Question

PSY 312 Power Analysis Homework

      h²     .02   .04 .06 .09 .12 .16   .20   .25   .30   .36   .42   .49

power

.30     93    53    34   24   18   14    11     9     8     7     6     5

.40      132    74    47   33   24   19    15    12    10     8     7     6

.50      170    95    60   42   30   23    18    14    12     9     8     7

.60      257 143    90   62   45   34    24    20    16    13    11     9

.70      300 167 105   72   52   39    29    23    18    15    12    10

.80      343 191 120   82   59   44    33    26    20    16    13    11

.90      459 255 160   109   78   58    44    34    27    21    17    13

all values are for a = .05

Above is a partial power table. Use that table to solve the following problems. Where math is required, show your work.

1. I am planning a study to examine the inter-relationships between four variables: preparedness (yes, no), practice (in minutes), handedness (left, right), and performance (% correct).

a) For preparedness and practice, I expect a ?² of about .09.

What sample size should I use to have power = .70?

b) For handedness and practice I expect a ?²of about .42.

What sample size should I use if I only want to risk a 30% chance of a Type II error?

c) For preparedness and performance I expect a ?²of about .20.

What sample size should I use to have a 70% chance of correctly rejecting H₀?    

d) Which of these three sample sizes do you suggest I use for the study? Explain your reasoning.

Answer 1

a) For preparedness and practice, I expect a ?2 of about .09.
What sample size should I use to have power = .70

We look at the table for h2 = .09 and power = 0.7
The value is 72. Hence we will need a sample size of 72 for this experiment.

b) For handedness and practice I expect a ?2of about .42.
What sample size should I use if I only want to risk a 30% chance of a Type II error?

We again look at the table for h2 = 0.42 and power = 0.3
The value is 6. Hence we will need a sample size of 6 for this experiment.

c) For preparedness and performance I expect a ?2of about .20.
What sample size should I use to have a 70% chance of correctly rejecting H0?

We look at the table for h2= 0.2 and power = 0.7
The value is 29. Hence we will need a sample size of 29 for this experiment.

d) Which of these three sample sizes do you suggest I use for the study? Explain your reasoning.
Part a compares preparedness and practice, part b compares handedness and practice and part c compares preparedness and performance.
In order to find the inter relationship between all 4, preparedness (yes, no), practice (in minutes), handedness (left, right), and performance (% correct)., we will need all 3 experiments (a, b and c).

Since out the 3 cparisons (a, b and c) the highest required sample size of 72 if for a ( comparing preparedness and practice). The sample sizes required to make the other 2 comparisons is lowe and there a sample size of 72 would be enough to find the inter relation between all 4 parameters.