CALCULATIONS & STATISTICS
GUIDE TO INTERPRETING
CALCULATION OF SCORES
Conversion of 1-5 scale to 0-100 scores
When you look at your report, you will notice that the scores are reported on a 0-100
scale, even though respondents rate your services on the survey on a 1-5 scale. We
convert respondents’ ratings because most people find it easier to interpret scores from
0-100.
Scale =
Score =
VERY
POOR POOR
1
2
0
25
FAIR
3
50
GOOD
4
75
VERY
GOOD
5
100
Calculation of Mean Scores
Each patient has a score for every question that was answered. For each patient, a
section score is calculated as the mean of the all the question scores in that particular
section. Similarly, for each patient, an overall score is calculated as the mean of that
patient’s section scores.
Sample Data for 5 Patients:
Patient A1 A2 A3 B1 B2 B3 B4 C1 C2 SECT A SECT B SECT C OVERALL
1
10 75 10 25 75 10 25 10 75
91.67
56.25
87.50
78.47
0
0
0
0
2
75 50 50 50 50 75 25 10 75
58.33
50.00
87.50
65.28
0
3
75 75 75 75 25 75 50 75 75
75.00
56.25
75.00
68.75
4
50 50 10 75 25 50 75 50 50
66.67
56.25
50.00
57.64
0
5
50 75 10 50 75 25 50 75 50
75.00
50.00
62.50
62.50
0
Mean:
73.33
53.75
72.50
66.5278
Mean rounded to one decimal place:
73.3
53.8
72.5
66.5
For the data listed in the above table, Patient #1’s score for section A (SECT A) is the
mean of Patient #1’s scores for the questions in section A (i.e., A1, A2, A3).
(A1 + A2 + A3) ÷
(100 + 75 + 100) ÷
1
3 =
3 =
SECT A
91.67
GUIDE TO INTERPRETING
Similarly, Patient #1’s OVERALL score is calculated:
(SECT A + SECT B + SECTC)
(91.67 + 56.25 + 87.50)
÷
÷
3 =
3 =
OVERALL
78.47
The section scores displayed in a report are the means of all the patients’ scores for
that section, rounded to one decimal place. (See bold face type at the bottom of SECT
A, SECT B, and SECT C columns). Similarly, the overall facility rating score displayed
in a report is the mean of all patients’ overall scores, rounded to one decimal place.
(See bold face type at the bottom of OVERALL column).
(78.47 + 65.28 + 68.75 + 57.64 + ÷
62.50)
5 =
66.5278 = 66.5
In a perfect world where every patient fills in every question, you could also calculate the
overall hospital rating by taking the mean of the section averages displayed in your
report.
(73.3 + 53.8 + 72.5) ÷
3 =
66.5
HOWEVER, there is always some missing data (i.e., patients do not fill in every
question on the survey). Patients may even skip an entire section if the questions do not
apply to them. Thus, the overall score in your section might represent 250 patients, but
a particular section score might represent only 245 patients. When this happens, it
makes it impossible to calculate your overall mean score from the section mean scores
displayed in your report. (See example below.)
Sample Data for 5 Patients with Missing Data:
Patient A1 A2 A3 B1 B2 B3 B4 C1 C2 SECT A
1
25 75 10 25 10 75
0
0
2
75 50 50 50 50 75 25 10 75
58.33
0
3
75 75 75
75 75
75.00
4
50 50 10 75 25 50 75 50 50
66.67
0
5
50 75 10 50 75 25 50
75.00
0
Mean:
68.75
Mean rounded to one decimal place:
68.8
SECT B SECT C OVERALL
56.25
87.50
71.88
50.00
87.50
65.28
56.25
75.00
50.00
75.00
57.64
50.00
53.13
53.1
62.50
75.00
75.0
66.4583
66.5
In the above table you can see that the overall hospital rating score that would be
displayed in a report is the mean of all patients’ overall scores. (See bold face type at
the bottom of OVERALL column).
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GUIDE TO INTERPRETING
(71.88 + 65.28 + 75.00 + 57.64 + 62.50) ÷
5 =
66.4583 = 66.5
Because of missing data, you cannot obtain the overall hospital rating score by taking
the mean of the section averages displayed in the report.
