Two t s for two conditions

1
Two t s for two conditions

• Comparing means for
• -Correlated groups
• -Independent groups

2
Which one to use?

• Use correlated groups t test for
• Repeated measures (before-after) designs
• Twin pair studies
• Matched pair studies
• Pair studies use what is often called paired
  groups or paired samples design, as in SPSS
• Use independent groups t test for designs which
  have different people randomly assigned to the
  two conditions

3
t for independent groups
t M1 - M2 sM1 - M2
SS1 SS2 1 1 (n1 n2 -2) n1
n2
sM1 - M2

4
Cohens d

• d (m1 - m2) / s

5
Assumptions underlying the t-test

• 1. Scores within the sample(s) must be based on
  independent measurements. If the responses of
  one participant influence the responses of
  another, then the two scores are not independent.
• 2. The underlying populations are normal.
• 3. The underlying populations have the same
  variance, within chance variation. This is known
  as the assumption of homogeneity.
• The t-test is robust to violations of the
  assumption of homogeneity if the sample sizes are
  equal.

6
Testing the assumption of homogeneity of variance

• Hartleys F test
• Form a ratio of the variances, to see how many
  times larger the greater variance is compared to
  the lesser variance.
• Thus, F larger variance/smaller variance
• Or F s1 / s2
• Compare the obtained value of F to the critical
  value from table B-3, with k-1 degrees of freedom
  between groups (numerator) and n-1 degrees of
  freedom within groups (denominator).

7
t for correlated groups

• For correlated groups, first find D, the
  differences between the members of the N paired
  scores.
• Then find SSD SD2 - (SD)2/N, where N is the
  number of pairs of scores.
• Finally, t