CHAPTER 25 Ten Easy Ways to Estimate How Many Participants You Need 363

Comparing Paired Values»

» ^{Applies to: Paired Student t test or Wilcoxon Signed-Ranks test.»}

» ^{Effect size (E): The average of the paired differences divided by the SD of the}

paired differences.»

» ^{Rule: You need 8}

2

/E participants (pairs of values).

Imagine that you’re studying test scores in struggling students before and after

tutoring. You determine a six-point improvement in grade points is the effect size

of importance, and the SD of the changes is ten points. Then E

6 10

/

, or 0.6, and

you need 8

0 6

2

/

.

, or about 22 students, each of whom provides a before score and

an after score.

Comparing Proportions between

Two Groups»

» ^{Applies to: Chi-square test of association or Fisher Exact test.»}

» ^{Effect size (D): The difference between the two proportions (P}1 ^{and P}2^{) that}

you’re comparing. You also have to calculate the average of the two propor-

tions: P

P

P

1

2

2

/ .»

» ^{Rule: You need 16}

1

2

P

P

D

/

participants in each group.

For example, if a disease has a 60 percent mortality rate, but you think your drug

can cut this rate in half to 30 percent, then P

0 6

0 3

2

.

.

/

, or 0.45, and

D

0 6

0 3

.

. , or 0.3. You need 16

0 45

1

0 45

0 3

2

.

.

/

.

, or 44 participants

in each group (88 total).

Testing for a Significant Correlation»

» ^{Applies to: Pearson correlation test. It is also a good approximation for the}

non-parametric Spearman correlation test.»

» ^{Effect size: The correlation coefficient (r) you want to be able to detect.»}

» ^{Rule: You need 8}

2

/r participants (pairs of values).