7.1-7.9

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36 Terms

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Interpreting P-value (Significance tests)
Assuming (context of Ho), there is a (percent) probability of getting a sample (proportion/mean) of (p/mu) or (more/less) purely by chance.
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Conclusion (Significance tests)
Because (p-value) is (less than/greater than) (alpha), we (reject/fail to reject) the Ho. We (have/do not have) convincing evidence of (Ho in context).
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p-value is less than significance level…
significant → reject null
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p-value is greater than significance level…
not significant → fail to reject the null
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Interpreting Power
If the true (mean/difference in mean) of (context) is (sample mean), there is a (Power) probability of correctly rejecting the null of (Ho).
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Type I Error
Truth: H0 true, Conclusion: Reject H0 P(Type I)=Alpha (Significance Level)
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Type II Error
Truth: Ha true, H0 false, Conclusion: Fail to reject H0
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Consequences…
Health consequences always considered worse
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Power
Truth: Ha true, Conclusion: Reject H0 P(Reject H0 I Ha is true) P(Power)=1-P(Type II)
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Increase Power by:
increasing n, increasing alpha, increasing distance btwn H0 & Ha
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Interpreting CI
We are (conf level)% confident the interval from (A) to (B) captures the true (mean/proportion) of (context).
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Interpreting CL
If we make many (conf level)% confidence intervals, we expect about (conf level)% to capture the true (mean/proportion) of (context).
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A CI gives…
plausible values
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normal/z-score smaller than t…
larger MOE for interval

for critical values the MOE of error is smaller and confidence interval is smaller
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Conf. Int. for Mu 1) state:
parameter (true mean…), confidence **level**
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Conf. Int. for Mu 2) plan:
1 sample t-interval, 3 conditions

a) random sample/assignment

b) 10% condition

c) normality (meets one of three options)

* population is normal → sample distribution is normal
* CLT n >= 30
* graph sample data for skew/outliers
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Conf. Int. for Mu 3) do:
x-bar +- t\* sx/root n (substitute #s in), interval

t\* → table B w/ tail % & df=n-1

If df not in table, round down
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Conf. Int. for Mu 4) conclude:
we are _% confident…

choosing sample size → t *unknown if n unknown, so use z*\* instead
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Conf. Int. for Difference in Means 1) state:
true difference in means, confidence **level**
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Conf. Int. for Difference in Means 2) plan:
2 sample t-int for Mu1-Mu2

3 conditions (x2)
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Conf. Int. for Difference in Means 3) do:
(xbar1-xbar2)+-t\*root(s1^2/n1+s2^2/n2)
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Conf. Int. for Difference in Means 4) conclude:
if 2 diff. n’s, use smaller n for df/t\* → gives a conservative estimate

real df is bigger 2-sample (show formula)
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(-,-)
x-bar2 is greater
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(+,+)
x-bar1 is greater
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(-,+)
no difference
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one sample t-int for Mdiff
x-bar diff+- t\* sdiff/rootn

mean diff → 1 mean = 1 sample
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paired data
2 specific data points that must be paired together (usually because they’re both from 1 individual)
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Test statistic (t-score)
t = x-bar - Mu/(Sx/rootn)
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Significance Test for Mu and CI
calculate test statistic (t-score) and use table B w/ df & tail probability OR tcdf(lower, upper, df)

**OR**

calculator → copy title up to x-bar
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If H0 in int.
H0 plausible → fail to reject
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If H0 not in int.
H0 not plausible → reject
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For 2-sided sig tests ONLY
a c% confidence int. will make the same decision as alpha = 1-C%
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Significance Test for a Difference in Means
t-score = (xbar1-xbar2)-(Mu1-Mu2 from H0) / root(s1^1/n1+s2^2/n2)

& graph & tcdf(labeled)

**OR**

2 sample t-test → copy title up to x
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paired data →
1 sample t-test for Mudiff

t=xbardiff - Mudiff / sdiff/rootn
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1 sample
* matched pairs creating 1 sample
* subtract then average
* 1 mean (Mudiff)
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2 samples
* 2 groups and 2 means
* average then subtract
* difference of means (Mu1-Mu2)