Chapter 8 Flashcards
Confidence Intervals
Point estimate: s__ statistic-o__ number as estimate of p__.
-e.g: m__
Margin of error
Interval estimates: Based on our s__ statistic, r__ of s__ statistics we would expect if we repeatedly sampled from same p__.
- e.g: c__ i__
- Interval estimate includes mean we would expect for s__ statistic a certain p__ of the time were we to sample from the same population r__. (typically set at __%)
The range around the mean when we add and subtract a m__ of e__.
•Confirms findings of h__ testing and adds more d__.
summary, one, population, mean
sample, range, sample, population, confidence interval
sample, percentage, repeatedly, 95%
margin of error
hypothesis, detail
Calculating Confidence Intervals
-Confidence intervals are always _ tailed.
- Step 1: Draw a picture of a distribution that will include confidence intervals (use s__ m__)
- Step 2: Indicate the bounds of the CI on the drawing (based on c__ i__ %)
- Step 3: Determine the _ s__ that fall at each line marking the middle 95%
- Step 4: Turn the z statistic back into r__ means
- (Step 5: Check that the CIs make s__)
2
sample mean
Confidence interval %
z statistics
raw
sense
Calculating Confidence Intervals ex:
Example: IQ Scores
•IQ scores are designed to have a mean of 100 and a standard deviation of 15. A school psychologist is convinced that the mean IQ score of the high school seniors in her district is different from 100. She administered an IQ test to random sample of 50 seniors in her district and found their mean IQ was 104.
-a 95% confidence interval
- Calculate confidence interval
- Write out in notation
- Make statement about what it means
So, draw out and see that each side has 2.5% because you divide the 5% evenly-look up 2.5% in z score chart which is 1.96 upper and -1.96 lower.
Next calculate raw means:
formula: z(σM)+M
σM is equal to the SD/square root of N
M lower: -1.96(2.12)+104= 99.84
M upper: 1.96(2.12)+104=108.16
Therefore, 95% confidence interval is:
[99.84, 108.16]
To write out in notation:
p(99.84 ≤ μ ≤ 108.16) = .95
The probability is .95 that an interval such as 99.84 to 108.16 contains the true average IQ score.
Is 100 (population mean) in this range? If so, fail to reject.
If it were 110, you would reject.
μ is f__ – not a v__
It’s either in the c.i. or it isn’t
-Only i__ varies from experiment to experiment
We never know whether it’s actually in there-we just tell the p__ given our s__ data.
fixed, variable
interval
probability, sample
Effect Size: Just how big is the difference?
- Increasing s__ s__ will make us more likely to find a statistically significant effect.
- but statistical significance does not mean p__ significance.
What is effect size?
-Size of difference that is u__ by s__ size.
S__ across studies
sample size
practical
unaffected, sample
standardization
How to Increase effect size:
- __ the amount of overlap between 2 distributions.
1) their m__ are farther apart.
2) smaller v__ within each population.
decrease
means
variation
Cohen’s d estimates effect size:
Assesses difference between means using standard d__ instead of standard e__.
write out equation
deviation, error
d= (M- μ)/σ
Calculate effect size using cohen’s d:
IQ scores are designed to have a mean of 100 and a standard deviation of 15.A school psychologist is convinced that the mean IQ score of the high school seniors in her district is different from 100. She administered an IQ test to random sample of 50 seniors in her district and found their mean IQ was 104.
What does effect size tell us?
-degree to which the participants’ mean exceeded the value expected by c__.
Interpret cohen’s d value for example above
Based on cohen’s guidelines, what size of an effect is it?
d= (M- μ)/σ
d= 104-100/15= 0.27
chance
the average score of the participants was 0.27 standard deviations higher than the known mean.
small
Cohen’s Conventions for Effect Sizes d:
-identify the number and amount of overlap
small:
medium:
large:
small: 0.2, 85% overlap
medium: 0.5, 67% overlap
large: 0.8, 53% overlap
Why do we need a confidence interval:
-To see how likely your m__ is to appear with a given c__
If the reference value specified in H0 lies outside the interval (that is, not beneath the lower or upper tail), you can __ H0.
If the reference value specified in H0 lies within the interval (that is, beneath the lower or upper tail), you __ to reject H0.
reject
fail
effect size doesn’t say anything about s__ s__
statistical significance.
Statistical Power:
Measure of our ability to r__ the null hypothesis, given that the null is f__.
aka: probability we will:
- reject null when we s__.
- find an e__, when it really exists.
- avoid type __ errors (β)
so power = (formula)
reject, false
should
effect
2
power = 1-β
Statistical Power:
In hypothesis-testing, we compare two states of the world: (H0 T__) and (H0 F__): can be represented as two d__ patterns of n__ distributions.
Alpha (α) cuts through the H0 True distributions, but also maps onto a point in the H0 False distributions for a given effect size, partitioning β and (1-β).
So as alpha decreases, power __.
•Just not in : proportion.
true, false
distinct, normal
decreases
1:1
Statistical Power:
If power is 80, beta is __.
-there is an __ chance you’ll find difference if it actually exists
everything to the right of alpha is __, everything to the left of alpha is __.
20
80
power, beta
Factors Affecting Power:
- Alpha level
•Higher level __ power (e.g., from .05 to .10)
•Potential problem?
•Increase chance for Type __ error - 1- or 2-tailed test
•_-tailed test increases power
•Potential problem?
•Only helpful if CERTAIN of d__ of effect - Sample size and variability
•__ sample size and __ standard deviation (reduce “noise”) __ power - Actual difference (effect size)
•Increase d__ between the means (stronger m__ = more p__ effect)
increases, 1
1, direction
larger, smaller, increases
difference, manipulation, pronounced
