Kate Athens
Anne Haldane
AP Statistics Final Project: Gender and Handwriting
Our project investigates whether there is a difference in the handwriting size of teenage
boys and girls. We consider the number of words per line to be a good indicator of how
much space a person’s handwriting takes up.
The Experiment:
We asked 60 subjects – 30 boys and 30 girls – to write one line of text as we dictated it to
them. For each person, we used the same Alice in Wonderland extract, which we felt
contained a good distribution of short, medium, and long words. We removed all
punctuation from the paragraph. We told our subjects to write freely, without attempting
to squeeze more words into one line than they would normally write. When reviewing the
samples, we adjusted for differences in where subjects chose to end on the page (i.e. if
one subject left a margin on the right side of the sheet, we asked them to go to the next
line and then measured how many more words they would have fit into the margin). We
then tallied the number of words per line.
Data and Calculations:
Table A – Number of words per line
Male
Subject
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
# Words
per line
15
15
15
10
18
14
15
14
9
16
13
15
9
8
12
Male
Subject
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
# Words
per line
18
12
7
12
9
9
10
17
15
11
12
10
16
9
15
Female
Subject
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
# Words
per line
10
12
9
10
15
12
15
12
13
16
15
16
12
8
7
Female
Subject
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
# Words
per line
18
10
9
9
11
15
8
10
9
13
7
9
11
9
5
Step 1:
Population of interest: Princeton High School teens
Parameter: mean number of words per line
H0: μM = μF
Ha: μM > μF
The mean number of words per line is identical in both teenage
males’ and females’ handwriting
The mean number of words per line is greater in teenage males’
handwriting than in teenage females’ handwriting
Step 2:
Inference procedure:
2-Sample t test of significance, as we do not know the population mean or standard
deviation.
Conditions:
Are the samples two SRS’s from two distinct populations? Though our samples were
not simple random samples, we approached the selection of the samples as randomly as
possible, asking the first 60 people we could effectively use as subjects. We will treat
these samples as SRS’s.
Are the two samples independent from one another? The two samples, teenage
females and males, are independent from one another, and we measured the same
variable (words per line) for each sample.
Are the samples normally distributed?
INSERT Female Histogram
Histogram: Female
8
7
Frequency
6
5
4
3
2
1
0
4
9
14
19
Words/Line
INSERT Male Histogram
Histogram: Male
8
7
Frequency
6
5
4
3
2
1
0
4
9
14
Words/Line
19
INSERT Female Words/Line Normal Probability Plot
Normal Probability Plot for Female Words/Line
99
ML Estimates
95
Percent
90
80
70
60
50
40
30
20
10
5
1
5
10
Data
INSERT Male Words/Line Normal Probability Plot
15
20
Mean:
11.1667
StDev:
3.09928
Normal Probability Plot for Male Words/Line
99
ML Estimates
95
Mean:
12.6667
StDev:
3.09121
Percent
90
80
70
60
50
40
30
20
10
5
1
5
10
15
20
Data
Though the two samples are not completely normal, they have a similar, slightly
symmetrical shape. The 2-sample t test is more robust than the one-sample t test, and we
have a large enough sample to use the t distribution. Also, the normal probability plots
for the two samples show a linear pattern, which means the distribution is approximately
normal.
Because the conditions are met, we can continue with the 2-sample t test.
Step 3:
Procedure: 2 sample mean t test of significance at the .05 level
Using calculator software, we calculated the following from the data in Table A:
Sample mean words per minute (X Bar) male = 12.66
Sample mean words per minute (X Bar) female = 11.16
Sample standard deviation words per minute (s) male = 3.14
Sample standard deviation words per minute (s) female = 3.15
df = 57.999
t-value = 1.845
P(t>1.845) = .035
Step 4:
Interpretation: The low p-value of .035 allows us to reject the null hypothesis
H0: μM = μF
and conclude that at the 0.05 significance level, the mean words per line in teenage
males’ handwriting is greater than the mean words per line in teenage females’
handwriting. Therefore, we can accept the alternative hypothesis:
Ha: μM > μF
Overall, we believe that this indicates that teenage boys’ handwriting is smaller/takes up
less space than teenage girls’ handwriting.
This is also supported by the modified boxplots of the two samples, which indicate that
the median number of words per line for teenage males (12.5) is higher than for females
(10.5), as is the entire spread. Also, the 1.5 x (Inter-quartile range) formula indicates that
there were no outliers.
INSERT Female Words/Line Boxplot
Histogram: Female
8
7
Frequency
6
5
4
3
2
1
0
4
9
14
Words/Line
INSERT Male Words/Line Boxplot
19
BOXPLOT
Words/Line
15
10
5
Male
Female
Sex
Sources of Error:
Response bias – because we briefly explained the purpose of the experiment beforehand,
this may have influenced the number of words that subjects attempted to write in one
line. Also, subjects seeing previous subjects’ lines may have been a source of influence.
“Space” is an objective term; for example, some people write letters with greater height
and width than others, but use shorter spaces between their words, while others may write
letters with short height and width but use wide spacing. However, even with this
variation, we believe our conclusion about space usage to be generally true.
Further experiments might be useful for testing hypotheses that teenage girls on average
tend to group their words more closely together than teenage boys, or that teenage boys
tend to write with smaller letters.