Nursing researchers investigated whether cancer information pamphlets were written at an appropriate reading level for patients. They assessed the reading levels of 63 patients and 30 pamphlets. The researchers conducted a two-sample t-test and found a non-significant difference between the mean reading levels of patients (8.6) and pamphlets (9.5). They failed to reject the null hypothesis that the reading levels were the same. Additional analyses of the distributions suggested some patients may struggle with higher-grade pamphlets. The conclusion was the pamphlets' readability could be improved by focusing on lower reading grades.

1. Nursing researchers in Philadelphia investigated whether pamphlets containing information for cancer
patients are written at an appropriate level that the cancer patients can comprehend. They applied
conventional methods to measure the reading levels of a sample 63 cancer patients and also the
readability levels of a sample of 30 cancer pamphlets (based on such factors as the lengths of sentences
and number of polysyllabic words). These numbers correspond to grade levels, but patient reading
levels of under grade 3 and above grade 12 were not determined exactly.
The following tables indicate the number of patients at each reading level and the number of pamphlets
at each readability level:
Patients’ reading levels < 3 3 4 5 6 7 8 9 10 11 12 > 12 Total
Count (number of patients) 6 4 4 3 3 2 6 5 4 7 2 17 63
Pamphlets’ readability levels 6 7 8 9 10 11 12 13 14 15 16 Total
Count (number of pamphlets) 3 3 8 4 1 1 4 2 1 2 1 30
Based on these data, conduct a statistical test/process to help the nursing researchers determine
whether the pamphlets are written at an appropriate level for the patients to understand. Be sure to
include a write-up that explains your process and clearly describes your results/conclusions.

2. Reading
Grade
Pamphlet
Count
Patient
Count
Pamphlet
Fraction
Patient
Fraction
Patients
Without
Pamphlets
< 3 0 6 0 0.0952381 0.0952381
3 0 4 0 0.0634921 0.06349206
4 0 4 0 0.0634921 0.06349206
5 0 3 0 0.047619 0.04761905
6 3 3 0.1 0.047619 0
7 3 2 0.1 0.031746 0
8 8 6 0.2666667 0.0952381 0
9 4 5 0.1333333 0.0793651 0
10 1 4 0.0333333 0.0634921 0.03015873
11 1 7 0.0333333 0.1111111 0.07777778
12 4 2 0.1333333 0.031746 0
>12 6 17 0.2 0.2698413 0.06984127
Total 30 63 1 1 0.44761905
Let the pamphlet count be the number of pamphlets at the specified reading grade.
Let the patient count be the number of patients at the specified reading grade.
Let the pamphlet fraction be the fraction of pamphlets at the specified reading grade.
Let the patient fraction be the fraction of patients at the specified reading grade.
Let the patients without pamphlets be the fraction of patients without pamphlets.
Fraction Patients with a reading grade above the lowest pamphet reading grade
0.73015873
Fraction of Patients with a reading level grade greater than 12
0.26984127
Fraction of Pamphlets unread assuming Better Readers Read Easier Pamphlets
At grade 12 At grade 9 At grade 8 At grade 7 At grade 6 Total
0.03174603 -0.053968 0.2253968 0.068254 0.052381 0.37777778

3. 0
2
4
6
8
10
12
14
16
18
< 3 3 4 5 6 7 8 9 10 11 12 >12
Amount
of
Patients
or
Pamphlets
at
the
Reading
Level
Readability Level by Grade
Readability Levels of the Pamphlets and Cancer Patients
Pamphlet Count Patient Count

4. 0
0.05
0.1
0.15
0.2
0.25
0.3
< 3 3 4 5 6 7 8 9 10 11 12 >12
Fraction
of
Sample
of
Pamphlets
and
Patients
Reading Grade
Fraction of the Sample of Patients and Pamphlets at Reading Grades
Pamphlet Fraction Patient Fraction

5. 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
< 3 3 4 5 6 7 8 9 10 11 12 >12
Fraction
of
Patients
without
Pamphlets
Readability Grade
Patients Without Pamphlets Using Fractions

6. Pamphlet
Reading
Grade
Patient
Reading
Grades
Patient
Reading
Grades
Patient
Reading
Grades
6 2 9 13
6 2 9 13
6 2 9 13
7 2 10 13
7 2 10 13
7 2 10 13
8 3 10 13
8 3 11 13
8 3 11 13
8 3 11 13
8 4 11
8 4 11
8 4 11
8 4 13
9 5 13
9 5 13
9 5 13
9 6 13
10 6 13
11 6 13
12 7 11
12 7 12
12 8 12
12 8 13
13 8 13
13 8 13
13 8 13
13 8 13
13 9 13
13 9 13
Pamphlet Reading Grades is the sample of reading grades of the pamphlets.
Patient Reading Grades is the sample of reading grades of the patients.

