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
  .        .            .        .         .
  .        .            .        .         .
  .        .            .        .         .


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.

dotplot of height

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.


dotplot of left ear length

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


boxplot of left ear lengths

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.

dotplot of height by gender . 

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. 

dotplot of left ear by gender

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.

scatterplot of height by left ear

Correlations: Left, Height

Pearson correlation of Left and Height = 0.320
P-Value = 0.012