STA 205 Lecture 12: Packet+12+ANOVA+

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19 Dec 2018
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for independent random samples
were selected one from each
fast food chain
for each observational unit
the drive through time was
recorded no quantitative
we ONLY used atechnique
for 2population Means
NEED to compare 3t
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Packet 12: Analysis of Variance (ANOA) Textbook material: Supplemental Chapter 28
After completing this material, you should be able to:
conduct an analysis of variance f-test with the appropriate StatCrunch output.
determine when it is appropriate to consider multiple comparisons and interpret the results provided in
StatCrunch output.
state when it is valid to use this procedure
Goal:
Example: For fast-food restaurants, the drive-through window is an increasing source of revenue. The chain that offers
the fastest service is likely to attract additional customers. Each month, QSR magazine publishes its results of drive-
through service times (from menu board to departure) at fast-food chains. In a recent month, the drive-through service
times of random sample of 20 customers from Burger King, McDonald’s, Wendy’s, and White Castle were recorded.
What type of samples were selected? What variable was recorded? Why can none of the inferences we’ve discussed
so far be used to analyze this data?
What hypotheses are we interested in testing?
Now we need a way to test these hypotheses. We cannot simply use a t-test because there is no way to “take the
difference” of more than two different means – it just doesn’t make sense. To get around this problem, we need to use a
different technique we will use a new test statistic, called an F-statistic. The F-statistic is constructed from two different
variances (hence, analysis of variance) even though our goal is to compare several means.
When comparing two variances, we look at the ratio of those variances and use the F-distribution. So, the test statistic
that we’re interested in is the following:
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to compare 3T population Means
4independent random samples
drivethrough times
Hott BK.M HC.M W.tt _WC
Ha some difference inthemedns
fMStydstat Mst _treatment
Mse Crunch NSE error
labels
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spread between
MSE sample Means
Fuse spread within a
distribution
if null hypothesis is true
then the corresponding
sample Means should be very
SIMILAR results in a
small numerator in the
Fstatistic Alarge spread
in the numerator suggests
the hull hypothesis is likely
Not true
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