Calculating t X -  t = s x X1 – X2 t = s x1 – x2 s d One sample test Calculate same regardless of 1 vs 2 tailed question t = X1 – X2 s x1 – x2 Two sample test (independent) d t = s d Two sample test (paired)

Determining critical t and p-value, and deciding whether to reject the null Always select  before running the test. Usually 0.05, need a good reason to change this  is the p level at which you will reject the null Once you have decide , you can determine the critical t, based on your df and whether you pose a 1 or 2-tailed question If you change , df, or 1vs.2 tails you will find a different critical t, but your calculated t will not change If t-calc is greater than t-crit you reject the null

Ex for a 2 tail test w/ 28 df =0.05 tcrit=2.101 Any t-calc that is equal to or exceeds 2.101 will allow you to reject the null at the given  t-critical Reject at your chosen 

Calculate actual p-value Assume t-calc=3.001 3.001 > 2.878 and indicates that the probability of seeing a difference as extreme as the observed was less than 0.01 (but we don’t know how much less)

Restate the meaning of your p-value probability of seeing a difference as extreme as the observed based on chance alone, assuming that the null hypothesis is true Low p-values suggest that the test statistic would be unlikely if the null were indeed true

2 approaches -- just stat that null rejected (or not) at , in this case you are only saying p <  (t-calc>t crit) -- calculate actual p-value (may be p< 0.0xx), gives more information than above approach

T-critical changes between one vs. two sided A t-value that is significant at 0.05 for a 1 tailed test, is significant only at the 0.10 level if it is really a 2-tailed test

original slightly modified Stays same Significant 1 tail Not significant 2 tail

Would be “cheating” to see significant one-tailed result and go back and decide that you really did have a reason to predict “ A would be greater/less than B” Statistical SWAT team will not enter your office to confiscate your computer, people do do this. But in class we must learn what is correct, what you do later is your business.

Type III error: rejecting null for wrong reason, not commonly encountered term Suggested solution is directional two-tailed test Conventional approach Null; H0: xbar1 = xbar2 Alternative; HA: xbar1 ≠ xbar2

Directional two tailed approach Left-tailed Alternative; HA: xbar1 < xbar2 Null; H0: xbar1 = xbar2 Right-tailed Alternative; HA: xbar1 > xbar2 Power = 1- (prob type II error)- (prob type III error) Power is lower because of subtracting prob of type III error