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1783Re: [ai-geostats] F and T-test for samples drawn from the same p

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  • Chaosheng Zhang
    Dec 5, 2004
      Dear all,
      I'm wondering if sample size (number of samples, n) is playing a role here.
      Since Colin is using Excel to analyse several thousand samples, I have checked the functions of t-tests in Excel. In the Data Analysis Tools help, a function is provided for "t-Test: Two-Sample Assuming Unequal Variances analysis". This function is the same as those from many text books (There are other forms of the function). Unfortunately, I cannot find the function for "assuming equal variances" in Excel, but I assume they are similar, and should be the same as those from some text books.
      From the function, you can find that when the sample size is large you always get a large t value. When sample size is large enough, even slight differences between the mean values of two data sets (x bar and y bar) can be detected, and this will result in rejection of the null hypothesis. This is in fact quite reasonable. When the sample size is large, you are confident with the mean values (Central Limit Theorem), with a very small stand error (s/(sqrt(n)). Therefore, you are confident to detect the differences between the two data sets. Even though there is only a slight difference, you can still say, yes, they are "significantly" different.
      If you still remember some time ago, we had a discussion on large sample size problem for tests for normality. When the sample size is large enough, the result can always be expected (for real data sets), that is, rejection of the null hypothesis.
      Dr. Chaosheng Zhang
      Lecturer in GIS
      Department of Geography
      National University of Ireland, Galway
      Tel: +353-91-524411 x 2375
      Direct Tel: +353-91-49 2375
      Fax: +353-91-525700
      Web 1: www.nuigalway.ie/geography/zhang.html
      Web 2: www.nuigalway.ie/geography/gis/index.htm
      ----- Original Message -----
      From: "Isobel Clark" <drisobelclark@...>
      To: "Donald E. Myers" <myers@...>
      Cc: "Colin Badenhorst" <CBadenhorst@...>; <ai-geostats@...>
      Sent: Saturday, December 04, 2004 11:49 AM
      Subject: [ai-geostats] F and T-test for samples drawn from the same p

      > Don
      > Thank you for the extended clarification of F
      and t
      > hypothesis test. For those unfamiliar with the
      > concept, it
      is worth noting that the F test for
      > multiple means may be more familiar
      under the title
      > "Analysis of variance".
      > My own brief
      answer was in the context of Colin's
      > question, where it was quite clear
      that he was talking
      > aboutthe simplest F variance-ratio and t comparison
      > means test.
      > Isobel

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