PSY 312 Power Analysis Homework h 2 .02 .04 .06 .09 .12 .16 .20 .25 .30 .36 .42
ID: 3367688 • Letter: P
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.
Explanation / Answer
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.
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