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lesson forty one
one-way analysis of variance
example 2
ecologists monitoring the population of rainbow trout
in california
examined and measured some specimens
in the Yuba
Sacramento and Truckee rivers
the weight in ounces
for the rainbow trout gathered by the ecologist
it's presented in the following table
by the location
where the specimen was caught
so here are the results
conduct a hypothesis test
using alpha equal to 0.05 to determine
whether the mean weight for the population of rainbow trout
in the Yuba
Sacramento and Truckee rivers are all equal
so miss example veronica dot the hypothesis test using the customary
alpha people's point oh fine
to determine whether the mean weight for the population of rainbow trout
bus this test involves
depopulation prabir u
for the mean way
into yuba sacramento and truckee rivers
that's we're dealing with three population means do you want
new to canoe three
where the first population reverse the rainbow trout caught me huber river
and the second population reverse the rainbow trout called the sacramento
river
and third population reverse the rainbow trout caught in the track here
so here in the stressful to determine whether the bean way
for the population rainbow trout
in the Yuba
Sacramento and Truckee rivers
are all equal
that is
does the new one
equally to equals new three
a one-way analysis and variance is used to determine if the means for more than
two populations are all equal
in order to apply a one-way analysis of variance
each of the independent random samples must be selected from populations that
we simply follow a normal distribution
with approximately equal pay resist
or standard deviations
dust will be conducting are one-way analysis of various under these
assumptions
so to follow the steps over one-way analysis of various hypothesis test
procedure
we begin by stating the hypotheses
eight show an h one always stayed in the same manner
and one-way analysis is correct
Ho is always that all of the population means are equal
and H1 is always that not all the population means are equal
now the state of the hypotheses feature on each one we've ended in a fight
parked off a level of significance
here we use in the customer alpha point oh five
now we can use that e_i_t_c_ for calculator
to calculate the key value to reach our decision
to do this we need to enter the sample data into the list
so here are the sample results of the weight of the rainbow trout
ka conduct for sample humor river
second sample
sacramento ever
and the third sample truckee river
the sample values can be entered into the t eighty-four calculator by pressing
stap
and enter
canada list editor
and then we need to arrow up
and press clear inter to clear out
lists of old data
to make room for the new data
now the first sample
the weight of the rainbow trout caught in the year ever
this in turn to the first list
thirty eight point four
sixteen point seven
sixty two point zero
forty five point one
there is seven point two
thirty nine point five
fifty three point four
thirty eight point nine
now in the second list will enter our second sample
the weight of the rainbow trout
in the sacramento where
sixty point five
seventy one point seven
forty six point two
seventy seven point four
forty nine point one
fifty six point three
sixty seven point nine
and finally sixty three point one else's
malcolm list three
will enter the wait for the rainbow trout
ka conduct rocky river
thirty-nine point six
fifty six point three
thirty eight point five
thirty two point one
fifty four point four
forty two point eight
forty point seven
nineteen point three
now that we can order three samples of data
intro three lives
we can continue
with our hypothesis test procedure
to calculate the key value for this test
we need to
execute the anova commitment
to get to the you know what command on the t ready for a calculator
repress
step
pero over two tests
and then the arrow up to the cursor is next to a no
pressed enter to select
and then injury and the list of data strained with
second one for list one
comma
second to fruitless to
comma
second three for this trip
close fantasy inter
calculates the people you forecast
and rounding the p dot two-three places after the decimal
we see that the p dot a
is approx one point zero zero three
that we have our peopel u
we can reach our decision
since the peopel your point zero zero three
did spoil fiberglass
the decision has to reject a child
and when we rejected shuttle
we have sample evidence indicating that it was not done
and hence
h one isabelle
that's our conclusion here would be that not all of the population means are
equal
so based on the results of hypothesis test procedure
we can make the following statement
therefore
the mean way
for the population of rainbow trout in the uba
sacramento in truckee rivers
are not halt equal
the results this hypothesis testing procedure only lead to the conclusion
that the means for these three populations are not all equal
it does not indicate which is a particular means are not equal or
specifically how they differ
in order to determine which particular population means are not quote and
specifically how we differ
all pairwise comparison confidence of course could be constructed
estimate the actual differences in the population means
with a one minus alpha times when a percent simultaneous level of confidence
the three
population means require
three pairwise comparison confidence levels