(68.8 + 53.1 + 75.0) ÷
3 =
65.6333 = 65.6
Note: The difference appears small in this example because there are so few patients in
the sample. In practice the difference would be much greater.
THE MEAN
The Mean (denoted X, and referred to as x-bar) is a measure of central tendency
representing the arithmetic center of a group of scores. In plainer language, it is the
average. In terms of your Press, Ganey report, the mean gives you information about
the average score for: an individual question, a section on the survey, the overall
satisfaction score for your facility, or the satisfaction scores for all facilities in our
database.
The mean is calculated by summing all scores and dividing by the number of scores.
For example, the mean of 88.0, 87.5, and 86.5 would be calculated:
(88.0 + 87.5 + 86.5) ÷
3 =
87.33
A more general formula can be written:
Mean = X =
X1 + X2 + X3...+ Xn
n
The mean can also be interpreted as the balancing point. Each score can be thought of
as a one pound weight and the range of values of scores could be plotted along a
supporting rod. The balancing point for the rod would be the mean of the values of the
scores. Interestingly, physicists determine the precise balancing point, or center of
gravity, using the same formula that statisticians use to find the mean.
84.5
85.0
85.5
]
86.0 86.5
]
]
87.0 87.5 88.0
90.0
X
87.33
3
88.5
89.0
89.5
GUIDE TO INTERPRETING
The mean, or balancing point, is easily influenced by outliers (i.e., scores that are much
higher or much lower than the rest of the scores). If you put a weight on the balancing
rod that was in about the same place as all the other weights (e.g., 87.0), the rod
wouldn’t tip very much and you wouldn’t have to move the balancing point very far. If,
however, you placed a weight way out on the end of the rod (e.g., 90.0), the rod would
tip considerably. You would need to move the balancing point closer to the extreme
value in order to make the rod balance. The same holds true with calculating the mean.
If you have a group of scores that are all within a close range, the mean value will likely
be towards the center of that range. However, having just one score that is much higher
or lower than the rest can pull the mean up or down, respectively.
Note: Remember that the mean score is an average, not a percent. Say you have a
sample of five patients who rate ‘skill of nurses’ as follows: 5 (very good), 4 (good), 4
(good), 4 (good), 5 (very good). Those ratings can be converted into the following
scores: 100, 75, 75, 75, 100. The average of these scores would be 85
((100+75+75+75+100)÷5). You wouldn’t want to say that your patients were 85%
satisfied with the skill of nurses, because in fact all (100%) of your patients rated the
nurses good or very good with 60% giving a rating of good and 40% giving a rating of
very good.
THE MEDIAN & PERCENTILE RANKING
The Median
The median is a measure of central tendency representing the mid-point in a distribution
of scores or the point at the 50th percentile. In other words, the median is the middle; it
is the score that splits the distribution in half. Fifty percent of scores will fall above the
median and fifty percent of scores will fall below the median. The median is determined
by ordering the scores from highest to lowest and finding the middle value. If there is an
odd number of scores, the median is the score in the middle. If there is an even number
of scores, then there is no score in the middle so the median is the average of the two
scores closest to the middle.
Comparison of the Mean and the Median
The mean and the median are each measures of central tendency, but they describe
the center in different ways. The mean is the average of the scores, whereas the
median is the middle of the scores. The average is not always in the middle of a
distribution. Another difference between the two is that the mean is influenced by
outliers (i.e., scores that are much higher or lower than the rest) but the median is not
influenced by outliers. To illustrate this point, let’s look at an imaginary sample of ten
facilities’ overall satisfaction scores:
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GUIDE TO INTERPRETING
Hos # 1
Hos # 2
Hos # 3
Hos # 4
69.4
98.5
84.6
87.1
Hos # 5
Hos # 6
Hos # 7
Hos # 8
Hos # 9
Hos # 10
78.3
93.3
81.7
86.2
90.5
89.8
Hos # 2
Hos # 6
Hos # 9
98.5
93.3
90.5
Hos # 10
89.8
Hos # 4
87.1
Hos # 8
Hos # 3
Hos # 7
86.2
84.6
81.7
Hos # 5
Hos # 1
78.3
69.4
Finding the Mean:
The mean of these scores is obtained by summing the
scores and dividing by the number of scores (ten) to get
85. 9.
