Pt 2: Sept. 26, 2013

• Probability that the study will produce a statistically significant result when the research hypothesis is in fact true
– That is, what is the power to correctly reject the null?
– Upper right quadrant in decision table
– Want to maximize our chances that our study has the power to find a true/real result
• Can calculate power before the study using predictions of means
– or after study using actual means

• Steps for figuring power:
1.
Gather the needed information: (N=16)
* Mean & SD of comparison distribution (the distrib of means from Ch 5 – now known as Pop 2)
* Predicted mean of experimental group (now known as Pop 1)
* “Crashed” example:
Pop 1 “crashed group” mean = 5.9
Pop 2 “neutral group/comparison pop”
μ = 5.5
,

= .8,
 m
= sqrt (

2
)/N
 m
= sqrt[(.8
2 ) / 16] = .2

2.
Figure the raw-score cutoff point on the comparison distribution to reject the null hypothesis (using Pop 2 info)
• For alpha = .05, 1-tailed test (remember we predicted the
‘crashed’ group would have higher fault ratings), z score cutoff
= 1.64.
• Convert z to a raw score (x) = z(
 m
) + μ x = 1.64 (.2) + 5.5 = 5.83
• Draw the distribution and cutoff point at 5.83, shade area to right of cutoff point  “critical/rejection region”

3. Figure the Z score for this same point, but on the distribution of means for Population 1 (see ex on board)
• That is, convert the raw score of 5.83 to a z score using info from pop 1.
– Z = (x from step 2 -
 from step 1exp group )
– (5.83 – 5.9) / .2 = -.35
 m
(from step 1 )
– Draw another distribution & shade in everything to the right of -.35

4. Use the normal curve table to figure the probability of getting a score higher than Z score from Step 3
• Find % betw mean and z of -.35 (look up .35)…
= 13.68%
• Add another 50% because we’re interested in area to right of mean too.
• 13.68 + 50 = 63.68%… that’s the power of the experiment.

• Our study (with N=16) has around 64% power to find a difference between the ‘crashed’ and ‘neutral’ groups if it truly exists.
– Based on our estimate of what the ‘crashed’ mean will be (=5.9), so if this is incorrect, power will change.
– In decision error table 1-power = beta (aka…type 2 error), so here:
– Alpha?
– Power?
– Beta?

• Main influences – effect size & N
• 1) Effect size – bigger d  more power
– Remember formula: d


1



2
– Bigger difference between the 2 group means, more
power to find the difference (that difference is the numerator of d)
– Also, the smaller the population standard deviation, the bigger the effect size (sd is the denominator)

• Figuring power from predicted effect sizes
– Sometimes, don’t know

1 for formula, can estimate effect size instead (use Cohen’s guidelines:
.2, .5, .8 or -.2, -.5, -.8)

1
 
2

d

Example:

• Rule of thumb: try for at least 80% power
– Interpretation of 80% power – we have a .8 probability of finding an effect if one actually exists
• See Table
• 1) Try to increase effect size before the experiment
(increase diffs betw 2 groups)
– Training/no training group – how could you do this?

• 2) Try to decrease pop SD – use standardization so subjects in 1 group receive same instructions
• 3) Increase N
• 4) Use less stringent signif level (alpha) – but trade-off in reducing Type 1 error, so usually choose .05 or .01.
• 5) Use a 1-tailed test when possible