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Put another way, Standard Error is the Standard Deviation of the population mean. If the SD of this distribution helps us to understand how far a sample mean is from the true population mean, then we can use this to understand how accurate any individual sample mean is in relation to the true mean. In fact, SE tells us that we can be 95% confident that our observed sample mean is plus or minus roughly 2 (actually 1.96) Standard Errors from the population mean.The below table shows the distribution of responses from our first (and only) sample used for our research.Standard Deviation and Standard Error are perhaps the two least understood statistics commonly shown in data tables.
At first glance (looking at the means only) it would seem that reliability was rated higher than value.Standard Deviation (often abbreviated as "Std Dev" or "SD") provides an indication of how far the individual responses to a question vary or "deviate" from the mean.SD tells the researcher how spread out the responses are -- are they concentrated around the mean, or scattered far & wide?The individual responses did not deviate at all from the mean.In Rating "B", even though the group mean is the same (3.0) as the first distribution, the Standard Deviation is higher.We then make inferences about the population from the results obtained from that sample.If a second sample was drawn, the results probably won't exactly match the first sample.If the mean value for a rating attribute was 3.2 for one sample, it might be 3.4 for a second sample of the same size.If we were to draw an infinite number of samples (of equal size) from our population, we could display the observed means as a distribution.Consider the following example showing response values for two different ratings.In the first example (Rating "A") the Standard Deviation is zero because ALL responses were the mean value.