Mean
= (69.4 + 98.5 + 84.6 + 87.1 + 78.3 +
93.3 + 81.7 + 86.2 + 90.5 + 89.8) ÷10
= 85.9
Finding the Median:
To find the median, the hospital scores are ordered from
highest
to lowest. In this case there is an even number of scores
so we
must take the average of the two closest to the middle
(i.e., 87.1
and 86.2).
Media
n
= (87.1+ 86.2) ÷ 2
= 86.65
Notice the relationship between the mean and the median. In this example, the mean is
lower than the median because an outlier (the low score of 69.5) pulled the mean down
a bit. The low outlier did not influence the median. If you were facility # 8, with a score of
86.2, you would notice that your facility score is above the mean (85.9) for the database
but below the median (86.65). The median for the database is equivalent to the 50th
percentile in the percentile ranking, so facility #8 would be below the 50th percentile. So
if your facility’s score is above the mean but below the 50th percentile it indicates that
there are low outliers in the database (facilities whose score are considerably lower than
all the other scores). Conversely, if your score is below the mean but above the 50th
percentile, it indicates that there are high outliers in the database (facilities whose
scores are considerably higher than all the other scores).
Percentile Ranking
Percentile ranking is a strategy for assigning a series of values to divide a distribution
into equal parts. More specifically, the percentile ranking tells you the proportion of
scores in the database which fall below your individual facility’s score. The median of
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GUIDE TO INTERPRETING
the database is the score associated with the 50th percentile. Percentile rankings
therefore give you information about where your hospital stands in relation to the
median of the database. Keep in mind that these numbers are percentiles, not actual
scores. For example, a 68 in the percentile rank column of your report means that the
hospital is in the 68th percentile for this item. Translation: this particular hospital scores
higher than 68% of the hospitals in the database and scores lower than 32 % of the
hospitals in the database. For more information on percentile rankings please see the
section on the Standard Deviation and the discussion of how percentile rankings relate
to the standard deviation.
THE STANDARD DEVIATION & STANDARD ERROR (SIGMA)
What is the Standard Deviation?
The standard deviation is a measure of variability of scores around the mean. Large
numbers for the standard deviation indicate that the data are very spread out (i.e., there
is a lot of variability). Conversely, a very small standard deviation would indicate that
most of the data are very similar to the mean (i.e., less variability).
How do you determine the Standard Deviation?
The standard deviation is calculated using the formula:
∑ (X − X )
2
n
In plainer terms, this formula tells you to (see example below):
X Find the mean of the sample you are interested in (bottom cell of second column).
Y Find the ‘distance from the mean’ for each individual score. You do this by
subtracting the mean from each hospital score (see third column).
Z Square all the ‘distances from the mean’ (fourth column).
[ Add all of the squared distances from the mean scores (bottom cell of fourth
column).
\ Divide the sum of the squared distances by the number of scores you are working
with, (in this example, there are five scores). The number you get, 92.99 is called
the variance.
] Take the square root of your answer from number \...This is the Standard Deviation...9.64!
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GUIDE TO INTERPRETING
Example 1
Y
Z
FACILITY SCORE (SCORE – MEAN) (SCORE – MEAN)2
X
(X-X)
(X-X)2
1
69.4 69.4 - 83.5 =
201.07
8
14.18
2
98.5 98.5 - 83.5 = 14.92
222.61
8
3
84.6 84.6 - 83.5 = 1.02
1.04
8
4
87.1 87.1 - 83.5 = 3.52
12.39
8
5
78.3 78.3 - 83.5 = -5.28
27.88
8
X
[
X
Sum of (X-X)2
= 83.58
= 464.99
\ 464.99 ÷ 5
= 92.998
] Square root
of 92.998
=9.64
For comparison, a second example (Example 2) is provided that shows the
computation of the standard deviation for a different set of five scores. Notice that the
mean is the same as in the first example (83.58). However the standard deviation is
considerably smaller (1.32) because the scores are much closer to the mean than were
the scores in the first example. In other words, two sets of data with the same mean
won’t necessarily be identical to one another.