want to compare at the difference between you one
commute to
a second one compare the difference between new one
canoe three
and the third one
compare the difference between you two canoe three
in this case
these would be comparing
difference in the mean wait for the trial card and a you back in the
sacramento rivers
the u_s_ and the truckee rivers
in the sacramento and the tricky rivers
for the three pairwise comparison confidence levels to achieving one minus
alpha times one nine percent level of confidence simultaneously
each individual confidence in the last minute
must be constructed
with a q group of one minus alpha level of confidence
use the data gathered by the ecologist
to construct all pairwise comparison confidence intervals
estimate the differences in the mean way
for the population of rainbow trout
in the u_s_
sacramento contract he reversed
with a simultaneous confidence level of ninety five percent
and interpret the results
so here we can use the day to gather to construct all pairwise comparison
confidence intervals
with a simultaneous confidence level ninety five percent
for three pairwise comparison confidence intervals to cheat this customer in
ninety five percent level of confidence simultaneously
each individual confidence in the last minute
must be constructed using
one might ask alpha equal to the q group the point nine five
also estimate that difference in the mean way
for the population of rainbow trout in the u_s_ sacramento attractive rivers
by doing this in paris
we need to conductor confidence interval testament
for the pairs of to population
means
that's the following crisis through the
confidence vote estimate for the difference in the pairs
of the population means
this involves conducting a two cm tea etc amid committee eighty-four
calculator
and this command would have to be repeated three times
to make the estimates for each of the repair wise comparisons
the new one minus me too
the new one minus new three
and then you two might see three
and after we
construct these three pairwise comparison confidence intervals
we then need to interpret the results so that we could tell which of the
population means differs significantly from the others
to conduct a to see if she had command committee ready for calculator
we would press
stap
arrow over to test
and then they wrote down until the cursor just next to to see a tuyet
and then we pressed enter to select
here we have data that was included
and for the first
pairwise difference between you and miss me too
we need to use the data enlist one unlisted
for the confidence level we need to do a q group of the point nine five
so we press three
and then math
narrowed down to the root symbol
inter
and then point nine five
pressing enter we'll try to make a q group of point ninety five
pulled as always no
for our case
and that arrow down to calculate press enter
so here we find investment of the difference between the one much need to
ranges from a negative thirty six point five eight
to negative three point six seven
now for the second compares
we pressed at
car over to test
and slept two seventy a
here for the difference between you one last new three we need to use the data
in list one
and list three
keeping everything else the same we wrote down to calculate press enter
and here we find that the difference between the one and new three ranges
from a negative sixteen-point away
to a positive seventeen point nine five
now for the third
comparison you too much sleep three requests tapped her over to test
and then we need to use the data and list too
gentlest three
arrow down
to calculate
press enter
and here we see the difference ranges from a positive five point seven three
to a positive thirty six point three nine
so now we can use these results
to reach a conclusion
when both health and you are negative
interpretation is that the first thing in the difference
is less than the second
in this case the first population
where the rainbow trout caught in the u were reversed
and the second population was the rainbow trout con the sacramento rivers
so this result
indicates to us that the
mean way
of the rainbow trout com humor revert is less than
demean wait for the rainbow trout caught the sacrament
when both bill and you are positive
interpretation is that the first name from the difference is greater than the
second thing
so in this case
u_-two the mean weight of the rainbow trout caught in the sacramento river
is greater than new three the mean wait for the rainbow trout caught in the
truckee river
when l is negative
and he was positive
the interpretation is that there is no significant difference between the means
so in this case
ranging from the negative sixteen point lead
to the positive seventeen point nine five
indicates that sarah was included in this confidence interval
thus making
the difference between new one in new three
not significant
that is the mean way
of the rainbow trout *** you were reversed is approximately equal to the
main wait for the rainbow trout card in the trekkie rivers
the mean wait for the population of rainbow trout in the sacramento river is
anywhere from three point six seven ounces
two thirty six point five eight ounces happier than those in the u will revert
and anywhere from five point seven three ounces
two thirty six point three nine it was heavier than those in the tricky part
furthermore
there is no significant difference in the mean wait for the population of
rainbow trout
in the yuba and traci rivers