Department

Psychological & Brain Sci (Psychology)Course Code

L33 Psych 300Professor

NestojkoChapter

8This

**preview**shows page 1. to view the full**5 pages of the document.**Chapter 08: Confidence Intervals, Effect Size, and Statistical Power

Confidence Intervals

●Point Estimate - a summary statistic from a sample that is just one number used as an

estimate of the population parameter

●Interval Estimate - based on a sample statistic and provides a range of plausible values

for the population parameter

●Calculating Confidence Intervals with Z Distributions

○Step #1: Draw a picture of a distribution that will include the confidence interval

○Step #2: Indicate the bounds of the confidence interval on the drawing

○Step #3: Determine the z statistics that fall at each line marking the middle 95%

○Step #4: Turn the z statistics back into raw means

○Step #5: Check that the confidence interval makes sense

Effect Size

●The Effect of Sample Size on Statistical Significance

○Statistical Significance - rejecting the null hypothesis means that we have

determined that an observed result is unlikely to have occurred by chance, if the

null hypothesis were actually true

○Statistical Significance is another term for ‘rejecting the null hypothesis’

○Statistical Significance does not

necessarily indicate practical importance

●Effect Size - indicates the size of a difference and is unaffected by sample size

○The less overlap between curves, the bigger the effect size

○If you have a large enough sample size (N), even a very small real difference in

population means will turn out to be statistically significant

○Effect Size is based on two things:

■The size of the difference between means

■Variability in distributions being compared

○The less

overlap between distributions, the larger

the effect

●Cohen’s D - a measure of effect size that assesses the difference between two means in

terms of standard deviation, not standard error

○Assesses the difference between means

using population standard deviation

instead of standard error (of sampling

distribution)

○The population standard deviation is not

affected by sample size, whereas

standard error is affected by sample size

- meaning that a z-score can change

dramatically based on a sample size but

the Cohen’s D score will not

■A more extreme z-statistic does not

indicate a larger effect size or a

rejection of the null hypothesis

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Rough Guideline on what’s a small, medium, or large Cohen’s D

Effect Size

Convention

Overlap

Small

0.2

85%

Medium

0.5

67%

Large

0.8

53%

●Meta-Analysis: a study that involves the calculation of a mean effect size from the

individual effect sizes of many studies

○Step #1: Select the topic of interest, and decide exactly how to proceed before

beginning to track down studies

○Step #2: Locate every study that has been conducted and meets the criteria

○Step #3: Calculate an effect size, often Cohen’s D, for every study

○Step #4: Calculate statistics - ideally, summary statistics, a hypothesis test, a

confidence interval, and a visual display of the effect sizes

Statistical Power

●Statistical Power - a measure of the likelihood that we will reject the null hypothesis,

given that the null hypothesis is false

○If we have an alpha of .05, what is the probability of having a Type I error?

■The probability is equal to the alpha, so it is .05

Null Hypothesis is True (no

effect)

Null Hypothesis is False

(effect)

Reject Null Hypothesis

Type I Error (false alarm)

Probability = alpha

Correct!

Probability = 1 - B (called

power) usually aim for power

at around .80 or 80%

Fail to Reject the Null

Hypothesis

Correct!

Type II Error (miss)

Probability = B

●The Importance of Statistical Power

○Step #01: determine the information needed to calculate statistical power - the

hypothesized mean for the sample; the population mean; the population standard

deviation; and the standard error based on this sample size.

○Step #02: determine a critical value in terms of the z distribution and the raw

mean so that statistical power can be calculated

○Step #03: calculate the statistical power - the percentage of the distribution of

means for population 1 (the distribution centered around the hypothesized

sample mean) that falls above the critical value

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