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GUIDE TO INTERPRETING
Example 2
FACILITY SCORE (SCORE – MEAN) (SCORE – MEAN)2
X
(X-X)
(X-X)2
6
83.8 83.8 - 83.5 = 0.22
0.05
8
7
82.5 82.5 - 83.5 = -1.08
1.17
8
8
84.6 84.6 - 83.5 = 1.02
1.04
8
9
81.7 81.7 - 83.5 = -1.88
3.53
8
10
85.3 85.3 - 83.5 = 1.72
2.96
8
X
Sum of (X-X)2
= 83.58
= 8.75
8.75 ÷ 5
= 1.75
Square root
of 1.75
=1.32
Importance of the Standard Deviation
Knowing the standard deviation of the database is important because it allows you to
compare your facility’s score to the larger group. We can do this based on the normal
distribution. The normal distribution (below) is a bell shaped curve representing a
theoretical distribution of data in which the mean, median, and mode (the score that
occurs most frequently) have the same value. In the normal distribution 68% of all data
falls within one standard deviation of the mean of the distribution. Further, 95% of the
data falls within two standard deviations of the mean.
The Normal Distribution
95.44%
68.26%
-2 S.D.
-1 S.D.
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X
+1 S.D. +2 S.D.
GUIDE TO INTERPRETING
Standard Deviation and the Percentile Ranking
Based upon information about the standard deviation you can figure out what proportion
of scores in the database are below your facility’s scores (see below).
50%
50%
34.1%
34.1%
13.6%
13.6%
2.3%
<<
-2 S.D.
2.3%
<
-1 S.D.
X
>
>>
+1 S.D. +2 S.D.
For example, if your score is above one standard deviation of the database mean (>)
you can deduce (based on the normal distribution) that 84.1% of the scores in the
database are below the score that your facility achieved. Similarly, if your score is above
two standard deviations of the database mean (>>) you can deduce that 97.7% of the
scores in the database are below the score your facility achieved. However, you may
look at your percentile ranking and find that the proportions based on the standard
deviation do not exactly match up with the proportions reported in the percentile rank
columns. This is attributable to the fact that the standard deviation is based on the
mean, whereas the percentile ranking is based on the median. Outliers (scores that are
much higher or lower than most) will influence the mean but will have no effect on the
median. If you had a distribution that was perfectly normal where the mean and the
median were equal, then your proportions based on the standard deviation would equal
the proportions based on the percentile ranking.
What is the Standard Error or Sigma?
So far we’ve been talking about the standard deviation, which we’ve defined as the
average distance that any individual score is from the distribution mean. In the
examples above we looked at the distance between individual hospitals and the
comparative database mean but you can also calculate the standard deviation for your
own sample of data. In this case you would be looking at the average distance that
your patients’ scores are from your own facility sample mean. Remember that the
facility's score is derived from the sample of patients who were sent surveys and chose
to return them in the last report cycle. The population of patients would be all of the
patients who were served during the last report cycle.
Imagine an ideal world with unlimited funds for research, patients who could always be
reached, and patients who always responded to the surveys. In this ideal world you
could randomly select many samples from your total patient population. So if your
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GUIDE TO INTERPRETING
hospital saw 50 patients in the last quarter you could randomly select 10 to be sample
1, then randomly select a different set of 10 to be sample 2, and so on until you had a
variety of samples from the same population. Each sample would have a mean score,
the average of the scores for all the patients in that sample. You could calculate how
spread out the sample means were around the mean for the total population using the
same formula that we used to find the standard deviation. Instead of calling this the
standard deviation of the sample scores (or the average distance that multiple sample
means are from the population mean), this is called the Standard Error (SE) or Sigma
(σ). Now the problem with this method of calculating the Standard Error is that we don’t
live in that ideal world with unlimited funds, patients who can always be reached, and
patients who always fill out surveys. So instead we estimate the Standard Error of the
sampling distribution using the standard deviation of the one sample that we do have.
