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T-Tests For Dummies

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									T-Tests For Dummies

As in the books, not you personally!
          From Yesterday’s Notes
• Note that the numerator of the formula for t is the
  difference between the means. The denominator is a
  measure of the experimental error in the two groups
  combined. The wider the difference between the
  means, the more confident you are in the data. The
  more experimental error you have, the less confident
  you are in the data. Thus, the higher the value of t, the
  greater the confidence that there is a difference.
• So, the t value gives you a statistical measure of (a
  degree of) how different your two means are, based on
  the size of your samples.
                   Bar Plots
• Sometimes it is easy to observe a difference
  between two means by using a bar plot, for
  example:




• But that’s not enough!
  You need to use a statistical test for proof.
• So you calculate two means and see that they
  are different… SO WHAT!!??
• What you really should be asking, is:

   “Is the fact that there is an observed
  difference between the two means significant,
  or not?”
• Well, to determine the answer to this
  question, we need something to compare to.
• So we use the t-table: a set of statistical
  measures of the amount of difference
  between two means that you can expect to
  see due to random sampling (chance)
• These measures are based on the size of the
  samples  specifically, what we calculate as
  the degrees of freedom
• Now, as with any statistical measure, there is
  going to be some degree of error.
• So, the t-table gives the expected t-values due
  to chance in terms of particular probabilities
  (it gives a measure of mean difference due to
  chance with different degrees of error)
• In biology, we are generally concerned with
  p=0.05 (in other words, 95% confidence), and
  p=0.01 (or 99% confidence).
          Putting it all together
• So let’s say for example that you take two
  samples of size 10 and calculate their means.
• You see that the means are different and use the
  null hypothesis as a basis for your t-test (as any
  skilled scientist would do)
• You calculate your t-value and obtain 4.73 (right
  off the bat, for a sample size of 10, you should be
  thinking: wow! that’s a large t-score)
• So you’re thinking that the difference you
  observed between the means is significant…
  WELL PROVE IT!!!!
                 THE PROOF
• So you consult your trusty t-table and see that
  for 18 d.f., your calculated t-value exceeds ALL
  of the theoretical t-values listed in the table
  (by A LOT, I might mention)
• So what, then, do you conclude?
                 THE PROOF
• Well, the fact that your t-value (a measure of the
  degree of difference in your means) exceeds the
  critical values in the table (measures of the
  degree of difference b/w means due to chance)
  means that the difference b/w the sample means
  that you observed IS SIGNIFICANT!
• So you REJECT the null hypothesis that there is no
  difference, and accept your alternative
  hypothesis that there is a difference between
  your means (and that it’s not due to sampling
  error or chance!)
                  TEST TIME!
•   Clear off your desks!
•   Stop reading this powerpoint!
•   Get your calculators out!
•   Good luck!!!!!!!

								
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