T-Tests For Dummies

1
T-Tests For Dummies

• As in the books, not you personally!

2
From Yesterdays 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.

3
Bar Plots

• Sometimes it is easy to observe a difference
  between two means by using a bar plot, for
  example
• But thats not enough! You need to use a
  statistical test for proof.

4

• 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?

5

• 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

6

• 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
  p0.05 (in other words, 95 confidence), and
  p0.01 (or 99 confidence).

7
Putting it all together

• So lets 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! thats a large t-score)
• So youre thinking that the difference you
  observed between the means is significant WELL
  PROVE IT!!!!

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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?

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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 its not due to sampling
  error or chance!)

10
TEST TIME!

• Clear off your desks!
• Stop reading this powerpoint!
• Get your calculators out!
• Good luck!!!!!!!