This is done using the following formula:
S
n
Where…
S= standard deviation of the sample
n= number of observations (patients) in the sample
One reason the standard error is important is that it is used in the calculation of
confidence intervals. Please see the section on confidence intervals for a continued
discussion of this statistic.
Note:
Often, clients state that they are interested in knowing the standard error when in
fact what they are looking for is the standard deviation or the confidence interval.
If you think you want to know about the standard error, ask yourself the following
questions:
1. Do I want to know how much variability there is in scores or how spread out
the scores are around the mean? If yes, then I really want to know about the
Standard Deviation.
2. Do I want to know how close my score, based on a sample, is to what the
score would be if we really had data from every single patient? If yes, then I
really want to know about the Confidence Interval.
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GUIDE TO INTERPRETING
CONFIDENCE INTERVAL
What is a Confidence Interval?
The confidence interval is the region in which a population score is likely to be found. In
other words, it is the range around your sample mean in which you would expect to find
your true population mean. When looking at the mean for a sample of a population, you
get a very good estimate of the mean for the whole population, but you don’t come up
with the exact number. The only way you could truly know the true population mean is if
you actually had data from everyone in the population (i.e., every single patient at your
facility received and completed a survey). The mean score that you get for the sample
of patients who returned the surveys is an accurate reflection of the opinions of those in
the sample and is considered to be an estimate of the score that would characterize the
whole population. The confidence interval tells you the range of values, around your
sample mean, that would be expected to contain the mean for the actual population.
For example, if your sample mean is 80 and your confidence interval is 2 then you
would say that the estimate for the mean of your entire patient population is 80 + 2
which would be 78-82. So the confidence interval answers the question: What is the
range of values around our sample mean that we are 95% sure contains the actual
population mean?
How do you calculate a confidence interval?
A 95% confidence interval is calculated using the following formula:
C.I . = X ± 1.96 SE ( X )
Which is read as the sample mean plus or minus 1.96 times the standard error.
Remember that if you wanted to know where 95% of your patients’ scores were, you
could take your sample mean plus or minus two standard deviations. Calculating a
confidence interval uses the same logic but applies it differently. For the confidence
interval we are not trying to find a range within a sample that contains 95% of scores,
but the range within a population that contains 95% of sample mean scores. The
standard error (SE) tells you the average distance that a sample mean would be from
the population mean (see discussion of the SE in the section on standard deviations);
it’s like saying the standard deviation of the sample means around the population mean.
We could just find the interval that is plus or minus two standard errors (like we do with
the standard deviation). However, if you remember from the picture of the normal
distribution, two standard deviations actually gives you slightly more than 95%. It gives
you 95.44 %. If we want to know exactly 95%, then we would want slightly less than two
standard errors ⎯ 1.96.
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GUIDE TO INTERPRETING
One last issue. We don’t know the exact standard error of the population because we
don’t have multiple samples drawn from the same population at the same time. We
have just one sample from the population. However, we can estimate the standard error
of the population based on the standard deviation of our one sample using the following
formula:
S
n
Where…
S= standard deviation of the sample
n= number of observations (patients) in the sample
So if a facility had an overall rating of 84.24 with a standard deviation of 4.5 and an n of
225 we could calculate the standard error as...
SE =
S
9 .5
=
= 0.63
n
225
And the confidence interval would be calculated ...
C.I . = X ± 1.96 SE (X ) = 84.24 ± 1.96(0.63) = 84.24 ± 1.24
Thus, with a sample mean of 84.24, we are 95% confident that the actual population
mean is between 83.00 and 85.48.
Note:
The Confidence Intervals that are listed in your report under the heading Facility
Statistical Analysis can be used to estimate the amount of change in mean score
you would need in order to show a statistically significant improvement. In order
to create this estimate you must multiply the number in the 95% Confidence
Interval column by 1.41 and add the result to your current mean. So, if you had a
mean of 84.24 and confidence interval of 1.24 you could estimate that increasing
your mean score by multiplying the 1.24 by 1.41. The result, 1.75, is an estimate
of how much you would have to increase your mean score (i.e., from 84.24 to
85.99). This estimate is a just a guide and assumes that your sample for the
next report has exactly the same n and standard deviation as the data for the
current report.
