Sample
Results Section
This data is from Stat51 students in Fall, 2004: Gender, Height,
Length of Left Ear in mm, and whether or not they wear an earring in
that ear. Here's how the data is stored. You don't have to
print this in
your Results section; I just wanted to show you what I'm working
with. Yours should be in a similar format.
Row
Gender Height Left LEarring
1
m
72 65
n
2
m
72 68
n
3
m
71 64 n
4
f
68 65
y
5
m
75 66
n
6
f
67 57 y
7
f
63 60 y
8
m
69 72
n
9
f
65 59
n
.
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. .
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Results
Univariate Results
A majority of the subjects in this study are female (about 69%), and a
majority wear an earring in their left ear (about 62%).
Gender
CountPercent LEarring Count Percent
f 42
68.85
n 23 37.70
m 19
31.15
y 38 62.30
N
=
61
N = 61
(Note to students: If there were more than 2 categories, a graph
would be informative -- either a pie chart or a bar graph)
Heights of subjects in this study are
somewhat bimodal. This was expected because the sample consists
of males and females. Average height is about 67.5", which
is between the expected mean heights for males and females.
Variable
N N* Mean
SE
Mean StDev
Minimum
Q1 Median Q3
Height
61 0 67.475
0.517 4.036 61.000
64.000 67.000 71.000
Variable Maximum
Height
76.000
The mean of left ear lengths is about 62mm. The distribution
appears skewed to the left, with 2 extreme values on the right
(72mm), and possible outliers on the left. A boxplot indicates
that the 48 is indeed an outlier. Since it is a correct value,
and not very far from the next lowest values, it will not be removed.
Variable
N N*
Mean SE Mean
StDev
Minimum Q1
Median Q3
Left
61
0 62.066
0.630 4.922
48.000 59.000 63.000 65.000
Variable Maximum
Left
72.000
Bivariate
Results
In looking at the relationship between
height and gender, we see, not
surprisingly, that males are taller than females: males are on
the average 72", while females' average height is 65.4".
Moreover, this difference is statistically significant, according to a
2-sample t test (p < .001). The
distribution of females' heights is fairly bell-shaped, while the
distribution of males' heights is somewhat skewed to the left.
Because there are fewer males in the sample, there is probably just not
enough data to fulfill the normal-shaped distribution that we would
expect.
.
Variable
Gender N N*
Mean SE Mean StDev
Minimum Q1 Median
Height
f
42 0 65.405 0.369
2.390 61.000 63.750 66.000
m 19 0
72.053 0.694 3.027 64.000
71.000 72.000
Variable
Gender Q3 Maximum
Height
f
67.000 72.000
m 75.000 76.000
Two-Sample
T-Test and CI: Height, Gender
Two-sample T
for Height
Gender
N Mean StDev SE Mean
f
42 65.40
2.39 0.37
m
19 72.05
3.03 0.69
Difference = mu (f) - mu (m)
Estimate for difference:
-6.64787
95% CI for difference:
(-8.25852, -5.03722)
T-Test of difference = 0 (vs
not =): T-Value = -8.45 P-Value
=
0.000 DF = 28
Left ear lengths also show a higher
average for males (63.8mm) versus
females (61.3mm), though this difference is not statistically
significant,
according to a 2-sample t test
(p = .102). Because the difference is not far from significance,
it could be that a larger sample of both men and women would give
statistically significant results. Both distributions are quite
skewed to the
left, and not particularly bell-shaped.
Variable
Gender N N*
Mean SE Mean StDev
Minimum Q1 Median
Left
f 42 0
61.286 0.673 4.363 48.000
58.750 61.500
m 19 0
63.79 1.31 5.73
51.00 62.00 65.00
Variable
Gender Q3 Maximum
Left
f 65.000 67.000
m 67.00
72.00
Two-Sample
T-Test and CI: Left, Gender
Two-sample T
for Left
Gender
N Mean StDev SE Mean
f
42 61.29
4.36 0.67
m
19 63.79
5.73 1.3
Difference = mu (f) - mu (m)
Estimate for difference:
-2.50376
95% CI for difference:
(-5.53452, 0.52700)
T-Test of difference = 0 (vs
not =): T-Value = -1.70 P-Value =
0.102 DF = 27
Females are far more likely to wear an
earring in the ear in
question: 88% of women wear an earring versus 5% of men.
This is clearly a statistically significant relationship,
according to a chi square test
(p<.001). Because of this fact, it is tricky to compare
ear lengths for those with and without earrings, since earring wear is
confounded with gender.
Tabulated
statistics: Gender, LEarring
Rows: Gender
Columns: LEarring
n y All
f
5 37 42
11.90 88.10 100.00
m
18 1 19
94.74 5.26 100.00
All
23
38 61
37.70 62.30 100.00
Cell
Contents: Count
% of Row
Pearson Chi-Square = 38.214, DF
= 1, P-Value = 0.000
Likelihood Ratio Chi-Square =
42.340, DF = 1, P-Value = 0.000
In
looking at the relationship between height and left ear length, there
is a weak positive correlation (r = .320) that is statistically
significant (p = .012). Specifically, for each additional inch in
height, there is an associated increase in ear length of 0.39mm.
Because the correlation coefficient is weak, predictions will not be
very accurate, but there does appear to be a tendency for taller people
to have bigger ears. Of course it's possible that the difference
is due to the fact that men and women are combined in this data set,
and men are taller and have bigger ears. A followup study looking
at males and females separately would be informative, though more male
data would need to be gathered.
Correlations:
Left, Height
Pearson correlation of Left and
Height = 0.320
P-Value =
0.012