# t-test information sheet Independent Samples

```CoS - December 3, 1996

Research report is due Thursday, Dec. 12th.
"For Next Time" is due Friday, Dec. 13th if Eval Conf is Monday or Tuesday.
"For Next Time" is due Monday, Dec. 16th if Eval Conf is Wednesday or Thursday.

Goal: Compute 1 inferential statistic, then close your stat book.
If you've got more than one question, you only have to compute the statistic for one.  Once you've got one computed, help other people (put your name on the board).  We'll help you with more if everyone else is this far (later).

End:
(from "In the Literature section")
Let's say your nominal variable has 2 groups: 1st group and 2nd group

The 1st group was higher on the interval variable (M = ____, s.d. = _____) than the 2nd group (M = ____, s.d. = _____).  This difference was significant, t(df) = ___, p < .05, two-tailed.

The multiple choice way:

The 1st group was (a. higher/ b. lower) on the interval variable (M = ____, s.d. = _____) than the 2nd group (M = ____, s.d. = _____).  This difference was (a. significant/b. not significant), t(__) = ___, p (a. ) .05, (a. two-tailed/ b. one tailed).

If you choose the "<", then you choose "significant".
If you choose the ">", then you choose "not significant".

Blanks:
M	- you need to calculate the mean on the interval scale for group 1 and group 2.
s.d.	- you need to calculate the standard deviation on the interval scale for group 1 and group 2.

A key is to organize the data.  Take all the scores for the second variable
(interval/ratio or close).  Divide them into the scores from those in the
first group (e.g. women) and second group (e.g. men) based on your nominal variable.

t = ____	  t = (X1 - X2) - (µ1 - µ2)  / sX1-X2

X1, X2	- these are the M's you calculated above

(µ1 - µ2)	- your null hypothesis says "no difference", right?  then this = 0

sX1-X2		- another formula
sX1-X2	=   square root of (s2p/n1  *  s2p/n2)

n1, n2		are the number of subjects in the 1st  group and the 2nd group.
notice that it is the same number (s2p) that is divided by each of
group n's, THEN they are added together, THEN take the square root.

s2p 		- s2p =      ( SS1 +  SS2 ) divided by (df1 + df2)

note that you add SS1 and SS2 together, and add df1 and df2 together, THEN divide.

SS		SS =  (Square each X and then sum)  - (Sum of X's)2/N.

do this separately for each of your groups (SS1, SS2)

< or >	- check the table, you need 3 things: t, alpha, df

df	  	- degrees of freedom, goes in the "t(   )".

= df1 + df2 = (n1 - 1) + (n2 - 1)

Now, how about trying a graph.  Goal: graph shows your point. Try a few different graphs.
In the end you might decide you don't need one, or that a table might be better, but look
at the data in a few different ways first.