# Confidence Interval Calculators

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```					Clinical Effectiveness & Audit Department

Confidence Interval calculators: Guidance

Confidence intervals (CI) are a method of statistical analysis that enable you to estimate the values from a population of
cases, based on the figures obtained from a sample taken from that population. A CI can be considered as the range of
values (a CI contains 2 values, called 'confidence limits') within which we can be sure, to a given percentage, that the
population value lies. The percentage of certainty used can vary, but is usually 95% (though 90% and 99% confidence can be
calculated, to provide less, or more certainty, respectively, in the figures).
As most clinical audit projects involve looking at samples rather than at entire populations, such projects are particularly suited
to confidence interval analysis. For instance, if you wanted to establish the level of adherence to a guideline in all relevant
King's patients over the course of a year, to obtain the exact level of adherence, you could examine the care of each & every
relevant case and report the findings as you find them, or examine the care from a sample of such cases, and report the
findings you obtain from the sample along with confidence intervals, to enable you to estimate the results you would have
obtained if you had examined every relevant case. As a general rule, the greater the size of your sample, the smaller the
confidence interval range will be, and therefore the greater the precision of your estimate.
The Excel worksheets presented here contain confidence interval calculators for proportions, means and medians. For
proportions and means, which calculator to use depends on whether you know the size of the population you are looking at.
For those unfamiliar with confidence interval analysis, further information can be found in the following text: Gardner MJ &
Altman DG (1989). Statistics with confidence. BMJ Publishing .
It should be borne in mind that CI analysis estimate the effects of sampling variation, but cannot correct for bias resulting from
poor design or conduct. Where possible, random samples should be chosen.

Kevin Rowan, Clinical Effectiveness & Audit Manager May 2000
Clinical Effectiveness & Audit Department
Confidence Interval calculator for proportions, when the population is UNKNOWN, or
if the sample size is less than 5% of the population size

Insert the proportion you obtained here (as a percentage):      74.0%

Insert confidence level required (click in the box & choose 90%, 95% or 99% from        95%
the drop-down list):

Insert the sample size here:            6

The confidence interval =    38.9%       to
109.1%
Clinical Effectiveness & Audit Department
Confidence Interval calculator for proportions, when the population is KNOWN.
But, if the sample size is less than 5% of the population size, use the calculator for

Insert population size here:       100

Insert the proportion you obtained here (as a percentage):       74.0%

Insert confidence level required (click in the box & choose 90%, 95% or 99%
from the drop-down list):      95%

Insert the sample size here:        50

The confidence interval =     65.4%    to   82.6%
Clinical Effectiveness & Audit Department
Confidence Interval calculator for means, with a large sample (60 or more)

Insert the mean of the sample here:         24.4

Insert the standard deviation of the sample here:            5.9

Insert confidence level required (click in the box & choose 90%, 95% or 99%
from the drop-down list):      95%

Insert the sample size here:           60

The confidence interval =     22.9         to   25.9
Clinical Effectiveness & Audit Department
Confidence Interval calculator for means, with a small sample (less than 60), for
95% confidence level only (see below if 90% or 99% confidence is required)

Insert the mean of the sample here:          10.0

Insert the standard deviation of the sample here:             2.4

Insert the sample size here:            248

IF your sample size is above 250, or if you require a confidence level of 90% or 99%, you'll need to look up the t-value that
matches the confidence level & number of degrees of freedom (df) (see the next sheet), and insert it in the box
below. OTHERWISE, DO NOT ENTER ANYTHING IN THIS BOX.

The confidence interval =      9.7         to
This gives 247 degrees of freedom (df)

or 99%, you'll need to look up the t-value that
next sheet), and insert it in the box
1.970

10.3
Clinical Effectiveness & Audit Department

t-distribution table for 90%, 95% & 99% confidence

This table shows the t distribution for associated Degrees of Freedom, at the 90%, 95% and 99% levels of confidence