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GUIDE TO INTERPRETING
t-TESTS
The statistical procedure used to determine if scores on a current report are significantly
different from the scores on the last report is the t-test. The calculation of a t-test
measures the difference between sample means, taking into account the size and
variability of each of the samples. It is important to note that the result of the t-test does
not simply tell you what the difference is, it tells you how confident you can be that the
difference is real and not due to random error. Conventionally, if you are at least 95%
confident that the difference is real and thus not due to random error, then the
difference is said to be statistically significant.
How do you calculate a t-test?
t-tests are calculated using the following formula...
t=
(X
− X 2)
S12 S 22
+
n1 n2
1
X1 = the mean of sample 1
X2 = the mean of sample 2
S12 = the variance (Stand. Dev.2 ) of sample
1
S22 the variance (Stand. Dev.2 ) of
sample 2
n1 = the number of observations in sample 1
n2 = the number of observations in
sample 2
In your report...
When a score on a Press, Ganey report is found to be significantly different from the
score on the last report, the score is highlighted with one of the following symbols:
+
95% certainty of significant increase (t >1.96).
++
99% certainty of significant increase (t >2.576).
95% certainty of significant decrease (t< -1.96).
-99% certainty of significant decrease (t< -2.576).
Two factors can influence whether or not a difference is found to be significant: the size
of the samples (n) and the variability of the samples.
Size: It is less likely that you will be confident enough to call a difference significant (i.e.,
not due to error) if there is less data available (lower n’s).
Variability: It is less likely that you will be confident enough to call a difference
significant (i.e., not due to error) when there is greater variability (i.e., the data are more
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spread out around the mean of the sample; larger standard deviations).
So if you have what appear to be large differences in scores that are not marked with an
indicator of statistically significant difference, it is likely that either the n’s were too low or
the standard deviations were too large for you to be confident that the difference was
real and not due to random error. Conversely, if you have what appear to be small
differences in scores that are marked with an indicator of statistically significant
difference, it is likely that either the n’s were so high or the standard deviation was so
small that it was possible to be very confident that the difference was real and not due
to random error.
How can we be sure that differences in scores are significant at the .05 level,
especially when sample sizes are small?
** Remember that a t-test takes into account both the size of the samples and the
variability of the samples, so if the results of a t-test indicate that a difference is indeed
significant, then you can be at least 95% confident that the difference is real and not
due to random error, no matter how small your samples are.
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CORRELATIONS
What is a correlation?
A correlation tells you the strength of the relation between variables. In other words, a
correlation tells us how much a change in one variable (e.g., a question score) is
associated with a concurrent, systematic change in another variable (e.g., overall
satisfaction). A correlation represents the strength of the relationship between two
variables numerically, with a correlation coefficient (called r) which can range from -1.0
to + 1.0. A positive correlation coefficient indicates that as the value of one variable
increases, the value of the other variable also increases. For example, the more you
exercise, the greater your endurance. A negative correlation coefficient indicates that
as the value of one variable increases the value of the other variable decreases. For
example, the more you smoke cigarettes, the less lung capacity you have. It is
important to recognize that when two variables are correlated it means that they are
related to each other, but it does not necessarily mean that one variable influences or
predicts the other. This is the basis of the statement, “Correlation does not imply
causation!”
How can you tell how strong the relationship is between two variables?
• The closer a correlation is to 1 (either positive or negative), the stronger the
relationship.
• The closer a correlation is to 0 (either positive or negative), the weaker the
relationship.
How is a correlation calculated?
Correlation coefficients are calculated using the formula below. This statistic basically
assesses the degree to which variables X and Y vary together (the numerator) taking
into account the degree to which each variable varies on its own (the denominator).
r=
∑ xy
∑x ∑y
2
Example of calculating the correlation between...
