# The Range of Interpretation The SEM, like the standard deviation, is multiplied by 1. Then subtract the result from the sample mean to obtain the lower limit of the interval. The resulting interval will provide an estimate of the range of values within which the population mean is likely to fall.

This interval is a crude estimate of the confidence interval within which the population mean is likely to fall. A more precise confidence interval should be calculated by means of percentiles derived from the t-distribution. Another use of the value, 1. Consider, for example, a researcher studying bedsores in a population of patients who have had open heart surgery that lasted more than 4 hours. Suppose the mean number of bedsores was 0.

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If the standard error of the mean is 0. This is interpreted as follows: The population mean is somewhere between zero bedsores and 20 bedsores. Given that the population mean may be zero, the researcher might conclude that the 10 patients who developed bedsores are outliers.

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That in turn should lead the researcher to question whether the bedsores were developed as a function of some other condition rather than as a function of having heart surgery that lasted longer than 4 hours. The standard error of the estimate S.

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Specifically, it is calculated using the following formula:. Therefore, the standard error of the estimate is a measure of the dispersion or variability in the predicted scores in a regression. In a scatterplot in which the S. When the S. Figure 1. Low S.

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Figure 2. Large S. Every inferential statistic has an associated standard error. Although not always reported, the standard error is an important statistic because it provides information on the accuracy of the statistic 4. As discussed previously, the larger the standard error, the wider the confidence interval about the statistic. In fact, the confidence interval can be so large that it is as large as the full range of values, or even larger. In that case, the statistic provides no information about the location of the population parameter.

And that means that the statistic has little accuracy because it is not a good estimate of the population parameter. In this way, the standard error of a statistic is related to the significance level of the finding. When the standard error is large relative to the statistic, the statistic will typically be non-significant.

## Range Interpretation by Wolfgang Iser - AbeBooks

However, if the sample size is very large, for example, sample sizes greater than 1,, then virtually any statistical result calculated on that sample will be statistically significant. For example, a correlation of 0. However, a correlation that small is not clinically or scientifically significant. When effect sizes measured as correlation statistics are relatively small but statistically significant, the standard error is a valuable tool for determining whether that significance is due to good prediction, or is merely a result of power so large that any statistic is going to be significant.

The answer to the question about the importance of the result is found by using the standard error to calculate the confidence interval about the statistic. This is true because the range of values within which the population parameter falls is so large that the researcher has little more idea about where the population parameter actually falls than he or she had before conducting the research. When the statistic calculated involves two or more variables such as regression, the t-test there is another statistic that may be used to determine the importance of the finding.

Consider, for example, a regression. Suppose the sample size is 1, and the significance of the regression is 0. The obtained P-level is very significant.

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However, one is left with the question of how accurate are predictions based on the regression? The effect size provides the answer to that question. It is an even more valuable statistic than the Pearson because it is a measure of the overlap, or association between the independent and dependent variables. See Figure 3. This capability holds true for all parametric correlation statistics and their associated standard error statistics. In fact, even with non-parametric correlation coefficients i.

In most cases, the effect size statistic can be obtained through an additional command. For some statistics, however, the associated effect size statistic is not available.

When an effect size statistic is not available, the standard error statistic for the statistical test being run is a useful alternative to determining how accurate the statistic is, and therefore how precise is the prediction of the dependent variable from the independent variable. The standard error is a measure of dispersion similar to the standard deviation. However, while the standard deviation provides information on the dispersion of sample values, the standard error provides information on the dispersion of values in the sampling distribution associated with the population of interest from which the sample was drawn.

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Standard error statistics measure how accurate and precise the sample is as an estimate of the population parameter. It is particularly important to use the standard error to estimate an interval about the population parameter when an effect size statistic is not available. The standard error is not the only measure of dispersion and accuracy of the sample statistic. It is, however, an important indicator of how reliable an estimate of the population parameter the sample statistic is. Taken together with such measures as effect size, p-value and sample size, the effect size can be a very useful tool to the researcher who seeks to understand the reliability and accuracy of statistics calculated on random samples.

Chapter 1, the introduction glances briefly at the marketplace of interpretation in order to spotlight the main trends and pinpoints what the different genres of interpretation have in common, namely, being acts of translation that transpose something into something else. Chapter 2, The Authority of the Canon, focuses on the rise of interpretation in the Rabbinic tradition, in which the commentary on the canon was meant to translate the holy text into the life of the community.

Reading the Torah opens up a space between the text and its exegesis, which makes the authority of the text oscillate between the canon and. An unknown error has occurred.

Please click the button below to reload the page. If the problem persists, please try again in a little while. No cover image. Read preview. Excerpt This book is an attempt to bring interpretation under close scrutiny, not least as there is a widespread opinion that such an activity is something that comes naturally. Read preview Overview. The Range of Interpretation The Range of Interpretation The Range of Interpretation The Range of Interpretation The Range of Interpretation The Range of Interpretation The Range of Interpretation The Range of Interpretation The Range of Interpretation

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