el

el

el
nce %

nce %

nce %
lev

lev

lev
fide r 90

fide r 95

fide r 99
fre s of

con ue fo

con fo

con ue fo
m
edo

lue
e
gre

l

l
t-va

t-va

t-va
De

1        6.314      12.706       63.657
2         2.92       4.303        9.925
3        2.353       3.182        5.841
4        2.132       2.776        4.604
5        2.015       2.571        4.032
6        1.943       2.447        3.707
7        1.895       2.365        3.499
8         1.86       2.306        3.355
9        1.833       2.262        3.250
10        1.812       2.228        3.169
11        1.796       2.201        3.106
12        1.782       2.179        3.055
13        1.771       2.160        3.012
14        1.761       2.145        2.977
15        1.753       2.131        2.947
16        1.746       2.120        2.921
17         1.74       2.110        2.898
18        1.734       2.101        2.878
19        1.729       2.093        2.861
20        1.725       2.086        2.845
21        1.721       2.008        2.831
22        1.717       2.074        2.819
23        1.714       2.069        2.797
24        1.711       2.064        2.787
25        1.708       2.060        2.787
26        1.706       2.056        2.779
27        1.703       2.052        2.771
28        1.701       2.048        2.763
29        1.699       2.045        2.756
30        1.697       2.042        2.750
31        1.696       2.040        2.744
32        1.694       2.037        2.738
33        1.692       2.035        2.733
34        1.691       2.032        2.728
35         1.69       2.030        2.724
36        1.688       2.028        2.719
37        1.687       2.026        2.715
38        1.686       2.024        2.712
39        1.685       2.023        2.708
40   1.684   2.021   2.704
41   1.683   2.020   2.701
42   1.682   2.018   2.698
43   1.681   2.017   2.695
44    1.68   2.015   2.692
45   1.679   2.014   2.690
46   1.679   2.013   2.687
47   1.678   2.012   2.685
48   1.677   2.011   2.682
49   1.677   2.010   2.680
50   1.676   2.009   2.678
51   1.675   2.008   2.676
52   1.675   2.007   2.674
53   1.674   2.006   2.672
54   1.674   2.005   2.670
55   1.673   2.004   2.668
56   1.673   2.003   2.667
57   1.672   2.002   2.665
58   1.672   2.002   2.663
59   1.671   2.001   2.662
60   1.671   2.000   2.660
61   1.671   2.000   2.659
62    1.67   1.999   2.657
63   1.669   1.998   2.656
64   1.669   1.998   2.655
65   1.669   1.997   2.654
66   1.668   1.997   2.652
67   1.668   1.996   2.651
68   1.668   1.995   2.650
69   1.667   1.995   2.649
70   1.667   1.994   2.648
71   1.667   1.994   2.647
72   1.666   1.993   2.646
73   1.666   1.993   2.645
74   1.666   1.993   2.644
75   1.665   1.992   2.643
76   1.665   1.992   2.642
77   1.665   1.991   2.641
78   1.665   1.991   2.640
79   1.664   1.990   2.640
80   1.664   1.990   2.639
81   1.664   1.990   2.638
82   1.664   1.989   2.637
83   1.663   1.989   2.636
84   1.663   1.989   2.636
85   1.663   1.988   2.635
86   1.663   1.988   2.634
87   1.663   1.988   2.634
88   1.662   1.987   2.633
89   1.662   1.987   2.632
90   1.662   1.987   2.632
91   1.662   1.986   2.631
92   1.662   1.986   2.630
93   1.661   1.986   2.630
94   1.661   1.986   2.629
95   1.661   1.985   2.629
96   1.661   1.985   2.628
97   1.661   1.985   2.627
98   1.661   1.984   2.627
99    1.66   1.984   2.626
100    1.66   1.984   2.626
101    1.66   1.984   2.625
102    1.66   1.983   2.625
103    1.66   1.983   2.624
104    1.66   1.983   2.624
105    1.66   1.983   2.623
106   1.659   1.983   2.623
107   1.659   1.982   2.623
108   1.659   1.982   2.662
109   1.659   1.982   2.622
110   1.659   1.982   2.621
111   1.659   1.982   2.621
112   1.659   1.981   2.620
113   1.658   1.981   2.620
114   1.658   1.981   2.620
115   1.658   1.981   2.619
116   1.658   1.981   2.619
117   1.658   1.980   2.619
118   1.658   1.980   2.618
119   1.658   1.980   2.168
120   1.658   1.980   2.617
121   1.658   1.980   2.617
122   1.657   1.980   2.617
123   1.657   1.979   2.616
124   1.657   1.979   2.616
125   1.657   1.979   2.616
126   1.657   1.979   2.615
127   1.657   1.979   2.615
128   1.657   1.979   2.615
129   1.657   1.979   2.614
130   1.657   1.978   2.614
131   1.657   1.978   2.614
132   1.656   1.978   2.614
133   1.656   1.978   2.613
134   1.656   1.978   2.613
