need to understand the notion of a sampling distribution.
  4. This applet estimates and plots the sampling distribution of various statistics.
  5. In carrying out NHSTP, only one sampling distribution is used (viz, the one contingent on H 0 being true).


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  Originally created: August 16, 2007.
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