X (Overall rating of care provided at this facility)
and
Y (Likelihood of recommending this hospital).
Please see the table on the following page.
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Note:
Each row represents a patient’s data. For example, the data in the first row
indicates that a patient at this hospital circled a 3 (fair) for the question Overall
rating of care given at this hospital, and circled a 4 (good) for the question
Likelihood of recommending this hospital to others.
X Determine the mean of X and the mean of Y (bottom of columns 1 and 2).
Y For each value of X (each patient), determine how much it deviates (differs) from
the mean of X . This deviation will be called x (in lower case).
Z For each value of Y (each patient), determine how much it deviates (differs) from
the mean of Y. This deviation will be called y.
[ For each row, multiply x and y.
\ For each row, square x, that is, multiply x by itself.
] For each row, square y, that is, multiply y by itself.
^ Sum all the xy scores (bottom of column 5).
_ Sum all the x2 scores (bottom of column 6).
` Sum all the y2 scores (bottom of column 7).
Table 1
X
Y
Y
x= (X - X)
Z
y= (Y - Y)
[
xy
\
x2
]
y2
3
4
-1.4
-.8
1.12
1.96
.64
4
5
-0.4
.2
-.08
.16
.04
5
5
.6
.2
.12
.36
.04
5
5
.6
.2
.12
.36
.04
5
5
.6
.2
.12
.36
.04
X
X=4.
4
X
Y=4.
8
^
∑xy=
1.4
_
∑x2=
3.2
`
∑y2=
0.8
a Fill in the formula below...
r=
∑ xy
∑x ∑y
2
with the numbers...
r=
1.4
3.2 0.8
and then…
16
2
GUIDE TO INTERPRETING
r=
1.4
1.79 * 0.89
which equals .88. A correlation of .88 indicates a strong relationship between two
variables. Additionally, the correlation is positive indicating that as scores on Overall
rating of care given at this hospital increase, scores on Likelihood of
recommending this hospital also increase.
Graphed representations of correlations…
The first graph depicts the positive correlation between “Friendliness of Nurses” and
“Likelihood of Recommending Hospital”. The positive correlation coefficient (r = .79)
means that high scores on “Friendliness” are associated with high scores on “Likelihood
to Recommend”, whereas low scores on “Friendliness” are associated with low scores
on “Likelihood to Recommend”. You can tell at a glance that the correlation is positive
because the line slants upward across the graph.
Friendliness and Recommendations
Likelihood of Recommending
100
r = .79
90
80
70
70
80
90
100
Friendliness of Nurses
464 hospitals - 3rd quarter 1996
In contrast, the second graph depicts the negative correlation between hospital bed size
and hospital overall satisfaction score. The negative correlation coefficient (r = -.46)
means that hospitals with more beds tend to have lower scores, whereas hospitals with
fewer beds have higher scores. You can tell at a glance that the second correlation is
negative because the line slants downward across the graph.
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GUIDE TO INTERPRETING
Overall Mean by Bed Size
Average Common Question Mean - 1993
10000
.
r = - .46
9000
.
8000
.
7000
.
0
200
400
600
800
1000
1200
1400
Total Facility Beds
Regression vs. Correlation
Press, Ganey reports list correlation coefficients between each question and the overall
satisfaction score (an average of all the other items in a questionnaire). This gives a
measure of the relative importance of each individual question for overall satisfaction.
Clients sometimes ask why we do not use multiple regression to demonstrate these
relationships. When the items of a survey are highly correlated, it is impossible to
separate the effect of one item from that of others with any degree of precision.
Because this problem (termed “multicollinearity”) violates one of the assumptions of
multiple regression, Press, Ganey does not report multiple regression analyses
performed to relate specific questions to overall satisfaction. Like regression analyses,
correlations are statistical measures of association that describe the strength of
relationship, or association, between factors, such as a doctor’s courtesy and patients’
overall satisfaction with care from that physician. Correlations have the advantage of
using all the information from each respondent to a survey, whereas regression
analyses eliminates all information from any respondents who do not answer every
question.
18
GUIDE TO INTERPRETING
PRIORITY INDEX
What is the priority index?