135   1.656   1.978   2.613
136   1.656   1.978   2.612
137   1.656   1.977   2.612
138   1.656   1.977   2.612
139   1.656   1.977   2.612
140   1.656   1.977   2.611
141   1.656   1.977   2.611
142   1.656   1.977   2.611
143   1.656   1.977   2.611
144   1.656   1.977   2.610
145   1.655   1.976   2.610
146   1.655   1.976   2.610
147   1.655   1.976   2.610
148   1.655   1.976   2.609
149   1.655   1.976   2.609
150   1.655   1.976   2.609
151   1.655   1.976   2.609
152   1.655   1.976   2.609
153   1.655   1.976   2.608
154   1.655   1.975   2.608
155   1.655   1.975   2.608
156   1.655   1.975   2.608
157   1.655   1.975   2.608
158   1.655   1.975   2.607
159   1.654   1.975   2.607
160   1.654   1.975   2.607
161   1.654   1.975   2.607
162   1.654   1.975   2.607
163   1.654   1.975   2.606
164   1.654   1.975   2.606
165   1.654   1.974   2.606
166   1.654   1.974   2.606
167   1.654   1.974   2.606
168   1.654   1.974   2.605
169   1.654   1.974   2.605
170   1.654   1.974   2.605
171   1.654   1.974   2.605
172   1.654   1.974   2.605
173   1.654   1.974   2.605
174   1.654   1.974   2.604
175   1.654   1.974   2.604
176   1.654   1.974   2.604
177   1.654   1.974   2.604
178   1.653   1.973   1.973
179   1.653   1.973   2.604
180   1.653   1.973   2.603
181   1.653   1.973   2.603
182   1.653   1.973   2.603
183   1.653   1.973   2.603
184   1.653   1.973   2.603
185   1.653   1.973   2.603
186   1.653   1.973   2.603
187   1.653   1.973   2.602
188   1.653   1.973   2.602
189   1.653   1.973   2.602
190   1.653   1.973   2.602
191   1.653   1.972   2.602
192   1.653   1.972   2.602
193   1.653   1.972   2.602
194   1.653   1.972   2.601
195   1.653   1.972   2.601
196   1.653   1.972   2.601
197   1.653   1.972   2.601
198   1.653   1.972   2.601
199   1.653   1.972   2.601
200   1.653   1.972   2.601
201   1.653   1.972   2.601
202   1.653   1.972   2.601
203   1.653   1.972   2.601
204   1.653   1.972   2.601
205   1.653   1.972   2.601
206   1.653   1.972   2.601
207   1.653   1.972   2.601
208   1.653   1.972   2.601
209   1.653   1.972   2.601
210   1.652   1.971   2.599
211   1.652   1.971   2.599
212   1.652   1.971   2.599
213   1.652   1.971   2.599
214   1.652   1.971   2.599
215   1.652   1.971   2.599
216   1.652   1.971   2.599
217   1.652   1.971   2.599
218   1.652   1.971   2.599
219   1.652   1.971   2.599
220   1.652   1.971   2.598
221   1.652   1.971   2.598
222   1.652   1.971   2.598
223   1.652   1.971   2.598
224   1.652   1.971   2.598
225   1.652   1.971   2.598
226   1.652   1.971   2.598
227   1.652   1.971   2.598
228   1.652   1.971   2.598
229   1.652   1.971   2.598
230   1.652   1.970   2.597
231   1.652   1.970   2.597
232   1.652   1.970   2.597
233   1.652   1.970   2.597
234   1.652   1.970   2.597
235   1.652   1.970   2.597
236   1.652   1.970   2.597
237   1.652   1.970   2.597
238   1.652   1.970   2.597
239   1.652   1.970   2.597
240   1.651   1.970   2.596
241   1.651   1.970   2.596
242   1.651   1.970   2.596
243   1.651   1.970   2.596
244   1.651   1.970   2.596
245   1.651   1.970   2.596
246   1.651   1.970   2.596
247   1.651   1.970   2.596
248   1.651   1.970   2.596
249   1.651   1.970   2.596
250   1.651   1.969   2.596
260   1.651   1.969   2.595
270   1.651   1.969   2.594
280    1.65   1.968   2.594
290    1.65   1.968   2.593
300    1.65   1.968   2.592
310    1.65   1.968   2.592
320    1.65   1.967   2.591
330   1.649   1.967   2.591
340   1.649   1.967   2.590
350   1.649   1.967   2.590
360   1.649   1.967   2.590
370   1.649   1.966   2.589
380   1.649   1.966   2.589
390   1.649   1.966   2.588
400   1.649   1.966   2.588
         1.645   1.960   2.576
0%, 95% and 99% levels of confidence
Clinical Effectiveness & Audit Department
Confidence Interval calculator for medians. This method is satisfactory for most sample
sizes, but is probably not suitable for very small samples (below 20).

Insert sample size here:        100

Insert confidence level required (click in the box & choose 90%, 95% or 99% from the
drop-down list):    90%

You need to sort your original data in ascending order.
The confidence interval values equate to the data contained in row numbers       42         &
in your original data (sorted in ascending order)
er.
59

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