document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019220>Question 1019220</A>: <I><SPAN STYLE=\"word-break: break-all;\"> when we are using S.E instead of standard deviation for probability determination  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635217 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=635217\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> standard error is used when you are dealing with the distribution of sample means.\r<BR>\n" );
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document.write( "the standard error is the standard deviation of the distribution of sample means.\r<BR>\n" );
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document.write( "this is different from the distribution of sample elements within one sample.\r<BR>\n" );
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document.write( "the difference is shown in the following example:\r<BR>\n" );
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document.write( "you have 3 samples.\r<BR>\n" );
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document.write( "each sample contains n elements.\r<BR>\n" );
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document.write( "each sample has a mean and a standard deviation.\r<BR>\n" );
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document.write( "sample 1 mean might be 20 and standard deviation is 30.<BR>\n" );
document.write( "sample 2 mean might be 30 and standard deviation is 70.<BR>\n" );
document.write( "sample 3 mean might be 40 and standard deviation is 50.\r<BR>\n" );
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document.write( "you create a distribution of sample means by taking the mean of each of these samples and forming a distribution from them.\r<BR>\n" );
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document.write( "your distribution of sample means might have a mean of 30 with a standard deviation of 10.\r<BR>\n" );
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document.write( "the standard deviation of the distribution of sample means will be smaller than the standard deviation of each sample.\r<BR>\n" );
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document.write( "the larger the sample size, the smaller the distribution of sample means will be.\r<BR>\n" );
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document.write( "this distribution of sample means is called the standard error of the mean.\r<BR>\n" );
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document.write( "there is a formula to estimate the size of the standard error.\r<BR>\n" );
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document.write( "it is standard error = standard deviation of the population divided by the sample size.\r<BR>\n" );
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document.write( "if you don't have the standard deviation of the population, you use the standard deviation of the sample you are working with.\r<BR>\n" );
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document.write( "that's the difference between using a z-score or a t-score.\r<BR>\n" );
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document.write( "with a z-score, you use the population standard deviation in the equation.\r<BR>\n" );
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document.write( "with a t-score, you use the sample standard deviation.\r<BR>\n" );
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document.write( "the formula is the same.\r<BR>\n" );
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document.write( "it's only a matter of where you get the standard deviation from.\r<BR>\n" );
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document.write( "the formula is se = sd / sqrt(n)\r<BR>\n" );
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document.write( "se is the standard error of the mean.<BR>\n" );
document.write( "sd is the standard deviation of the population or of the sample, whichever you can get.<BR>\n" );
document.write( "n is the sample size.\r<BR>\n" );
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document.write( "what this is telling you is that, the larger your sample size is, the smaller the standard error of the distribution of sample means will be.\r<BR>\n" );
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document.write( "what is the sample size in the distribution of sample means?\r<BR>\n" );
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document.write( "it is the sample size of each sample where the mean is being calculated from.\r<BR>\n" );
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document.write( "in my example above, i had 3 samples.\r<BR>\n" );
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document.write( "if each of those samples contained 100 elements, then the sample size would be 100.\r<BR>\n" );
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document.write( "iof each of those samples contained 1000 elements, then the sample size would be 1000.\r<BR>\n" );
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document.write( "the theory behind standard error assumes that each of the samples taken are of the same size.\r<BR>\n" );
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document.write( "here's one tutorial on the subject.\r<BR>\n" );
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document.write( "what happens if the sample size is 1?\r<BR>\n" );
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document.write( "the formula is se = sd / sqrt(n) which becomes se = sd / sqrt(1) which becomes se = sd.\r<BR>\n" );
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document.write( "if the sample size is 1, then the standard error or the mean is the same as the standard error of the population or the sample, whichever is used.\r<BR>\n" );
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document.write( "that's because, with a sample size of 1, each mean is the only element in the sample which means it's not a mean, but an element.\r<BR>\n" );
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document.write( "it's complicated and confusing, but, in general:\r<BR>\n" );
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document.write( "if you are dealing with a distribution of elements, then use standard deviation.\r<BR>\n" );
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document.write( "if you are dealing with a distribution of sample means, then use standard error.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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