7. Two-Sample T-Test and CI: C5, C6
Two-sample T for C5 vs C6
N Mean StDev SE Mean
C5 30 9.53 2.46 0.45
C6 63 8.60 3.89 0.49
Difference = μ (C5) - μ (C6)
Estimate for difference: 0.930
95% CI for difference: (-0.392, 2.253)
T-Test of difference = 0 (vs ≠): T-Value = 1.40 P-Value = 0.166
Patient Reading Grades
Pamphlet Reading Grade
14
12
10
8
6
4
2
Data
Pamphlet and Patient Reading Grade Box Plot

8. Interpretation of Graphs
Notes
-On the pamphlet and patient reading grade samples, the reading level of 2 indicates all reading
grades less than 3 (not just 2) and the reading level of 13 indicates all reading grades above
twelve (not just 13). The justification for that is Minitab will not allow any text that is not a
number into a cell that is not a text cell and cannot do calculations with text.
-The pamphlet and patient reading grades on Minitab are the samples of reading grades. That is
to say, since there are 3 pamphlets with a reading grade of 6, the number “6” is entered into 3
cells of the pamphlet reading level column. This is done because Minitab makes distributions
and boxplots based on the number of times a number has been entered in a column.
-The reading grade of the pamphlets greater than 12 was not specified. To compare the two
samples, all the patients with a reading level greater than 12 were grouped together to create
comparable samples without losing data.
-The patient sample was significantly larger than the pamphlet sample. It did not specify in the
problem why this is. The situation may be that only a few people could be in the waiting room
at a time. In that case it makes most sense to look at distributions.
-The N on the two sample T-Test is the number of points from each sample and µ(x) is the mean
of x.

9. Boxplot
-The lack of an upper whisker on the patient reading level indicates that the amount of patients
above the reading grade of 12 (as previously symbolized by the number “13”) accounts for
more than 25% of the data, and as calculated in Excel it accounts for 26.9842% of the data.
-The two boxes and lack of an upper whisker on the patient reading level boxplot spanning the
entire spread of the pamphlet reading grade’s boxplot means that a little less than 75% of the
patients are above the lowest reading grade of the pamphlet. In Excel this is calculated to be
73.0159%.
-The two plots share the same midpoint of the reading grade 9. With the fraction of patients
with reading levels above thirteen to be about a quarter, the two graphs also share the same
upper 25% quartile range. This means that the upper 50% of the separate samples of patients
and pamphlets are distributed similarly. However, all of the lowest 25% of the patients reading
grades are below the reading grade of 6, the lowest reading grade of a pamphlet. The lower
middle 25% of the patients are at a reading grade of the lower 50% of the pamphlets.
Therefore, the lower 50% of the separate samples of pamphlets and patients are not similarly
distributed.
-The pamphlets are moderately readable from this analysis.
Bar Graph
-I initially graphed the number of people and pamphlets at each reading grade, but I was not
sure what to make of it at first. After making a boxplot, I wondered if it would make more sense

10. to graph the fraction of pamphlets and patients at each reading grade, seeing as both samples
are of different sizes.
-I decided to see if the reading grades of the pamphlets were appropriate by comparing the
distributions at each grading level. A person can read at a reading grade lower than them but
not higher than them, so I decided to determine the fraction of people who would be unable to
read a pamphlet if the samples were equal. So I assigned the extra people from the higher
reading grades to the lower reading grades and found the amount of unread pamphlets by this
formula: U(x) = P(x)- (C(x) + ∑(y)
i = x + 1(C(i) – P(i))) if U(x) is the amount of unread pamphlets at a
reading grade of x, P(x) is the amount of pamphlets at a reading grade of x, C(x) is the amount
of patients at a reading grade of x, and y is highest reading grade below the last reading grade
with unread pamphlets. U(x) was a negative number for grade nine, which means there extra
patients assigned to grade 9 and they were assigned to grade 8. After all the amounts of unread
pamphlets of each grade were added together, 37.77778% of the pamphlets were unread and
37.77778% of the patients lacked pamphlets. The pamphlets are inappropriately readable here.
-If instead it were decided that pamphlets of a reading grade lower the than the patients’ were
where too trivial for them, the formula for the amount of unread pamphlets is instead
U(x) = ∑(13)
i = <3 Max{0, P(i) – C(i)}. With this formula it is determined that 44.7619% of patients
will not have a pamphlet. By restricting the patients to one reading grade of pamphlets I
increased the amount of unread pamphlets, and it is certain that the pamphlets are at an
inappropriate reading grade.

11. The 2 Sample T-Test and Confidence Interval
-This method is probably the way the people who created this problem wanted to approach it.
-During the t-test, I decided not to round to whole numbers (although it would technically be
incorrect to say “The average reading grade was 9.53”) because the domain of reading grades
was small enough that rounding to whole numbers would create too much error in Minitab.
-The 95% confidence interval means that, if we could take multiple samples, 95% of the time
the pamphlet reading grade mean less the patient reading grade mean will be between -0.392
and 2.253 (with -0.392 meaning that the patient reading grades are greater than the pamphlet
reading grades). Also, because 0 is within the interval, the null hypothesis cannot be rejected.
-The null hypothesis is that the mean of the pamphlets’ reading grades is the same as the
patients’ reading grades. The alternative hypothesis is that the two means are not the same.
With the p-value of 0.166 > 0.100, there is little evidence against the null hypothesis, so we fail
to reject the null hypothesis. (The p-value is the odds that the null hypothesis is accepted.) This
means the pamphlets are of an appropriate reading for the patient.
Conclusion
Though there may be a degree of subjectivity in determining whether a number
indicates that the pamphlets are readable, it is certain that the appropriateness of the
pamphlets would be greatly improved by producing pamphlets of a reading grade of 5 and
lower.