The priority index is a way of combining two very important pieces of information: (1) the
actual score achieved on a particular question, and (2) the degree to which that
particular question is associated with overall satisfaction. Combining these two pieces of
information helps a facility to know where efforts should be placed for quality
improvement. For example, one question might be very low in score (e.g., quality of
food) but not particularly associated with overall satisfaction. Because it is not highly
associated with satisfaction the facility might chose to place quality improvement
resources elsewhere. Conversely, a question might be very highly associated with
overall satisfaction (e.g., overall cheerfulness of hospital) but not low in score.
Attempting to raise the score would probably be difficult and may perhaps be
unnecessary if most of your patients are very satisfied already.
How is the priority index calculated?
The priority index is derived through a three-step process. For the purpose of this
example, let’s assume that the survey has 50 questions.
1. SCORE RANK Questions are ordered from the highest score down to the lowest
score. Each question is then given a score rank; the highest mean score gets a rank of
1, the second highest score gets a rank of 2, the third highest score gets a rank of 3 and
so on down the line until the lowest score is given a rank of 50. It may help to remember
the meaning of the score rank to think of a high score as a small issue and a low score
as a big issue--something the facility should be concerned about. The high score, a
small issue, has a small score rank (e.g., 1, 2 , 3..). Conversely, a low score, a big issue
of concern, has a big score rank (e.g., 48, 49, 50). The score rank for each question
appears in parentheses to the right of the mean score column on the priority index
page.
2. CORRELATION RANK Next, questions are ordered from the least correlated with
overall satisfaction to the most associated with overall satisfaction. Each question is
then given a correlation rank. The question that is the least correlated with satisfaction
gets a rank of 1, the question that is the second least correlated with satisfaction gets a
rank of 2 and so on down the line until the question that is the most correlated with
satisfaction gets a rank of 50. Again, it helps to keep in mind what would be a small
issue and what would be a big issue. A question that is not very correlated with
satisfaction would be a small issue so it would have a small rank (e.g., 1, 2, 3...),
whereas a question that was highly correlated with satisfaction would be a big issue-something to pay attention to--and would have a big rank (e.g. 48, 49, 50). The
correlation rank for each question appears in parentheses to the right of the correlation
coefficient column on the priority index page.
19
GUIDE TO INTERPRETING
3. COMPUTING THE PRIORITY INDEX The priority index is derived by adding the
score rank (from step 1) to the correlation rank (from step 2). The questions are then
ordered on the priority index page with the largest priority index score coming first on
down to the lowest priority index score coming last. In order to be first in the priority
index list a question would have to have two big issues: a big score rank (that means a
low score) and a big correlation rank (that means a high association with satisfaction).
Questions that appear at the bottom of the priority index list would have two small
issues, a high overall score (which gets a small score rank) and a low association with
satisfaction (which gets a small correlation rank). Questions that appear in the middle of
the priority index list would likely have just one big issue (either a low score or a high
association with satisfaction).
PRIORITY
INDEX
High Priority
(Top of priority index page)
Medium Priority
(Middle of priority index
page)
=
=
=
or
Low Priority
(Bottom of priority index
page)
=
SCORE
RANK
A big issue!
Big score rank
(Low actual score)
A big issue!
Big score rank
(Low actual score)
A small issue
Small score rank
(High actual
score)
A small issue
Small score rank
(High actual score)
+
+
+
+
+
CORRELATION
RANK
A big issue!
Big correlation rank
(High correlation with
satisfaction)
A small issue
Small correlation rank
(Low correlation with
satisfaction)
A big issue!
Big correlation rank
(High correlation with
satisfaction)
A small issue
Small correlation rank
(Low correlation with
satisfaction)
External Priority Indices
Priority indexes are also provided with an external focus. The internal priority index, as
described above, uses your question mean scores as an internal measure of
performance. The external priority indices use your question percentile ranks as an
external measure of performance. The same basic steps are used to create the
external priority indices. However, in the first step, the questions are ranked according
to their percentile ranks (highest to lowest) instead of according to their mean scores.
20