Calculating t

1
Calculating t
One sample test
Calculate same regardless of 1 vs 2 tailed
question
Two sample test (independent)
Two sample test (paired)
2
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
3
Ex for a 2 tail test w/ 28 df ?0.05
tcrit2.101 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 ?
4
Calculate actual p-value Assume t-calc3.001
3.001 gt 2.878 and indicates that the
probability of seeing a difference as extreme as
the observed was less than 0.01 (but we dont
know how much less)
5
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
6
2 approaches
-- just stat that null rejected (or not) at ?, in
this case you are only saying p lt ? (t-calcgtt
crit) -- calculate actual p-value (may be plt
0.0xx), gives more information than above
approach
7
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
8
original
slightly modified
Stays same
Significant 1 tail
Not significant 2 tail
9
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.
10
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
11
Directional two tailed approach Left-tailed
Alternative HA xbar1 lt xbar2 Null H0 xbar1
xbar2 Right-tailed Alternative HA xbar1 gt
xbar2
Power? 1- ?(prob type II error)- ?(prob type
III error)
Power is lower because of subtracting prob of
type III error