Hard to tell where the confusion lies from what you gave here. I assume that perhaps there is some confusion between SE and SD of the sample data?
The explanation is talking about the idea that when working with experimental data you are working with a sample of the original population and you are trying to approximate the sample mean (true mean). So a 95% CI is suggesting that you are 95% confident the true mean lies within that range of measurements. So you use (SD of the sample data)/sqrt
. So 95%CI= mean+or-1.96SD/sqrt
. So this accounts for the ability of the data to estimate the true mean of the population by taking into account the spread and sample size. This can be seen by the fact that as the n on the bottom approaches infinity (or as the SD approaches 0) the SE approaches 0 I.e you are exactly approximating the true (population) mean. So the bigger the sample size (and/or the smaller the scatter), the more narrow the CI, and the more precise the estimate.
So just to back up a little SD just measures the spread of your data and isn't, by itself used for CI calculation (as a side note, as the size of your sample increases this SD should approach the population SD). So using just SD you could say that 95% of your measurements are between 1.96SD's of the mean but again that is spread not CI. SE takes SD into account and teams it with sample size to help estimate the precision of your estimate of the mean. Thought of another way. The SE can be seen if you replicated the experiment a bunch (with the same sample size) and then calculated the SD of those measurements would approximate your calculated SE. As the sample size gets bigger those estimates get closer to approximating the true mean.
Simply put: SD is a measure of the scatter and SE quantifies how precisely you know the measure of the true mean, taking into account the scatter (SD) and the sample size sqrt
.
Hopefully that is helpful...if it's not perhaps consider stating the question you had in mind, or where the confusion was stemming from.
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