Transcript Overview (cont.)

Analyzing Two Samples
for Differences in
Meristic/Mensural Means I
BIOL457
8 February 2016
The t-Test for
Paired Data,
Equal Variances
Paired t-Test
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DV meristic/mensural
Two DV records per subject
Ex: H0: There is no difference in stem
diameter between hemlocks on tip-up
mounds and on adjacent flat areas.
Paired t-Test
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Compares mean difference between
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observations (x) to a hypothesized mean of
zero*
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t = x/(SD/√N)
SD is standard deviation of differences
N is number of pairs
df = N1
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*Or, another hypothesized mean difference may be substituted via subtraction from x
in the formula for t
HANDOUT
Tellería et al., 1995
Spanish Juniper Woodland Birds
HANDOUT
Manter et al., 2000
Firs, Fungi, and CO2
The t-Test for
Unpaired Data,
Equal Variances
t-Test—Equal Variances
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DV meristic/mensural
One DV record per subject, two independent
sets of subjects to compare
Data pass test for equality of variance using Ftest
Ex: H0: There is no difference in carapace
length between Oklahoma and Arkansas
razorback musk turtle females
The F-test for Equality of Variances
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Divide larger variance by smaller variance
Compare to F-test tabular values (Table B)
Calculated F < Ftabular:
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Variances not shown to differ
Calculated F > Ftabular:
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Variances differ significantly—don’t use t-test that
assumes equal variances!
The F-test for Equality of Variances
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Exs:
Var1 = 8.31, N1 = 21
Var2 = 7.29, N2 = 21
F=1.14, dfnum=20, dfden=20, Ftabular[0.05]=2.12
Data pass test (p0.40)
Var1 = 14.46, N1 = 26
Var2 = 5.52, N2 = 25
F= 2.62, dfnum=25, dfden=24, Ftabular[0.05]=1.96
Data fail test (p=0.01)
Var1 = 31.6, N1 = 29
Var2 = 18.4, N2 = 31
F=1.72, dfnum=28, dfden=30, Ftabular[0.05]=1.87
Data pass test (p0.075)
t-Test for Equal Variances
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(x1x2)
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/√[Vpooled(1/N1+1/N2)], where
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t=
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Vpooled = [(N11)V1+(N21)V2]/(N1+N22)
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df = N1+N22
The t-Test for
Unpaired Data,
Unequal Variances
t-Test—Unequal Variances
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DV must be meristic or mensural
One DV record per subject, two independent
sets of subjects to compare
Data fail test for equality of variance using Ftest
Less powerful than t-test for equal variance
t-Test for Unequal Variances
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(x1x2)
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/√(V1/N1+V2/N2)
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t=
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df = (V1/N1+V2/N2)2 [(V1/N1)2/(N11)+ (V2/N2)2/(N21)]
/
(Not necessarily a whole number—round to nearest whole number to look
up critical value of t in Table C, or integrate between values)
HANDOUT
Negro et al., 1998
Kestrel Carotenoids
One Tail or Two?
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Two-tailed test
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No a priori assumption which group will have larger
mean
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Ex: Female crickets preferring or avoiding male groups
One-tailed test
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Good a priori reason to believe A may have larger mean
than B
/2
Ex: Bees learning to associate shape with food
One Tail or Two?
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Two-tailed tests have twice the p values of
one-tailed tests
HANDOUT
Ferguson and Fox, 1984
Juvenile Side-Blotched Lizards
Standard Error
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SE = SD/√N
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SE decreases as N
increases
Shows up as tic
marks on bar
graphs—overlap
relates to p-value
in test for
differences
Fig. 5-10 p. 128
Confidence Interval on the Mean
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Range of probable population mean under a set
level of confidence
95% CL = Sample mean ± 1.96(SE)
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95% of samples with mean and variance like the one
drawn will be drawn from populations with their true
mean within this range
98% CL = Sample mean ± 2.33(SE)
99% CL = Sample mean ± 2.58(SE)