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Biostatistics and Bioaerosols
Published in Harriet A. Burge, Bioaerosols, 2020
Lynn Eudey, H. Jenny Su, Harriet A. Burge
Properties of sampling distributions. Sampling distributions have the same properties as the distributions discussed above; this is because a sample statistic is a random variable. A statistic and its corresponding sampling distribution will usually have a mean and a variance. The mean of the statistic, as for other random variables, is the average of all possible values that the statistic can assume (recall that we hold the sample size constant). The variance of the sample statistic is a measurement of the variability in the sampling distribution. It is the average of all the squared deviations from the mean of the statistic. Again, the standard deviation is the square root of the variance. We refer to the standard deviation of a statistic as the standard error (SE) because, if the statistic is unbiased for a parameter (defined below), the standard deviation is measuring the “average error” of the statistic in estimating that parameter (see section on estimation). In other words, the standard error is a measurement of the accuracy of the sample statistic.
Descriptive Statistics
Published in Robert M. Bethea, R. Russell Rhinehart, Applied Engineering Statistics, 2019
Robert M. Bethea, R. Russell Rhinehart
As you can see, the standard error is always smaller than the standard deviation, indicating that the sample mean is less variable than the original data from which it was calculated. Do not confuse these two estimates of variability; the sample standard deviation is used to test hypotheses about individual population values, but the sample standard error is used to test hypotheses about the mean of the population from which the sample was drawn. You should distinguish SX and SX¯ for another reason. If the sample data are badly scattered, some people will report the standard error as if it were the standard deviation, thus trying to conceal what they perceive as poor data. When you hear the word “standard” used in describing the variability of data, always ask whether standard deviation or standard error is meant. If in doubt, ask to see the calculations.
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Published in Bruce Ratner, Statistical and Machine-Learning Data Mining, 2017
The answer rests on the well-known, fundamental relationship between sample size and confidence interval length: increasing (decreasing) sample size increases (decreases) confidence in the estimate. Equivalently, increasing (decreasing) sample size decreases (increases) the standard error [5]. The sample size and confidence length relationship can serve as a guide to increase confidence in the bootstrap Cum Lift estimates in two ways: If ample additional customers are available, add them to the original validation dataset until the enhanced validation dataset size produces the desired standard error and confidence interval length.Simulate or bootstrap the original validation dataset by increasing the bootstrap sample size until the enhanced bootstrap dataset size produces the desired standard error and confidence interval length.
Power Analysis, Sample Size, and Assessment of Statistical Assumptions—Improving the Evidential Value of Lighting Research
Published in LEUKOS, 2019
To adequately assess deviations from normality, it is necessary to convert the skewness or kurtosis statistic to a z-score by dividing it by its standard error. These transformed values can be compared against values you would expect to get by chance alone, based on a normal distribution. A z-score of ±1.96 is significant at P < 0.05, at ±2.58 it is significant at P < 0.01, and ±3.29 is significant at P < 0.001. A significant z-score may indicate that the distribution has significant levels of skewness/kurtosis, although the threshold to use is a matter of judgment. As the sample size increases, the standard error becomes smaller, resulting in a larger z-score. Large samples are therefore more likely to provide transformed skewness and kurtosis statistics that appear significant, and it may therefore be appropriate to use a larger threshold to indicate whether the distribution of a large sample of data shows significant skewness or kurtosis. Field et al. (2012) suggested that it is not appropriate to utilize z-score values of kurtosis and skewness for samples larger than 200. The z-score values of skewness and kurtosis for the simulated normal set of data are −0.30 and 0.23 respectively, indicating no evidence of skewness or kurtosis. The values for the nonnormal data set were 7.91 and 10.44, confirming significant skewness and kurtosis. These values have been calculated using the “stats.desc” function in the “pastecs” R package (Grosjean and Ibanez 2014).
Structure–activity relations for antiepileptic drugs through omega polynomials and topological indices
Published in Molecular Physics, 2022
Medha Itagi Huilgol, V. Sriram, Krishnan Balasubramanian
and x is the set of experimental Log(ED50) values of 20 compounds shown in Table 6 while y is the set of predicted Log(ED50) from the SAR equation, the sum is over all n data set points, and k is the number of independent variables; in this case, k is simply 1. The standard error of the regression (S. E.), also known as the standard error of the estimate, represents the average distance that the observed values fall from the regression line or plane. The S.E. indicates how far the observations from the SAR fit are, and consequently, the smaller the S.E. value, more robust is the SAR equation. The F value indicates the overall confidence of the multiple regression, that is, a higher F indicates greater confidence.
Evaluating students’ conceptual and procedural understanding of sampling distributions
Published in International Journal of Mathematical Education in Science and Technology, 2019
Zeynep Medine Ozmen, Bulent Guven
According to Chance et al. [6], students should be able to understand the following aspects of sampling distributions: A sampling distribution of sample means is a distribution of all possible sample means.The sampling distribution for means has the same mean as the population.As the sample size gets larger, the variability of the sample means gets smaller.The standard error of the mean is a measure of variability of sample statistics.The building block of a sampling distribution is a sample statistic.Different sample sizes lead to different probabilities for the same statistic value.Sampling distributions tend to have the shape of a normal distribution, rather than the shape of the population distribution, even for small samples.Students should be able to distinguish between a distribution of observations in one sample and a distribution of sample means from many samples (n > 1) that have been randomly selected. (p. 301)